Urban parking-oriented Internet of Things mobile charging system and dynamic pricing method

Abstract

The invention belongs to the technical field of mobile Internet of Things, and particularly relates to an Internet of Things mobile charging system and a dynamic pricing method for urban parking, and the method comprises the steps: 1, enabling the Internet of Things mobile charging system to collect the real-time parking space occupancy rate data of each parking lot of a city through a geomagnetic sensor, arranging the observation symbols at a plurality of continuous sampling moments according to a time sequence to form an observation symbol sequence of each parking lot; 2, extracting a hidden state corresponding to the current sampling moment from the optimal hidden state sequence as a current supply and demand hidden state of the corresponding parking lot; and step 3, when the response rate and the candidate rate satisfy a preset convergence determination threshold condition, determining the response rate of each parking lot as a dynamic parking rate and issuing the dynamic parking rate to the outside. The utilization efficiency of parking resources can be remarkably improved, invalid location searching is reduced, and the use experience of a mobile application end of a vehicle owner is enhanced.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of mobile Internet of Things, and particularly relates to a mobile charging system for urban parking based on Internet of Things and a dynamic pricing method. BACKGROUND

[0002] In the current urban traffic management system, the space-time distribution of parking resources and the vehicle travel demand have obvious uneven characteristics. With the continuous growth of urban motor vehicle ownership, roadside parking and parking lot resources are increasingly strained, and the parking demand in different regions at different times shows strong volatility and aggregation. In order to improve the efficiency of parking spaces, many places have begun to deploy Internet of Things communication technology, which uses geomagnetic sensors, video recognition terminals and other devices to monitor the status of parking spaces in real time, and provides parking space query, navigation guidance and online payment services to vehicle owners through mobile applications. Such systems usually rely on stable wireless communication networks and large-scale data collection mechanisms to transmit real-time occupancy information of parking lots to the background server for analysis and processing. Although the existing systems have made significant progress in data collection capacity and visualization services, they still have deficiencies in dealing with uneven supply and demand, predicting future parking pressure, and dynamically adjusting parking rates according to supply and demand changes.

[0003] The existing technology relies on simple threshold judgment or fixed rules based on single-time occupancy rate when analyzing the status of parking spaces. When the demand for urban parking rises or falls rapidly, the occupancy rate data at a single sampling time cannot effectively reflect the continuous supply and demand trend. For example, some parking lots may have a rapid increase in occupancy rate due to temporary concentration of vehicles in a short period of time, but this phenomenon may not mean a long-term tight situation. The existing system cannot automatically identify the potential patterns of supply and demand changes from continuous time series, resulting in a lack of stability in the evaluation of the tightness of parking spaces and easy misjudgment.

[0004] Moreover, the parking rate management of the prior art generally adopts a static pricing mode, i.e., the parking rate is fixed for a long period and cannot be flexibly adjusted according to the real-time supply-demand relationship. The static pricing cannot effectively divert the parking demand in the peak period, nor can it encourage the vehicle owners to use the parking lot in the low demand period, resulting in that the valuable parking resources cannot be fully utilized. Some systems attempt to adopt a time period split pricing mode, but this mode is usually preset based on historical statistical rules and cannot respond to the fluctuation of real-time demand, nor can it differentiate the rate according to the instant load difference of different parking lots. With the maturity of the mobile application development platform, the vehicle owners' demand for instant and intelligent parking service is increasing. The vehicle owners hope to obtain accurate parking space availability prediction, estimated cost assessment and directly lock the parking space through the mobile application before reaching the destination. However, the prior art lacks effective dynamic modeling capability when analyzing large-scale real-time data, especially when involving the global game relationship among multiple parking lots, the conventional linear rules are difficult to depict the mutual influence among the parking lots under the supply-demand pressure. SUMMARY

[0005] In view of this, the main purpose of the present application is to provide an Internet of Things mobile charging system and dynamic pricing method for urban parking, which collects continuous parking space occupation information through the Internet of Things mobile charging system and constructs an observation symbol sequence, introduces a parking supply-demand hidden Markov model to stably infer the supply-demand tight hidden state, supply-demand balance hidden state and supply-demand loose hidden state of each parking lot in the city, and then generates a dynamic parking rate conforming to the overall supply-demand pattern through mean field game pricing iteration, so that the parking rate can be adaptively adjusted with the change of supply and demand. The present application not only realizes continuous description of the parking demand trend and effectively avoids misjudgment caused by single-time fluctuation, but also constructs the global coordination relationship among multiple parking lots through the mean field mechanism, so that the dynamic rate can still converge smoothly under the interaction of multiple participants, and guide the reasonable distribution of vehicle flow under different supply-demand scenarios, significantly improve the utilization efficiency of parking resources, reduce invalid searching, and enhance the use experience of the vehicle owner's mobile application end.

[0006] The technical scheme adopted by the present application is as follows: An Internet of Things mobile charging system and dynamic pricing method for urban parking, comprising the following steps: Step one: the Internet of Things mobile charging system collects real-time parking space occupancy rate data of each parking lot in the city through a geomagnetic sensor, converts the real-time parking space occupancy rate data into observation symbols according to a preset discretization interval division rule, and arranges the observation symbols of continuous multiple sampling time points in time sequence to form the observation symbol sequence of each parking lot; Step two: the Internet of Things mobile charging system loads the parking supply and demand hidden Markov model, the parking supply and demand hidden state set of the parking supply and demand hidden Markov model includes a supply and demand tight hidden state, a supply and demand balance hidden state and a supply and demand loose hidden state, the Internet of Things mobile charging system performs hidden Markov model Viterbi decoding for each parking lot to obtain an optimal hidden state sequence, and extracts a hidden state corresponding to a current sampling time from the optimal hidden state sequence as a current supply and demand hidden state of the corresponding parking lot; Step three: the Internet of Things mobile charging system performs mean field game pricing iteration based on the current supply and demand hidden states of all parking lots, sets a candidate rate for each parking lot and constructs a mean field according to the candidate rate, calculates a response rate of each parking lot according to the mean field rate corresponding to each supply and demand hidden state and the benchmark rate of each parking lot, and determines the response rate of each parking lot as a dynamic parking rate and publishes it externally when the response rate and the candidate rate meet a preset convergence judgment threshold condition.

[0007] Further, step one includes: the Internet of Things mobile charging system collects real-time parking occupancy rate data of each parking lot in the city through a geomagnetic sensor deployed in each parking lot in the city, divides the real-time parking occupancy rate data into a plurality of value intervals according to a preset discretization interval division rule, each value interval corresponds to a unique observation symbol, and the Internet of Things mobile charging system arranges observation symbols obtained by each parking lot at a plurality of continuous sampling times in chronological order to form an observation symbol sequence corresponding to each parking lot, which is used to represent the parking occupancy state change of each parking lot at a plurality of sampling times.

[0008] Further, the parking supply and demand hidden Markov model includes a parking supply and demand hidden state set, a transition probability table between hidden states, an emission probability table of each observation symbol under each hidden state, and an initial probability table of each hidden state, the parking supply and demand hidden state set includes three hidden state types of a supply and demand tight hidden state, a supply and demand balance hidden state and a supply and demand loose hidden state, the supply and demand tight hidden state is used to represent a supply and demand state in which parking spaces are in short supply and the parking occupancy rate is in a preset high occupancy interval, the supply and demand balance hidden state is used to represent a supply and demand state in which the difference between the number of parking space supply and the number of parking space demand does not exceed a preset balance threshold and the parking occupancy rate is in a preset intermediate occupancy interval, and the supply and demand loose hidden state is used to represent a supply and demand state in which the number of idle parking spaces is greater than a preset surplus threshold and the parking occupancy rate is in a preset low occupancy interval.

[0009] Further, the initialization process of the hidden Markov model Viterbi decoding in step two includes: the Internet of Things mobile charging system reads the first observation symbol in the observation symbol sequence of the target parking lot for any parking lot, reads the initial probability value of the supply and demand tight hidden state, the initial probability value of the supply and demand balance hidden state and the initial probability value of the supply and demand loose hidden state from the initial probability table, reads the probability value of the supply and demand tight hidden state emitting the first observation symbol, the probability value of the supply and demand balance hidden state emitting the first observation symbol and the probability value of the supply and demand loose hidden state emitting the first observation symbol from the emission probability table, multiplies the initial probability value of the supply and demand tight hidden state and the probability value of the supply and demand tight hidden state emitting the first observation symbol to obtain the local path probability value of the supply and demand tight hidden state at the first observation symbol time, multiplies the initial probability value of the supply and demand balance hidden state and the probability value of the supply and demand balance hidden state emitting the first observation symbol to obtain the local path probability value of the supply and demand balance hidden state at the first observation symbol time, and multiplies the initial probability value of the supply and demand loose hidden state and the probability value of the supply and demand loose hidden state emitting the first observation symbol to obtain the local path probability value of the supply and demand loose hidden state at the first observation symbol time.

[0010] Further, the recursive calculation process of the hidden Markov model Viterbi decoding in step two includes: the Internet of Things mobile charging system traverses from the second observation symbol of the observation symbol sequence to the last observation symbol, for the currently traversed observation symbol, the Internet of Things mobile charging system reads the transition probability value from the transition probability table of the transition from the supply and demand tight hidden state to the supply and demand tight hidden state, the transition probability value from the supply and demand balance hidden state to the supply and demand tight hidden state and the transition probability value from the supply and demand loose hidden state to the supply and demand tight hidden state, multiplies the local path probability value of the supply and demand tight hidden state at the previous observation symbol time by the transition probability value from the supply and demand tight hidden state to the supply and demand tight hidden state to obtain a first candidate transition probability product, multiplies the local path probability value of the supply and demand balance hidden state at the previous observation symbol time by the transition probability value from the supply and demand balance hidden state to the supply and demand tight hidden state to obtain a second candidate transition probability product, multiplies the local path probability value of the supply and demand loose hidden state at the previous observation symbol time by the transition probability value from the supply and demand loose hidden state to the supply and demand tight hidden state to obtain a third candidate transition probability product, compares the numerical values of the first candidate transition probability product, the second candidate transition probability product and the third candidate transition probability product and selects the maximum value as the optimal predecessor transition probability product of the supply and demand tight hidden state, records the hidden state at the previous time when the optimal predecessor transition probability product is generated as the predecessor pointer of the supply and demand tight hidden state at the current observation symbol time, reads the probability value of the supply and demand tight hidden state emitting the current observation symbol from the emission probability table, and multiplies the optimal predecessor transition probability product of the supply and demand tight hidden state by the probability value of the supply and demand tight hidden state emitting the current observation symbol to obtain the local path probability value of the supply and demand tight hidden state at the current observation symbol time. The Internet of Things mobile charging system calculates the local path probability value and the predecessor pointer of the supply and demand balance hidden state at the current observation symbol time and the local path probability value and the predecessor pointer of the supply and demand loose hidden state at the current observation symbol time in the same recursive calculation manner.

[0011] Further, the backtracking process of the hidden Markov model Viterbi decoding in step two includes: after the Internet of Things mobile charging system completes the traversal of the observation symbol sequence, the numerical values of the local path probability value of the supply and demand tight hidden state at the last observation symbol time, the local path probability value of the supply and demand balance hidden state and the local path probability value of the supply and demand loose hidden state are compared, the hidden state with the largest local path probability value is selected as the terminal hidden state of the optimal hidden state path, the terminal hidden state is taken as the starting hidden state corresponding to the first observation symbol time, all the hidden states on the backtracking path are arranged in time sequence to form the optimal hidden state sequence of the target parking lot, and the hidden state corresponding to the current sampling time is extracted from the optimal hidden state sequence of the target parking lot as the current supply and demand hidden state of the target parking lot.

[0012] Further, the mean field game pricing iteration in step three comprises: the Internet of Things mobile charging system sets an initial candidate rate of each parking lot equal to the benchmark rate of each parking lot, traverses all parking lots and screens parking lots whose current supply-demand hidden state is the supply-demand tight hidden state to form a supply-demand tight parking lot set, sums up the current candidate rates of all parking lots in the supply-demand tight parking lot set and divides the number of parking lots in the supply-demand tight parking lot set to obtain the mean field rate corresponding to the supply-demand tight hidden state, and calculates the mean field rate corresponding to the supply-demand balance hidden state and the mean field rate corresponding to the supply-demand loose hidden state in the same way to represent the mean field level of the candidate rate of the parking lot under the three supply-demand hidden states.

[0013] Further, the response rate calculation in step three comprises: the Internet of Things mobile charging system reads the current supply-demand hidden state of each parking lot and queries the mean field rate corresponding to the current supply-demand hidden state for each parking lot, adds the current candidate rate of each parking lot and the mean field rate corresponding to the current supply-demand hidden state and divides the sum by two to obtain an intermediate adjustment rate of each parking lot, adds the intermediate adjustment rate of each parking lot and the benchmark rate of each parking lot and divides the sum by two to obtain the response rate of each parking lot when the current supply-demand hidden state is the supply-demand tight hidden state, takes the intermediate adjustment rate of each parking lot as the response rate of each parking lot when the current supply-demand hidden state is the supply-demand balance hidden state, adds the intermediate adjustment rate of each parking lot and the mean field rate corresponding to the current supply-demand hidden state and divides the sum by two to obtain the response rate of each parking lot when the current supply-demand hidden state is the supply-demand loose hidden state, so as to differentially adjust the response rate of different parking lots according to different supply-demand hidden state types.

[0014] Further, the convergence judgment and candidate rate updating in step three comprises: the Internet of Things mobile charging system calculates the absolute value of the difference between the response rate and the current candidate rate of each parking lot as the rate variation amplitude of each parking lot, selects the maximum value from the rate variation amplitudes of all parking lots as the maximum rate variation amplitude of the current iteration round, compares the maximum rate variation amplitude of the current iteration round with a preset convergence judgment threshold, determines that the mean field game reaches Nash equilibrium when the maximum rate variation amplitude of the current iteration round is less than the preset convergence judgment threshold, and determines the response rate of each parking lot as the dynamic parking rate of each parking lot, updates the response rate of each parking lot to the current candidate rate of each parking lot when the maximum rate variation amplitude of the current iteration round is greater than or equal to the preset convergence judgment threshold, and returns to continue executing the mean field game pricing iteration.

[0015] By adopting the above technical solutions, the application has the following beneficial effects: the application realizes accurate expression of the urban parking supply and demand state and self-adaptive adjustment of the dynamic rate by constructing a parking supply and demand hidden Markov model with an observation symbol sequence as input and combining mean field game pricing iteration, and has comprehensive advantages in many aspects compared with the prior art. Through the observation symbol sequence generated by continuous sampling, the application can extract the parking demand change trend from the time dimension, so that the judgment of the supply and demand tight hidden state, the supply and demand balance hidden state and the supply and demand loose hidden state is more stable and reliable, and no longer depends on the single-time occupancy rate information, thereby avoiding frequent misjudgment caused by short-time fluctuations. By using the state inference mechanism of the hidden Markov model, the application can maintain the continuous tracking ability of the supply and demand situation in the Internet of Things scene with more noise, so that the potential mode of the change of the parking space occupancy can be accurately described, thereby providing a solid foundation for dynamic pricing.

[0016] In terms of pricing strategy, the application adopts a mean field game structure, so that each parking lot considers not only its own supply and demand conditions when making decisions, but also the average rate of other parking lots under the same supply and demand hidden state, thereby forming a stable rate evolution process. In this game framework, the candidate rate of each parking lot gradually converges to the equilibrium state, so that the dynamic parking rate still has global consistency and interpretability under complex multi-party interaction, which is beneficial to improving the overall resource coordination efficiency in the city. The application adjusts the pricing strategy in different supply and demand scenarios by using differentiated response rate rules, so that the parking lot under the supply and demand tight hidden state appropriately increases the rate to relieve the high demand pressure, the parking lot under the supply and demand loose hidden state reduces the rate to improve the idle parking space utilization rate, and the parking lot under the supply and demand balance hidden state maintains stable rate change, thereby making the pricing strategy more suitable for the real demand.

[0017] In addition, the dynamic rate generation process of the application has convergence constraints, so that the final output dynamic parking rate will not fluctuate sharply, thereby enhancing the experience of car owners and improving the predictability of the mobile application end. Through the above comprehensive mechanism, the application has significant practical effects in improving the utilization rate of parking lot resources, optimizing urban traffic operation, reducing invalid searching, improving the decision-making efficiency of car owners and the like. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 A distribution relationship between the benchmark rate and the candidate rate in the mean field game pricing process of the plurality of parking lots provided by the embodiment of the application is shown in the figure; Figure 2 A Viterbi decoding principle of the parking supply and demand hidden Markov model provided by the embodiment of the application is shown in the figure; Figure 3 A transition probability table between the hidden states in the parking supply and demand hidden Markov model provided by the embodiment of the application is shown in the figure; Figure 4The emission probability table of different observation symbols in each hidden state in the parking supply and demand hidden Markov model provided in the embodiments of the present invention. Detailed Implementation

[0019] All features disclosed in this specification, or all steps in all disclosed methods or processes, may be combined in any way, except for mutually exclusive features and / or steps.

[0020] Any feature disclosed in this specification (including any appended claims and abstract) may be replaced by other equivalent or similar features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0021] Example 1: An IoT mobile payment system and dynamic pricing method for urban parking, comprising the following steps: Step 1: The IoT mobile toll collection system collects real-time parking space occupancy data of various parking lots in the city through geomagnetic sensors, converts the real-time parking space occupancy data into observation symbols according to the preset discretization interval division rules, and arranges the observation symbols of multiple consecutive sampling times in chronological order to form the observation symbol sequence of each parking lot.

[0022] In one implementation, the IoT mobile toll collection system installs a geomagnetic sensor in each parking space across multiple parking lots in a city. Each geomagnetic sensor is fixed at the center of the corresponding parking space or slightly off-center from the vehicle's center of gravity to reduce the impact of different parking postures on the geomagnetic signal. During the deployment phase, the IoT mobile toll collection system assigns a unique identifier to each geomagnetic sensor and associates this identifier with the parking lot identifier, parking space identifier, and geographic coordinates. This ensures that the data reported by the geomagnetic sensors can be accurately mapped to specific parking lots and parking spaces during subsequent data collection. The IoT mobile toll collection system synchronizes the time of all geomagnetic sensor terminals. This time synchronization can be accomplished through a network time server, aligning the sampling times of different parking lots to a unified time reference, facilitating the construction of observation symbol sequences on a unified time axis.

[0023] In the normal operation process, the Internet of Things mobile charging system obtains real-time parking occupancy rate data from the geomagnetic sensor according to the preset sampling period. Specifically, the geomagnetic sensor reports the current geomagnetic intensity change and the parking occupancy determination result to the Internet of Things mobile charging system at each sampling time. The Internet of Things mobile charging system counts the number of occupied parking spaces and the total number of parking spaces in a parking lot based on the occupancy determination result of each parking space. For example, the sampling period can be set to 60 seconds, the total number of parking spaces in a certain parking lot is 100, and 80 parking spaces are determined to be occupied at a certain sampling time. The Internet of Things mobile charging system records the real-time parking occupancy rate data corresponding to the sampling time as 0.8. In order to improve the reliability of the occupancy determination, the Internet of Things mobile charging system can perform time smoothing processing on the geomagnetic intensity change of the geomagnetic sensor at several consecutive sampling times, for example, using a sliding window to take the median or majority decision. Only when the vehicle is present at consecutive sampling times, the parking status is confirmed as occupied. In this way, the false triggering caused by pedestrians passing by, rain and snow weather, or large metal objects temporarily approaching can be reduced, and the real-time parking occupancy rate data is more stable, thereby providing more reliable input for the subsequent construction of observation symbols of the hidden Markov model.

[0024] In another embodiment, the Internet of Things mobile charging system can introduce the concept of subdivided areas when counting real-time parking occupancy rate data, divide a large parking lot into several functional partitions, such as the area near the entrance, the core commercial area, the long-time parking area, etc., count the number of occupied parking spaces and the total number of parking spaces in each functional partition, and obtain multiple real-time parking occupancy rate data. In this way, the supply and demand differences of different areas in the same parking lot can be described more finely, and more spatial resolution observation symbol sequences can be provided for subsequent dynamic pricing.

[0025] In order to use the continuous real-time parking occupancy data in the parking supply and demand hidden Markov model, the Internet of Things mobile charging system pre-sets a discretization interval division rule. The discretization interval division rule is configured by the operation personnel in the deployment stage, and can be designed according to the overall utilization of urban parking, policy requirements and historical statistical data. In a specific implementation, the discretization interval division rule can divide the real-time parking occupancy data into three intervals, for example, the interval with an occupancy rate between 0 and 0.3 is defined as a free interval, the interval with an occupancy rate between 0.3 and 0.7 is defined as a medium occupancy interval, and the interval with an occupancy rate between 0.7 and 1 is defined as a high occupancy interval. The Internet of Things mobile charging system sets three observation symbols for the three intervals, for example, the observation symbol “F” corresponds to the free interval, the observation symbol “M” corresponds to the medium occupancy interval, and the observation symbol “H” corresponds to the high occupancy interval. Through this interval division method, the continuous real-time parking occupancy data is divided into a limited number of observation symbols, the size of the observation symbol set is controlled, which is conducive to the convergence and operation efficiency of the hidden Markov model, and can also reduce the influence of collection noise and individual abnormal samples on state decoding.

[0026] In another optional implementation, in order to better reflect the individualized use characteristics of different parking lots, the Internet of Things mobile charging system can use an adaptive discretization interval division rule based on historical data statistics. Specifically, the Internet of Things mobile charging system can collect real-time parking occupancy data of a parking lot within a statistical period, divide the occupancy rate distribution of the parking lot within the statistical period into several quantile intervals, for example, determine multiple interval boundaries according to the 25th percentile, 50th percentile and 75th percentile, map the occupancy rate data below the 25th percentile to the observation symbol “F”, map the occupancy rate data between the 25th percentile and the 75th percentile to the observation symbol “M”, and map the occupancy rate data above the 75th percentile to the observation symbol “H”. This quantile-based discretization interval division rule can automatically adapt to the average busy degree of different parking lots, and can stretch the coverage of the medium occupancy interval for parking lots with a high long-term vacancy rate, and can refine the division of the high occupancy interval for popular parking lots that are often in a full state, so that the observation symbol more sensitively reflects the actual supply and demand changes in the local area.

[0027] After the Internet of Things mobile charging system completes the conversion of real-time parking occupancy rate data into observation symbols at each sampling time, it arranges the observation symbols generated by each parking lot at a plurality of continuous sampling times in chronological order to form an observation symbol sequence corresponding to the parking lot. In order to avoid misalignment on the time axis, the Internet of Things mobile charging system assigns a sampling time label to each sampling time, stores the sampling time label in one-to-one correspondence with the observation symbol, and sorts the sampling time labels from early to late when constructing the observation symbol sequence, and sequentially connects to form the observation symbol sequence. For example, the real-time parking occupancy rate data of a parking lot at five continuous sampling times is 0.2, 0.35, 0.6, 0.85 and 0.9, and under the condition of using the aforementioned three-interval discretization interval division rule, the corresponding observation symbol sequence can be "F, M, M, H, H". This sequence intuitively reflects the dynamic change process of the parking lot from the idle state to the high occupancy state, and the hidden Markov model can infer the transition trend of the supply-demand tight hidden state, the supply-demand balance hidden state and the supply-demand loose hidden state through the observation symbol sequence in the learning and decoding process.

[0028] In order to handle the data loss that may occur in actual operation, the Internet of Things mobile charging system can add a data integrity processing step before constructing the observation symbol sequence. For example, when the geomagnetic sensor is temporarily offline or the communication link is interrupted for a short time at some sampling time, resulting in no real-time parking occupancy rate data being received, the Internet of Things mobile charging system can use the interpolation method of adjacent sampling times or the extension method of the last valid sampling result to fill in the missing data. For example, if a parking lot generates valid observation symbols at sampling times with time labels of 10:00 and 10:02, and there is a data gap at the sampling time with a time label of 10:01, the Internet of Things mobile charging system can set the observation symbol at 10:01 to the observation symbol at 10:00, thereby maintaining the continuity of the observation symbol sequence in time and avoiding the creation of new state changes. In addition, in some embodiments, the Internet of Things mobile charging system can also exclude obviously abnormal real-time parking occupancy rate data based on statistical rules, for example, the occupancy rate suddenly jumps from 0.1 to 1 and then immediately returns to 0.1 at a single sampling time. This can be identified by checking whether the occupancy rate change at adjacent sampling times exceeds a preset change threshold, and corrected according to the adjacent valid sampling time.

[0029] In yet another embodiment, the Internet of Things mobile charging system can perform time smoothing on the real-time parking occupancy rate data before converting the real-time parking occupancy rate data into observation symbols. For example, a sliding window with a length of 3 can be used to weight average the occupancy rate data at the current sampling time with the occupancy rate data at the previous sampling time and the occupancy rate data at the next sampling time, and the weighted average result can be used as the parking occupancy rate data at the current sampling time for discretization. By smoothing before discretization, the observation symbol sequence can better reflect the true supply and demand trend, and is not easily interrupted by a single parking peak or short-term departure fluctuations, which has a positive effect on the training and state decoding of the subsequent parking supply and demand hidden Markov model, can reduce the interference of observation noise on hidden state judgment, and makes the identification of supply and demand tight hidden state, supply and demand balance hidden state and supply and demand loose hidden state more stable.

[0030] In summary of the above embodiments, the Internet of Things mobile charging system collects real-time parking occupancy rate data of various parking lots in the city through a geomagnetic sensor, converts the real-time parking occupancy rate data into observation symbols in combination with a preset discretization interval division rule, and arranges the observation symbols of continuous multiple sampling times in time sequence on a time axis to form an observation symbol sequence, thereby providing a unified, standardized and structured input basis for subsequent Viterbi decoding and mean field game pricing iteration of the parking supply and demand hidden Markov model.

[0031] Step two: the Internet of Things mobile charging system loads the parking supply and demand hidden Markov model, the parking supply and demand hidden state set of the parking supply and demand hidden Markov model includes a supply and demand tight hidden state, a supply and demand balance hidden state and a supply and demand loose hidden state, and the Internet of Things mobile charging system performs hidden Markov model Viterbi decoding for each parking lot to obtain an optimal hidden state sequence, and extracts the hidden state corresponding to the current sampling time from the optimal hidden state sequence as the current supply and demand hidden state of the corresponding parking lot.

[0032] In one embodiment, after the Internet of Things mobile charging system completes the construction of the observation symbol sequence of each parking lot, it first loads the parking supply and demand hidden Markov model from the storage medium. The parking supply and demand hidden Markov model has been trained through historical data during the deployment stage and is solidified with a set of probability parameters, including a parking supply and demand hidden state set, a transition probability table between hidden states, an emission probability table of each observation symbol under each hidden state, and an initial probability table of each hidden state. The parking supply and demand hidden state set contains three types of hidden states, i.e., a supply and demand tight hidden state, a supply and demand balance hidden state and a supply and demand loose hidden state, which are used to abstractly describe the comprehensive supply and demand situation between the real parking occupancy and the parking demand intensity, rather than directly equivalent to a specific occupancy rate value.

[0033] Reference Figure 3 , Figure 3A table of transition probabilities between hidden states in the parking supply and demand hidden Markov model is shown. The table is a three-by-three square matrix, with row indices representing the hidden state of the system at time instant t minus one, and column indices representing the hidden state to which the system transitions at time instant t. Each element in the table represents a probability value of transitioning from one hidden state to another, with all probability values being real numbers between zero and one. The first row corresponds to transition probabilities from the supply and demand tight hidden state, with the first column first row element value being 0.85, representing a self-transition probability of eighty-five percent for the supply and demand tight hidden state to remain in the supply and demand tight hidden state. This relatively high self-transition probability reflects the fact that a parking lot often maintains a high demand state for a period of time before returning to a relaxed state.

[0034] The value of the element in the first row and the second column is 0.12, which means that the probability of transferring from the supply-demand tight hidden state to the supply-demand balance hidden state is 12 percent, which usually occurs after the end of the peak period when part of the vehicles leave the parking lot. The value of the element in the first row and the third column is 0.03, which means that the probability of directly transferring from the supply-demand tight hidden state to the supply-demand loose hidden state is only 3 percent, which is a very low probability, because it is extremely rare for the parking lot to directly jump from the full state to the largely empty state. The second row corresponds to the transfer probability starting from the supply-demand balance hidden state. The value of the element in the second row and the first column is 0.15, which means that the probability of transferring from the supply-demand balance hidden state to the supply-demand tight hidden state is 15 percent, which usually occurs in the process of gradually increasing demand. The value of the element in the second row and the second column is 0.75, which means that the self-transfer probability of the supply-demand balance hidden state is 75 percent, indicating that the parking lot has a certain stability when the supply and demand are relatively balanced, but not as persistent as the tight state. The value of the element in the second row and the third column is 0.10, which means that the probability of transferring from the supply-demand balance hidden state to the supply-demand loose hidden state is 10 percent. The third row corresponds to the transfer probability starting from the supply-demand loose hidden state. The value of the element in the third row and the first column is 0.05, which means that the probability of directly transferring from the supply-demand loose hidden state to the supply-demand tight hidden state is 5 percent, which is a relatively low probability, indicating that it is less likely for the parking lot to directly jump from the largely empty state to the full state. The value of the element in the third row and the second column is 0.20, which means that the probability of transferring from the supply-demand loose hidden state to the supply-demand balance hidden state is 20 percent, which usually occurs in the early stage of gradually increasing parking demand. The value of the element in the third row and the third column is 0.75, which means that the self-transfer probability of the supply-demand loose hidden state is 75 percent, indicating that the parking lot also has a certain persistence in the low utilization state. The sum of the probability values in each row of the table is equal to 1, which is a normalization condition that the transfer probability table must satisfy. The table uses gray-scale filling, and the darker the color, the greater the corresponding probability value. This visualization makes the high values of the self-transfer probability form a clear dark area on the diagonal, while the elements off the diagonal are generally lighter, indicating that the jump probability between states is relatively low. This transfer probability table is used to calculate the path probability of transferring from a certain hidden state at the previous time to another hidden state at the current time in the Viterbi decoding process, and is one of the core parameters of the hidden Markov model.

[0035] In a more typical implementation, the set of parking supply-demand hidden states can be denoted as . The set contains three hidden state elements , and , where represents the supply-demand tight hidden state, represents the supply-demand balance hidden state, represents the supply-demand loose hidden state. The parameters in the initial probability table can be represented as wherein denotes the probability of being in a hidden state at the beginning of a sequence. The parameters in the transition probability table between hidden states can be represented as wherein denotes the probability of transitioning from a hidden state to a hidden state between two adjacent time instants. The parameters in the emission probability table can be represented as wherein denotes the probability of observing an observation symbol when the current hidden state is . With this set of parameters, the transition tendency between the tight supply-demand hidden state, the balanced supply-demand hidden state and the loose supply-demand hidden state, as well as the likelihood of different observation symbols appearing under different supply-demand hidden states can be characterized.

[0036] In the model training phase, the IoT mobile charging system can estimate the initial probability table, the transition probability table and the emission probability table of the parking supply-demand hidden Markov model based on the historical observation symbol sequences and the historical human-labeled data. For example, a training period containing 30 consecutive days of data can be selected, and the observation symbol sequences of multiple parking lots in the training period are aggregated. For parking lots that have been determined by the operating personnel to have long-term high utilization rate, the prior weight of the tight supply-demand hidden state can be increased in the training process; for parking lots with large utilization rate fluctuations, the flexibility of the transition probability between the balanced supply-demand hidden state and the loose supply-demand hidden state can be increased. In this way, after the parking supply-demand hidden Markov model is trained, it can reflect the differences in supply-demand dynamics of different types of parking lots. In the implementation without human-labeled data, the IoT mobile charging system can also use unsupervised training methods to iteratively estimate the hidden state parameters based on the historical observation symbol sequences, so that the interpretation ability of the hidden state for the observation symbol gradually improves.

[0037] Reference is made to Figure 4 , Figure 4A table of emission probabilities of different observation symbols under each hidden state in the parking supply-demand hidden Markov model is shown. The table is a square matrix of three rows and three columns. The row index represents the type of hidden state that the system is currently in, and the column index represents the type of observation symbol that can be observed. Each element in the table represents the probability of observing a particular observation symbol given a hidden state. All probability values are real numbers between 0 and 1. The first row corresponds to the emission probability distribution of the supply-demand tight hidden state. The element in the first column of the first row has a value of 0.05, indicating that the probability of observing the free interval observation symbol F when the parking lot is in the supply-demand tight hidden state is only 5%. This extremely low probability is consistent with the characteristic that the occupancy rate is generally high in the tight state. The element in the second column of the first row has a value of 0.15, indicating that the probability of observing the medium occupancy interval observation symbol M in the supply-demand tight hidden state is 15%. This situation may occur at the beginning or end of the tight state. The element in the third column of the first row has a value of 0.80, indicating that the probability of observing the high occupancy interval observation symbol H in the supply-demand tight hidden state is as high as 80%. This significantly high probability enables the hidden Markov model to accurately identify the supply-demand tight state. The second row corresponds to the emission probability distribution of the supply-demand balance hidden state. The element in the first column of the second row has a value of 0.10, indicating that the probability of observing the observation symbol F in the supply-demand balance hidden state is 10%. The element in the second column of the second row has a value of 0.75, indicating that the probability of observing the observation symbol M in the supply-demand balance hidden state is 75%, which is the maximum value in this row. This indicates that medium occupancy is a typical characteristic of the supply-demand balance state. The element in the third column of the second row has a value of 0.15, indicating that the probability of observing the observation symbol H in the supply-demand balance hidden state is 15%. The third row corresponds to the emission probability distribution of the supply-demand relaxed hidden state. The element in the first column of the third row has a value of 0.85, indicating that the probability of observing the observation symbol F in the supply-demand relaxed hidden state is as high as 85%. This extremely high probability makes the free observation symbol a strong signal for identifying the relaxed state. The element in the second column of the third row has a value of 0.12, indicating that the probability of observing the observation symbol M in the supply-demand relaxed hidden state is 12%. The element in the third column of the third row has a value of 0.03, indicating that the probability of observing the observation symbol H in the supply-demand relaxed hidden state is only 3%. This extremely low probability is consistent with the actual situation that a large number of parking spaces are empty in the relaxed state. The sum of the probability values in each row of the table is equal to 1, satisfying the normalization condition of the probability distribution. The table is also visualized using grayscale filling. The three elements from the lower left to the upper right of the diagonal line are 0.85, 0.75, and 0.80, respectively, forming a clear dark band. This indicates that there is a strong correlation between the observation symbol and the corresponding hidden state, i.e., the supply-demand relaxed state mainly emits the observation symbol F, the supply-demand balance state mainly emits the observation symbol M, and the supply-demand tight state mainly emits the observation symbol H.The emission probability table is used to calculate the likelihood probability of observing the current observation symbol in a given hidden state in the process of Viterbi decoding, and together with the transition probability table, forms a complete parameter system of the hidden Markov model, so that the system can infer the optimal hidden state sequence from the observation symbol sequence.

[0038] After the parameters of the parking supply-demand hidden Markov model are determined, the Internet of Things mobile charging system performs Viterbi decoding of the hidden Markov model for each parking lot respectively. The goal of Viterbi decoding is to find the most likely hidden state sequence occurring in the entire time period given the observation symbol sequence of a certain parking lot, thereby obtaining the optimal hidden state sequence. Compared with separately selecting the hidden state with the maximum probability at each time point, Viterbi decoding comprehensively considers the transition probability between hidden states in the time dimension and takes the joint probability of the entire hidden state path into account, so as to avoid frequent switching between the supply-demand tight hidden state, the supply-demand balanced hidden state and the supply-demand loose hidden state, making the change of the current supply-demand hidden state smoother and closer to the real supply-demand evolution process.

[0039] In one embodiment, the Internet of Things mobile charging system performs Viterbi decoding for the observation symbol sequence of the target parking lot. The observation symbol sequence can be represented as , where represents the observation symbol at time , and represents the length of the observation sequence. In order to perform path search, the Internet of Things mobile charging system internally maintains two arrays. The first array can be represented as , where represents the joint probability value of the path with the maximum joint probability among all hidden state paths with the hidden state at the end of time . The second array can be represented as , where represents the index of the hidden state at time in the optimal path with the hidden state at the end of time , used to record the optimal predecessor hidden state.

[0040] Referring to Figure 2 , Figure 2 , a schematic diagram of the Viterbi decoding principle of the parking supply-demand hidden Markov model provided by the embodiment of the present application is shown. As Figure 2As shown, the parking supply-demand hidden Markov model contains three types of hidden states, which are a supply-demand tight hidden state, a supply-demand balance hidden state and a supply-demand loose hidden state, and are respectively identified by symbols q1, q2 and q3 in the figure. The supply-demand tight hidden state is used to represent a supply-demand state in which the parking lot is short of parking spaces and the parking space occupancy rate is in a preset high occupancy interval. The supply-demand balance hidden state is used to represent a supply-demand state in which the difference between the number of parking space supply and the number of parking space demand does not exceed a preset balance threshold and the parking space occupancy rate is in a preset intermediate occupancy interval. The supply-demand loose hidden state is used to represent a supply-demand state in which the number of idle parking spaces is greater than a preset surplus threshold and the parking space occupancy rate is in a preset low occupancy interval. The five columns of nodes arranged horizontally in the figure correspond to five consecutive sampling time points in the observation symbol sequence, and are sequentially labeled as t1 to t5. Each column contains three nodes, which respectively correspond to the state values of the three hidden states at the time point.

[0041] Figure 2 The light-colored arrows in the table represent all possible transition paths between the hidden states. Each arrow connects the hidden state nodes of adjacent time points, and the arrow direction points from the previous time point to the next time point. The transition probability table stores the transition probability values from any hidden state to any hidden state. For example, the transition probability a33 from the supply-demand loose hidden state to the supply-demand loose hidden state is equal to 0.85, the transition probability a32 from the supply-demand loose hidden state to the supply-demand balance hidden state is equal to 0.10, the transition probability a21 from the supply-demand balance hidden state to the supply-demand tight hidden state is equal to 0.30, and the transition probability a11 from the supply-demand tight hidden state to the supply-demand tight hidden state is equal to 0.90. These transition probabilities reflect the statistical regularity of the change of the parking supply-demand state between adjacent time points. A higher self-transition probability indicates that the supply-demand state has a certain time continuity and stability.

[0042] Figure 2 The yellow square at the bottom represents the observation symbol sequence, which is formed by arranging the observation symbols of consecutive sampling time points in chronological order. In this embodiment, the observation symbol sequence contains five observation symbols, which are F, M, M, H and H in sequence, where the observation symbol F corresponds to the idle interval, the observation symbol M corresponds to the medium occupancy interval, and the observation symbol H corresponds to the high occupancy interval. The blue dashed arrow represents the emission probability, i.e., the probability of observing a certain observation symbol under a certain hidden state. For example, the emission probability b3(F) of observing the observation symbol F under the supply-demand loose hidden state is equal to 0.90, the emission probability b3(M) of observing the observation symbol M under the supply-demand loose hidden state is equal to 0.10, the emission probability b2(M) of observing the observation symbol M under the supply-demand balance hidden state is equal to 0.80, and the emission probability b1(H) of observing the observation symbol H under the supply-demand tight hidden state is equal to 0.85.

[0043] Figure 2The thick red arrows in the diagram represent the optimal hidden state paths obtained by the Viterbi decoding algorithm. The goal of Viterbi decoding is to find the hidden state sequence with the highest joint probability given a sequence of observed symbols. In the initialization phase, the IoT mobile toll collection system calculates the local path probability value for each hidden state for the first observed symbol F. The local path probability value is equal to the product of the initial probability and the emission probability. In the recursive phase, the IoT mobile toll collection system iterates sequentially from the second observed symbol to the last observed symbol. For each hidden state, it calculates the candidate transition probability product derived from all predecessor hidden states, selects the maximum value as the optimal predecessor transition probability product, and multiplies it by the emission probability of the current observed symbol to obtain the local path probability value of that hidden state at the current time. Simultaneously, it records the index of the predecessor hidden state that generated the maximum value as a predecessor pointer. The symbol δt(qi) marked inside each node in the diagram represents the local path probability value at time t when the hidden state is qi. In the backtracking phase, the IoT mobile toll collection system compares the local path probability values ​​of each hidden state at the last time, selects the hidden state corresponding to the largest value as the terminating hidden state, and then backtracks sequentially along the predecessor pointer to form a complete optimal hidden state sequence.

[0044] like Figure 2 As shown in the numerical example of this embodiment, the optimal hidden state path starts from the supply-demand imbalance hidden state at time t1, remains in the supply-demand imbalance hidden state at time t2, transitions to the supply-demand balance hidden state at time t3, transitions to the supply-demand tension hidden state at time t4, and remains in the supply-demand tension hidden state at time t5. This optimal hidden state sequence reflects the supply-demand evolution process of the parking lot gradually transitioning from an idle state to a highly occupied state, which is consistent with the parking space occupancy rate change trend represented by the observed symbol sequence F, M, M, H, H. The IoT mobile toll collection system extracts the hidden state corresponding to the current sampling time from the optimal hidden state sequence as the current supply-demand hidden state of the target parking lot, providing input for subsequent mean-field game pricing iterations.

[0045] During the initialization phase, the IoT mobile toll collection system targets specific times. Observation symbols For each hidden state in the parking supply and demand hidden state set, calculate the initial path probability. Specifically, for each hidden state... Perform calculation ,in Indicates a moment in time When it ends and the hidden state is The joint probability value of the optimal path, Indicates a moment in time. Previously in hidden state The prior probability, Indicates that in the hidden state is Observation symbol observed at time the probability of the optimal path ending at time and having state .

[0046] In the recursion phase, the IoT mobile toll system iterates from time to time . At any time , for each state in the set of parking supply and demand hidden states, the IoT mobile toll system computes all the candidate paths from all possible hidden states at the previous time to the hidden state and selects the path with the maximum joint probability among the candidate paths. Specifically, it can compute where is the optimal path joint probability value ending at time and having state , is the probability of transitioning from state to state between adjacent times, is the probability of observing observation symbol when the hidden state is , is the optimal path joint probability value ending at time and having state . While computing , the IoT mobile toll system records the previous time hidden state index that produces the maximum value, i.e., computes the hidden state index that satisfies and records in for the subsequent backtracking phase to recover the entire optimal hidden state path.

[0047] In the termination phase, the IoT mobile toll system compares the path probabilities of the three hidden states in the set of parking supply and demand hidden states at time . It selects the value with the maximum value from , and as the termination hidden state probability value of the optimal hidden state path, and records the corresponding hidden state index, e.g., as . This selection means that, within the entire observation symbol sequence length range, the hidden state path with the hidden state as the termination hidden state from time to time has the maximum joint occurrence probability.

[0048] Then the retrospective phase began, with the IoT mobile toll collection system working from specific times... To begin, using arrays The entire optimal hidden state sequence is gradually recovered by moving forward. Specifically, at time [time value missing]... The optimal hidden state index is; at time t, The optimal hidden state index is; at time t, The optimal hidden state index is, and so on, until time t. The IoT mobile toll collection system arranges the obtained hidden state index sequence in chronological order to form the optimal hidden state sequence of the target parking lot throughout the entire observation period. Since each hidden state index corresponds to a supply-demand tension, supply-demand balance, or supply-demand slack hidden state in the parking supply-demand hidden state set, the optimal hidden state sequence can intuitively show the trajectory of the supply-demand tension of the target parking lot over a period of time.

[0049] In practical use, the IoT mobile toll collection system periodically performs Hidden Markov Model (HMM) Viterbi decoding. After each decoding, the IoT mobile toll collection system extracts the hidden state corresponding to the current sampling time from the optimal hidden state sequence and uses this hidden state as the current supply and demand hidden state of the corresponding parking lot. For example, we can assume that the index of the current sampling time is... The IoT mobile toll collection system directly reads the location from the optimal hidden state sequence. The system uses a hidden state index. If the index corresponds to a tight supply-demand hidden state, the current supply-demand hidden state is determined to be tight; if the index corresponds to a balanced supply-demand hidden state, the current supply-demand hidden state is determined to be balanced; and if the index corresponds to a loose supply-demand hidden state, the current supply-demand hidden state is determined to be loose. This method considers not only the observation sign at the current moment but also the continuous changes in the observation sign over a past period and the transition probability between supply-demand hidden states. Therefore, it is more stable than single-point threshold judgment and better reflects the cumulative effect of parking demand and the recovery process of parking space vacancy.

[0050] In a numerical example, it can be assumed that the observation symbol sequence of a parking lot at consecutive 5 sampling instants is F, M, M, H, H, where F corresponds to the observation symbol of the free interval, M corresponds to the observation symbol of the medium occupancy interval, and H corresponds to the observation symbol of the high occupancy interval. In the parking supply-demand hidden Markov model, the self-transition probability of the supply-demand tight hidden state can be set to 0.9, the self-transition probability of the supply-demand balance hidden state can be set to 0.8, and the self-transition probability of the supply-demand loose hidden state can be set to 0.85. At the same time, the transition probability from the supply-demand loose hidden state to the supply-demand tight hidden state is small, for example, 0.05, and the transition probability from the supply-demand balance hidden state to the supply-demand tight hidden state is 0.3. For the emission probability, the probability of observing the observation symbol H in the supply-demand tight hidden state can be set to 0.85, the probability of observing the observation symbol M in the supply-demand balance hidden state can be set to 0.8, and the probability of observing the observation symbol F in the supply-demand loose hidden state can be set to 0.9. Under this parameter configuration, the Viterbi decoding tends to generate an optimal hidden state sequence gradually transitioning from the supply-demand loose hidden state to the supply-demand tight hidden state, for example, the supply-demand loose hidden state, the supply-demand balance hidden state, the supply-demand balance hidden state, the supply-demand tight hidden state, and the supply-demand tight hidden state. The Internet of Things mobile charging system extracts the hidden state of the current sampling instant at the end of the hidden state sequence, that is, the current supply-demand hidden state is the supply-demand tight hidden state. It can be seen that even if the observation symbol of an individual sampling instant does not reach the full bit state, the hidden Markov model can still identify the continuous high occupancy trend and map it to the supply-demand tight hidden state, which is very useful for subsequent dynamic increase of the parking fee to suppress new demand.

[0051] In another embodiment, the Internet of Things mobile charging system can configure different parking supply-demand hidden Markov models for different types of parking lots. For example, commercial parking lots, residential parking lots, and parking lots for transportation hubs are divided into different categories, and a set of initial probability tables, transition probability tables, and emission probability tables are trained for each category. For commercial parking lots, the transition probability from the supply-demand balance hidden state to the supply-demand tight hidden state can be increased during the rush hour to reflect the rapid increase in demand during the rush hour; for residential parking lots, the self-transition probability of the supply-demand tight hidden state can be increased during the night to reflect the stability of long-term parking at night. Although the set of parking supply-demand hidden states includes three types of hidden states, the supply-demand tight hidden state, the supply-demand balance hidden state, and the supply-demand loose hidden state, in various embodiments, the differences in transition probabilities and emission probabilities enable the hidden Markov model to give more realistic optimal hidden state sequences and current supply-demand hidden state judgments for different scenarios.

[0052] In yet another embodiment, in order to reduce the decoding delay, the Internet of Things mobile charging system can perform the Hidden Markov Model Viterbi decoding in a sliding window manner. For example, the Internet of Things mobile charging system can maintain the observation symbols of the last 120 sampling times for each parking lot, input the observation symbol sequence with a length of 120 as a decoding window into the parking supply and demand Hidden Markov Model, and calculate the corresponding optimal hidden state sequence. The Internet of Things mobile charging system only extracts the current supply and demand hidden state from the end position of the optimal hidden state sequence, without repeatedly decoding the entire historical observation symbol sequence. As time goes on, the decoding window slides forward, and a balance between decoding accuracy and computing resources can be achieved, which is suitable for scenarios with a large number of parking lots and large-scale observation data in a city. Through the above various embodiments, the Hidden Markov Model Viterbi decoding of the parking supply and demand provides clear supply and demand tight hidden state, supply and demand balance hidden state, and supply and demand loose hidden state input for the subsequent mean field game pricing iteration, so that the dynamic pricing decision can be based on a unified, stable, and interpretable supply and demand state description.

[0053] Step three: The Internet of Things mobile charging system performs the mean field game pricing iteration based on the current supply and demand hidden state of all parking lots, sets a candidate rate for each parking lot, and constructs a mean field according to the candidate rate. The response rate of each parking lot is calculated according to the mean field rate corresponding to each supply and demand hidden state and the benchmark rate of each parking lot. When the response rate and the candidate rate meet the preset convergence judgment threshold condition, the response rate of each parking lot is determined as the dynamic parking rate and is published externally.

[0054] In one embodiment, the Internet of Things mobile charging system performs the mean field game pricing iteration within a unified pricing period after determining the current supply and demand hidden state of each parking lot. For ease of illustration, it is assumed that there are parking lots in the city, denotes the total number of parking lots, and each parking lot has a unique number. The parking lot numbered is denoted as the parking lot. The Internet of Things mobile charging system pre-configures a benchmark rate for each parking lot, and the benchmark rate is denoted as , where denotes the basic charging level of the parking lot without dynamic pricing, which can be determined according to factors such as administrative district, historical cost, policy upper limit, etc. The benchmark rate reflects the long-term average charging benchmark, and plays an anchoring role in the mean field game pricing iteration, avoiding the dynamic parking rate deviating from a reasonable range.

[0055] At the beginning of the pricing period, the Internet of Things mobile charging system sets an initial candidate rate for each parking lot. The initial candidate rate is denoted as , where denotes the iteration round number. Time Candidate rates for each parking lot. In a common implementation, this can be directly set... In other words, the initial candidate rate is equal to the benchmark rate. With this setting, the mean-field game pricing iteration starts from a long-term stable rate level and then gradually adjusts it based on this, making the dynamic parking rate adjustment more smooth and easier for car owners to accept.

[0056] refer to Figure 1 , Figure 1 This diagram illustrates the distribution relationship between benchmark and candidate rates for multiple parking lots during a mean-field game pricing process. The diagram uses a two-dimensional scatter plot. The horizontal axis represents the benchmark rate for each parking lot, in yuan per hour, ranging from 3 yuan per hour to 13 yuan per hour. The vertical axis represents the candidate rate for each parking lot in a given iteration, also in yuan per hour, ranging from 2 yuan per hour to 14 yuan per hour. The diagram contains data points for 50 parking lots, each corresponding to a parking lot's position in the two-dimensional rate space. Based on the current implicit supply and demand state of the parking lots, three different markers are used to distinguish the data points. Parking lots in a relaxed supply and demand state are marked with hollow triangles; these data points are mainly distributed in the lower left area of ​​the diagram, with lower benchmark rates and further downward adjustments to candidate rates. Parking lots in a balanced supply and demand state are marked with gray-filled squares; these data points are mainly distributed in the middle area of ​​the diagram, with smaller deviations between their candidate and benchmark rates. Parking lots experiencing a hidden supply-demand imbalance are marked with black-filled circles. These data points are mainly distributed in the upper right area of ​​the graph, and their candidate rates are significantly higher than the benchmark rate. A diagonal line is drawn from the lower left to the upper right of the graph, representing the ideal state where the candidate rate equals the benchmark rate.

[0057] When a data point for a parking lot falls on the diagonal, it indicates that the parking lot has not yet adjusted its rates in the current iteration or has reached local stability. When the data point is above the diagonal, it means the candidate rate is higher than the benchmark rate, and the parking lot is implementing an upward adjustment strategy to cope with higher demand. When the data point is below the diagonal, it means the candidate rate is lower than the benchmark rate, and the parking lot is implementing a downward adjustment strategy to attract more vehicles to use available parking spaces. The figure also shows three horizontal dashed lines, corresponding to the mean field rate levels under three implicit supply and demand states. The mean field rate corresponding to the tight supply and demand state is approximately 9.45 yuan per hour; this horizontal line is located in the upper region of the figure, and the candidate rates of all parking lots in the tight supply and demand state will converge towards this horizontal line. The mean field rate corresponding to the balanced supply and demand state is approximately 6.18 yuan per hour; this horizontal line is located in the middle region of the figure.

[0058] The average field rate corresponding to the supply-demand loose hidden state is about 3.68 yuan per hour, and the horizontal line is located in the lower area of the figure. From the distribution of data points, it can be observed that the candidate rates of parking lots in the same supply-demand hidden state tend to converge to the corresponding average field rate, which is the core feature of the average field game method, that is, the individual decision-making is consistent through the guidance of the group average level. Two typical cases are marked with arrows and text boxes in the figure, one pointing to a parking lot in the supply-demand tight hidden state, indicating that the parking lot is implementing an upward adjustment strategy, and its candidate rate has increased significantly relative to the benchmark rate. The other arrow points to a parking lot in the supply-demand loose hidden state, indicating that the parking lot is implementing a downward adjustment strategy, and its candidate rate has decreased significantly relative to the benchmark rate. Through the figure, one can intuitively understand how each parking lot adjusts its rate dynamically based on its supply-demand state and the group average level in the average field game pricing iteration process, and ultimately forms a dynamic parking rate system that reflects individual differences and has overall consistency.

[0059] To construct the average field, the Internet of Things mobile charging system needs to consider the current supply-demand hidden state of each parking lot. The set of parking supply-demand hidden states can be denoted as , and the set contains three hidden state elements , and , where represents the supply-demand tight hidden state, represents the supply-demand balance hidden state, represents the supply-demand loose hidden state. For each parking lot, the Internet of Things mobile charging system has determined its current supply-demand hidden state in step two, denoted as , , where represents the supply-demand hidden state to which the th parking lot currently belongs, and is one of the three hidden states in the set .

[0060] In any iteration round , the Internet of Things mobile charging system holds the current candidate rate of each parking lot , where represents the candidate rate of the th parking lot at iteration round number . To depict the overall rate level of each supply-demand hidden state at the current iteration round, the Internet of Things mobile charging system constructs the average field rate based on the candidate rates of all parking lots in the same supply-demand hidden state. Taking the supply-demand tight hidden state as an example, the average field rate corresponding to the supply-demand tight hidden state can be denoted as , where represents the average field rate of the supply-demand tight hidden state at iteration round number .The average candidate rate for all parking lots currently in a state of supply-demand imbalance is given by [reference to a specific location]. The set of indices for all parking lots currently in a state of supply-demand imbalance can be denoted as [reference to a specific location]. ,in Includes all that satisfy Parking index. At this time, the average parking fee rate. It can be done The average of the candidate rates is obtained, i.e. ,in Represents a set The number of elements in the middle, This represents the summation of candidate rates for all parking lots currently in a state of supply and demand imbalance. Using this method, we can obtain the average overall parking fee level under the state of supply and demand imbalance, simplifying the complex multi-party interaction into the average impact each parking lot faces from the "supply and demand imbalance group." This is precisely the approach used in mean-field game theory to characterize group effects using the mean, ensuring the algorithm's scalability even with a large number of participants.

[0061] Similarly, we can define the mean market rate corresponding to the implicit state of supply-demand equilibrium and the mean market rate corresponding to the implicit state of supply-demand easing. The mean market rate corresponding to the implicit state of supply-demand equilibrium can be denoted as... The mean market rate corresponding to a state of ample supply and demand can be denoted as: The IoT mobile toll collection system separately counts the sets of parking lots currently in a supply-demand equilibrium state and a supply-demand surplus state. The average of the candidate rates within these two sets yields the final toll rate. and By constructing average field rates for the three supply and demand hidden states in the same iteration round, the IoT mobile toll collection system provides an "environmental signal" for each parking lot. This environmental signal not only reflects the average toll level of other parking lots in the same supply and demand hidden state, but also reflects the price level of the overall market under different supply and demand hidden states.

[0062] After obtaining the average parking fee rate, the IoT mobile toll collection system calculates an intermediate adjustment rate for each parking lot. This intermediate adjustment rate can be denoted as... ,in This indicates that in iteration round number 1 Time Intermediate adjustment rate for each parking lot. This can be defined as the current candidate rate for this parking lot. The average of the mean market rates corresponding to the current implicit state of supply and demand, for example, can be written as... ,in Indicates the first The average parking fee rate corresponding to the current supply and demand status of a parking lot. If This is equivalent to a hidden state of supply and demand tension. equal ;if If this equals the implicit state of supply and demand equilibrium, then... equal ;if This is equivalent to a state of implicit supply and demand easing. equal By averaging the candidate rates of this parking lot with the mean rates under the same supply and demand implicit conditions, the intermediate adjustment rate will numerically converge towards the group average level, thereby reducing the impact of excessively high or low candidate rates of individual parking lots on the overall game outcome, and making parking rates show a more consistent trend under the same supply and demand implicit conditions.

[0063] After the intermediate adjustment rate is determined, the IoT mobile toll collection system differentiates the response rate based on three different supply and demand implicit state types. This can be done by... The parking lot is in iteration round numbered as The response rate at that time is recorded as ,in This indicates that the IoT mobile payment system is the first in the mean-field game pricing iteration. The response rate is calculated for each parking lot. For parking lots where the current supply and demand situation is one of supply shortage, the intermediate adjustment rate is combined with the base rate to enhance the rate's ability to be adjusted upwards in scenarios with high demand, while retaining the constraint on the base rate. Specifically, this can be achieved using... ,in This indicates the intermediate adjustment rate. This represents the base rate. With this setting, if the average rate is high and the base rate is relatively low, the intermediate rate will be higher than the base rate, and the final response rate will be the average of the two. This allows parking rates to be adjusted upwards during periods of supply and demand tension, but without a sudden increase to an extreme level. This helps to suppress new demand through price signals during peak demand periods, while avoiding abrupt price jumps for car owners.

[0064] For parking lots where the current supply and demand are in a state of implicit equilibrium, the IoT mobile payment system can directly use the intermediate adjustment rate as the response rate, that is... . In the supply-demand balance hidden state, the parking space supply and demand are in a relatively balanced state, and at this time the dynamic pricing does not need to be obviously biased upward or downward. By directly adopting the intermediate adjustment rate, the response rate of the parking lot will be affected not only by the candidate rate based on itself, but also by the average lot rate under the same supply-demand hidden state, so that the parking lots maintain a relatively consistent charging level under the supply-demand balance hidden state, which is conducive to maintaining fairness and predictability within the same functional area.

[0065] For the parking lot in the current supply-demand loose hidden state, the Internet of Things mobile charging system can introduce a stronger downward adjustment trend, so that the response rate is closer to the average lot rate corresponding to the supply-demand loose hidden state. Specifically, the response rate can be adjusted by , and at this time is equal to the average lot rate corresponding to the supply-demand loose hidden state . Since the intermediate adjustment rate itself is the average of the candidate rate and the average lot rate, and the average lot rate is further averaged, the response rate will further approach the average lot rate, so that the parking lot rate under the supply-demand loose hidden state as a whole presents a moderate downward trend, which helps to attract more vehicles to use the idle parking spaces and improve the overall resource utilization.

[0066] In a numerical example, it can be assumed that there are 3 parking lots, numbered 1, 2 and 3, of which the first parking lot is in the supply-demand tight hidden state, the second parking lot is in the supply-demand balance hidden state, and the third parking lot is in the supply-demand loose hidden state. It can be assumed that the reference rates are , 30 yuan per hour, , 20 yuan per hour, , 10 yuan per hour. At iteration round 0, the initial candidate rates are , 40 yuan per hour, , 30 yuan per hour, , 20 yuan per hour. It is assumed that in this round, the parking lot set corresponding to the supply-demand tight hidden state only contains the first parking lot, so , 40 yuan per hour; the parking lot set corresponding to the supply-demand balance hidden state only contains the second parking lot, so , 30 yuan per hour; the parking lot set corresponding to the supply-demand loose hidden state only contains the third parking lot, so , 20 yuan per hour. At this time, the intermediate adjustment rates are , 35 yuan per hour, , 25 yuan per hour, , 15 yuan per hour. After adjusting the response rate according to the different supply-demand tight hidden state, supply-demand balance hidden state and supply-demand loose hidden state, the response rate is , 35 yuan per hour, , 25 yuan per hour, Yen per hour. As the candidate rates of the parking lots change in the subsequent iteration rounds, for example, the candidate rates of the parking lots in the tight supply-demand state are gradually increased, and the candidate rates of the parking lots in the loose supply-demand state are gradually decreased, the corresponding average lot rate and response rate will also be adjusted, and finally a set of dynamic parking rates that take into account the supply-demand situation and price smoothness will be formed in the city.

[0067] At the end of each iteration round, the Internet of Things mobile charging system needs to determine whether the current iteration round has converged. To this end, the rate variation range of each parking lot can be defined as , wherein represents the absolute value of the difference between the response rate and the candidate rate of the th parking lot at the iteration round number . For example, the rate variation range can be defined as , wherein represents the absolute value of the difference between the response rate and the candidate rate of the th parking lot in the current iteration round. Subsequently, the Internet of Things mobile charging system selects the maximum value of the rate variation range in all parking lots, denoted as , wherein , represents the maximum value operation on all parking lot indexes. To make the convergence determination, the Internet of Things mobile charging system pre-sets a preset convergence determination threshold in the system configuration stage, denoted as , wherein represents the maximum rate variation range upper limit allowed, which can be set to 0.1 yuan per hour or 0.2 yuan per hour, for example. When is less than , it means that the rate adjustment range of all parking lots in the current iteration round is already very limited, and the benefit obtained by further iteration is small, so the mean field game pricing iteration can be considered to have reached a stable state.

[0068] If is less than the preset convergence determination threshold , the Internet of Things mobile charging system takes the current response rate set as the final dynamic parking rate set, directly determines the response rate of each parking lot as the dynamic parking rate of the parking lot in the current pricing period, and pushes these dynamic parking rates to the mobile application of the vehicle owner and the entrance display terminal of the parking lot through the mobile communication network. At this time, the mean field game has converged to an approximate Nash equilibrium state, that is, after considering that each parking lot makes a response rate selection based on the mean field rate and the benchmark rate, no single parking lot can significantly improve its own benefit by unilaterally changing its parking rate without disrupting the current equilibrium.

[0069] If greater than or equal to a preset convergence determination threshold , it indicates that there is still a large deviation between the response rate of this round and the candidate rate, at this time the Internet of Things mobile charging system will not immediately output the dynamic parking rate, but use the response rate of each parking lot as the candidate rate of the next round. That is, let , where represents the candidate rate of the th parking lot in the th iteration round. Subsequently, the Internet of Things mobile charging system recalculates the average field rate, the intermediate adjustment rate and the response rate in the new iteration round, and performs the convergence determination again. Through such a cyclic iteration process, the candidate rate gradually approaches the equilibrium state, and the change range of the response rate gradually reduces, and finally stops iteration within the preset convergence determination threshold.

[0070] In an optional embodiment, in order to further control the smoothness of the dynamic parking rate, the Internet of Things mobile charging system can introduce a factor that punishes too fast change when updating the candidate rate. For example, the form of can be used, where represents a smoothing coefficient between 0 and 1, used to control the degree of influence of the response rate of this round on the candidate rate of the next round, represents the response rate of this round, represents the candidate rate of this round. Through such a design, it can avoid large fluctuations in the candidate rate in the iteration process, while making the average field game pricing iteration more stable when approaching convergence, suitable for urban scenarios with high price sensitivity.

[0071] Through the above embodiments, the Internet of Things mobile charging system integrates the supply and demand tight hidden state, the supply and demand balance hidden state and the supply and demand loose hidden state from the Hidden Markov Model into the average field game pricing iteration, and correlates the candidate rate of each parking lot, the average field rate, the benchmark rate and the response rate, constantly iterates under the constraint of the preset convergence determination threshold, and finally generates a set of dynamic parking rates. This process not only reflects the response of a single parking lot to its own supply and demand state, but also takes into account the overall price level of the same supply and demand hidden state group in the global range, so as to balance between improving resource utilization and ensuring price acceptability in dynamic pricing.

[0072] While specific embodiments of the application have been described above, it will be appreciated that those skilled in the art within the scope of the application can make modifications, substitutions and changes in the form and details of the method and system described above without departing from the spirit and scope of the application. For example, it is well within the scope and spirit of the application to combine various of the illustrative steps of the above methods to carry out essentially the same function to achieve essentially the same result in substantially the same way. Accordingly, the scope of the application should be determined sole by the appended claims.

Claims

1. A mobile Internet of Things (IoT) system and dynamic pricing method for urban parking, characterized in that, The method comprises the following steps: Step one: the Internet of Things mobile charging system collects real-time parking space occupancy rate data of each parking lot in the city through the geomagnetic sensor, converts the real-time parking space occupancy rate data into observation symbols according to a preset discretization interval division rule, and arranges the observation symbols of continuous multiple sampling time points in time sequence to form an observation symbol sequence of each parking lot. Step two: the Internet of Things mobile charging system loads a parking supply and demand hidden Markov model, the parking supply and demand hidden state set of the parking supply and demand hidden Markov model includes a supply and demand tight hidden state, a supply and demand balance hidden state and a supply and demand loose hidden state, and the Internet of Things mobile charging system performs hidden Markov model Viterbi decoding for each parking lot to obtain an optimal hidden state sequence, and extracts a hidden state corresponding to a current sampling time point from the optimal hidden state sequence as a current supply and demand hidden state of the corresponding parking lot. Step three: the Internet of Things mobile charging system performs mean field game pricing iteration based on the current supply and demand hidden states of all parking lots, sets a candidate rate for each parking lot, constructs a mean field according to the candidate rate, calculates a response rate of each parking lot according to the mean field rate corresponding to each supply and demand hidden state and the benchmark rate of each parking lot, and determines the response rate of each parking lot as a dynamic parking rate and publishes it externally when the response rate and the candidate rate meet a preset convergence judgment threshold condition.

2. The method of claim 1, wherein, Step one includes: the Internet of Things mobile charging system collects real-time parking space occupancy rate data of each parking lot in the city through the geomagnetic sensor deployed in each parking lot in the city, and divides the real-time parking space occupancy rate data into multiple value intervals according to a preset discretization interval division rule, each value interval corresponds to a unique observation symbol, and the Internet of Things mobile charging system arranges the observation symbols obtained by each parking lot at continuous multiple sampling time points in time sequence to form an observation symbol sequence corresponding to each parking lot, which is used to represent the parking space occupancy state change of each parking lot at multiple sampling time points.

3. The method of claim 1, wherein, The parking supply and demand hidden Markov model includes a parking supply and demand hidden state set, a transition probability table between hidden states, an emission probability table of each observation symbol under each hidden state, and an initial probability table of each hidden state, the parking supply and demand hidden state set includes three hidden state types of a supply and demand tight hidden state, a supply and demand balance hidden state and a supply and demand loose hidden state, the supply and demand tight hidden state is used to represent a supply and demand state in which the parking lot is short of parking spaces and the parking space occupancy rate is in a preset high occupancy interval, the supply and demand balance hidden state is used to represent a supply and demand state in which the difference between the parking space supply quantity and the parking space demand quantity does not exceed a preset balance threshold and the parking space occupancy rate is in a preset intermediate occupancy interval, and the supply and demand loose hidden state is used to represent a supply and demand state in which the number of idle parking spaces is greater than a preset surplus threshold and the parking space occupancy rate is in a preset low occupancy interval.

4. The method of claim 1, wherein, The initialization process of the hidden Markov model Viterbi decoding in the step two comprises the following steps: the Internet of Things mobile charging system reads the first observation symbol in the observation symbol sequence of the target parking lot for any parking lot, reads the initial probability value of the supply-demand tight hidden state, the initial probability value of the supply-demand balance hidden state and the initial probability value of the supply-demand loose hidden state from the initial probability table, reads the probability value of the supply-demand tight hidden state emitting the first observation symbol, the probability value of the supply-demand balance hidden state emitting the first observation symbol and the probability value of the supply-demand loose hidden state emitting the first observation symbol from the emission probability table, multiplies the initial probability value of the supply-demand tight hidden state and the probability value of the supply-demand tight hidden state emitting the first observation symbol to obtain the local path probability value of the supply-demand tight hidden state at the first observation symbol time, multiplies the initial probability value of the supply-demand balance hidden state and the probability value of the supply-demand balance hidden state emitting the first observation symbol to obtain the local path probability value of the supply-demand balance hidden state at the first observation symbol time, and multiplies the initial probability value of the supply-demand loose hidden state and the probability value of the supply-demand loose hidden state emitting the first observation symbol to obtain the local path probability value of the supply-demand loose hidden state at the first observation symbol time.

5. The method of claim 4, wherein, The recursive calculation process of the hidden Markov model Viterbi decoding in step two includes: the Internet of Things mobile charging system traverses from the second observation symbol of the observation symbol sequence to the last observation symbol, for the currently traversed observation symbol, the Internet of Things mobile charging system reads the transition probability value from the transition probability table of the transition from the supply-demand tight hidden state to the supply-demand tight hidden state, the transition probability value from the supply-demand balance hidden state to the supply-demand tight hidden state and the transition probability value from the supply-demand loose hidden state to the supply-demand tight hidden state, multiplies the local path probability value of the supply-demand tight hidden state at the previous observation symbol time by the transition probability value from the supply-demand tight hidden state to the supply-demand tight hidden state to obtain a first candidate transition probability product, multiplies the local path probability value of the supply-demand balance hidden state at the previous observation symbol time by the transition probability value from the supply-demand balance hidden state to the supply-demand tight hidden state to obtain a second candidate transition probability product, multiplies the local path probability value of the supply-demand loose hidden state at the previous observation symbol time by the transition probability value from the supply-demand loose hidden state to the supply-demand tight hidden state to obtain a third candidate transition probability product, compares the numerical values of the first candidate transition probability product, the second candidate transition probability product and the third candidate transition probability product and selects the maximum value as the optimal predecessor transition probability product of the supply-demand tight hidden state, records the hidden state at the previous time when the optimal predecessor transition probability product is generated as the predecessor pointer of the supply-demand tight hidden state at the current observation symbol time, reads the probability value of the supply-demand tight hidden state emitting the current observation symbol from the emission probability table, and multiplies the optimal predecessor transition probability product of the supply-demand tight hidden state by the probability value of the supply-demand tight hidden state emitting the current observation symbol to obtain the local path probability value of the supply-demand tight hidden state at the current observation symbol time. The Internet of Things mobile charging system calculates the local path probability value and the predecessor pointer of the supply-demand balance hidden state at the current observation symbol time and the local path probability value and the predecessor pointer of the supply-demand loose hidden state at the current observation symbol time by using the same recursive calculation method.

6. The method of claim 5, wherein, The backtracking process of the hidden Markov model Viterbi decoding in step two includes: after the Internet of Things mobile charging system completes the traversal of the observation symbol sequence, the numerical values of the local path probability value of the supply-demand tight hidden state, the local path probability value of the supply-demand balance hidden state and the local path probability value of the supply-demand loose hidden state at the last observation symbol time are compared, the hidden state with the largest local path probability value is selected as the terminal hidden state of the optimal hidden state path, the terminal hidden state is taken as the starting hidden state, the starting hidden state corresponding to the first observation symbol time is taken as the starting hidden state, all the hidden states on the backtracking path are arranged in time sequence to form the optimal hidden state sequence of the target parking lot, and the hidden state corresponding to the current sampling time is extracted from the optimal hidden state sequence of the target parking lot as the current supply-demand hidden state of the target parking lot.

7. The method of claim 1, wherein, The mean field game pricing iteration in step three comprises: the Internet of Things mobile charging system sets an initial candidate rate of each parking lot equal to the benchmark rate of each parking lot, traverses all parking lots and screens parking lots whose current supply-demand hidden state is the supply-demand tight hidden state to form a supply-demand tight parking lot set, sums up the current candidate rates of all parking lots in the supply-demand tight parking lot set and divides the number of parking lots in the supply-demand tight parking lot set to obtain the mean field rate corresponding to the supply-demand tight hidden state, and calculates the mean field rate corresponding to the supply-demand balance hidden state and the mean field rate corresponding to the supply-demand loose hidden state in the same way to represent the mean field level of the candidate rate of the parking lot under the three supply-demand hidden states.

8. The method of claim 7, wherein, The response rate calculation in step three comprises: the Internet of Things mobile charging system reads the current supply-demand hidden state of each parking lot and queries the mean field rate corresponding to the current supply-demand hidden state for each parking lot, adds the current candidate rate of each parking lot and the mean field rate corresponding to the current supply-demand hidden state and divides the sum by two to obtain an intermediate adjustment rate of each parking lot, adds the intermediate adjustment rate of each parking lot and the benchmark rate of each parking lot and divides the sum by two to obtain the response rate of each parking lot when the current supply-demand hidden state is the supply-demand tight hidden state, takes the intermediate adjustment rate of each parking lot as the response rate of each parking lot when the current supply-demand hidden state is the supply-demand balance hidden state, adds the intermediate adjustment rate of each parking lot and the mean field rate corresponding to the current supply-demand hidden state and divides the sum by two to obtain the response rate of each parking lot when the current supply-demand hidden state is the supply-demand loose hidden state, so as to differentially adjust the response rate of different parking lots according to different supply-demand hidden state types.

9. The method of claim 1, wherein, The convergence judgment and candidate rate updating in step three comprise: the Internet of Things mobile charging system calculates the absolute value of the difference between the response rate of each parking lot and the current candidate rate as the rate variation amplitude of each parking lot, selects the maximum value from the rate variation amplitudes of all parking lots as the maximum rate variation amplitude of the current iteration round, compares the maximum rate variation amplitude of the current iteration round with a preset convergence judgment threshold, when the maximum rate variation amplitude of the current iteration round is less than the preset convergence judgment threshold, the Internet of Things mobile charging system judges that the mean field game reaches Nash equilibrium and determines the response rate of each parking lot as the dynamic parking rate of each parking lot, when the maximum rate variation amplitude of the current iteration round is greater than or equal to the preset convergence judgment threshold, the Internet of Things mobile charging system updates the response rate of each parking lot to the current candidate rate of each parking lot and returns to continue executing the mean field game pricing iteration.

Images