Simulation and optimization method of online ride-hailing pick-up area in transportation hub based on double-ended queuing theory

Abstract

The present invention discloses a simulation and optimization method for a ride-hailing boarding area at a transportation hub based on a double-ended queuing theory, which belongs to the technical field of traffic organization optimization. The method includes: obtaining the passenger arrival rate, vehicle arrival rate, service rate and number of activated service desks at the ride-hailing boarding area at the transportation hub; simulating the ride-hailing boarding area at the transportation hub through a Markov chain according to the passenger arrival rate and the vehicle arrival rate to obtain a steady-state probability distribution, and calculating the average queue length of vehicles and passengers according to the steady-state probability distribution; calculating the service intensity according to dynamic parameters, judging the service intensity, and adjusting the service rate and the number of activated service desks according to the judgment result; constraining the adjusted service rate and the number of activated service desks according to the passenger arrival rate and the vehicle arrival rate; performing a threshold judgment on the service intensity, and performing a hysteresis control on the constrained number of activated service desks according to the threshold judgment result, so as to realize the simulation optimization of the ride-hailing boarding area at the transportation hub.

Description

Technical Field

[0001] The present invention belongs to the technical field of traffic organization optimization in transportation hubs, and in particular relates to a simulation and optimization method for online car-hailing boarding areas in transportation hubs based on double-ended queuing theory. Background Art

[0002] With the continued advancement of smart development at domestic high-speed rail hubs, the dispatch efficiency of ride-hailing shuttle systems has become a critical factor affecting passenger collection and distribution speeds and station operational efficiency. Modern high-speed rail hubs have innovatively implemented P2 (Pick-Up) smart pick-up areas for ride-hailing. Their operating logic is as follows: After a passenger completes a ride-hailing request, the vehicle enters a parking space through a gate identification system. The system then displays the vehicle's license plate and parking space information on a display screen in the waiting hall, guiding passengers to find their own rides. While this model offers improvements over traditional curbside shuttles, it still faces significant operational bottlenecks. First, the dynamic, two-way matching of parking resources and passenger demand lacks theoretical support. The traditional "first-come, first-served" approach leads to an imbalance between vehicle holdup time and passenger wait time. Second, during peak hours, limited parking capacity leads to significant congestion in two-way queues. When vehicle arrival rates surge or passenger search efficiency decreases, a vicious cycle of "cars waiting for spaces, passengers waiting for rides" is easily triggered. Furthermore, existing systems lack a quantitative assessment mechanism for the service intensity of two-way queueing models, making it impossible to predict the risk of system overload and even more difficult to maintain matching stability under dynamic fluctuations. Summary of the Invention

[0003] In order to solve the above technical problems, the present invention proposes a simulation and optimization method for the online car-hailing boarding area in a transportation hub based on the double-ended queuing theory to solve the problems existing in the above-mentioned existing technologies.

[0004] To address the aforementioned technical issues, the present invention provides a simulation and optimization method for ride-hailing pickup areas at transportation hubs based on double-ended queuing theory. This system considers the overall operational status of the transportation hub and fully utilizes lane resources in the ride-hailing area, reducing overall vehicle delays and improving passenger satisfaction. The system provided by the present invention can determine the optimal ride-hailing pickup area optimization solution that meets the needs of the transportation hub. Specifically, it dynamically schedules the arrival rates of ride-hailing vehicles and passengers based on time series.

[0005] To achieve the above objectives, the present invention provides a simulation and optimization method for the pick-up area of ​​online ride-hailing vehicles at transportation hubs based on double-ended queuing theory, comprising:

[0006] Obtain dynamic parameters of ride-hailing pickup areas at transportation hubs, including passenger arrival rate, vehicle arrival rate, service rate, and the number of activated service stations.

[0007] Based on the passenger arrival rate and vehicle arrival rate, the Markov chain is used to simulate the ride-hailing pick-up area of ​​the transportation hub to obtain a steady-state probability distribution;

[0008] According to the steady-state probability distribution, the average queue length of vehicles and the average queue length of passengers are calculated;

[0009] Calculate service intensity based on dynamic parameters, judge service intensity, and adjust service rate and number of activated service desks based on the judgment results;

[0010] Constrain the adjusted service rate and the number of activated service desks based on the passenger arrival rate and vehicle arrival rate;

[0011] A threshold judgment is made on the service intensity, and based on the threshold judgment result, a hysteresis control is performed on the number of activated service stations after the constraint, so as to realize the simulation optimization of the online car-hailing boarding area in the transportation hub.

[0012] Optionally, the steady-state probability distribution is:

[0013]

[0014] in, is the distribution probability of each queue length in steady state, represents the passenger arrival rate, represents the arrival rate of online ride-hailing vehicles, represents the service rate, i and j represent the index variables of the passenger dimension and vehicle dimension in the state space respectively, Indicates time The number of passengers waiting to be matched, Indicates time The number of ride-hailing vehicles waiting to be matched.

[0015] Optionally, the calculation process of the average queue length of vehicles and the average queue length of passengers is:

[0016] ;

[0017] in, is the average queue length of passengers; is the average queue length of vehicles; is the number of service desks that can currently work simultaneously in the system, Represents vehicle end load; Represents the passenger side load.

[0018] Optionally, the calculation process of the vehicle-side load and the passenger-side load is:

[0019]

[0020] in Represents vehicle end load; Represents the passenger side load; Represents the number of service desks currently enabled. represents the vehicle arrival rate, represents the passenger arrival rate, Represents service rate.

[0021] Optionally, the service intensity calculation process includes:

[0022] ;

[0023] in, Indicates service intensity.

[0024] Optionally, the process for adjusting service rates and the number of active service desks includes:

[0025] The service intensity is judged, wherein when the service intensity is higher than a first threshold and lower than a second threshold, the number of enabled service stations is adjusted:

[0026] ;

[0027] When the service intensity is higher than the second threshold, the service rate is adjusted:

[0028] .

[0029] Optionally, the process of constraining the adjusted service rate and the number of enabled service desks includes:

[0030] .

[0031] Optionally, the process of performing hysteresis control on the number of enabled service desks after the constraint includes:

[0032] A threshold value is determined for the service intensity, and based on the threshold value determination result, the number of activated service stations after the constraint is gradually hysteresis-controlled:

[0033]

[0034] in, is the lower limit of service intensity, is the upper limit of server strength, is the state holding time, k(t - ) indicates the number of enabled service desks at the previous moment.

[0035] Optionally, the hysteresis control of the number of enabled service desks after the constraint also includes:

[0036] To constrain the number of enabled service desks in hysteresis control:

[0037] .

[0038] Optionally, an upper limit and a lower limit of the service intensity are constrained:

[0039]

[0040]

[0041] in, is the sensitivity coefficient.

[0042] Compared with the prior art, the present invention has the following advantages and technical effects:

[0043] Compared to traditional ride-hailing pickup areas, the dual-ended single-queue, multi-service-station queuing model proposed in this paper more accurately describes the matching and service mechanisms between ride-hailing vehicles and passengers. Furthermore, based on the structure of ride-hailing pickup areas at similar transportation hubs like Hangzhou West Railway Station, the number of service stations is defined based on the number of lanes, enabling more flexible control strategies.

[0044] 2. By quantifying the system load, it helps managers adopt more scientific management strategies and comprehensively plan the optimal allocation of the number of open service desks (lanes). At the same time, setting early warning thresholds allows the platform and transportation hub to jointly manage and control the system.

[0045] 3. Using the Lyapunov method to analyze two-terminal stability, we prove that the queue length is bounded in the expected sense (weak stability) or converges to a steady-state distribution (strong stability). This method is applicable to matching strategies with time-varying arrival rates and non-first-come, first-served delivery. This ensures that during the matching process, there will be no system imbalance caused by a surge in the real-time arrival rate of either the ride-hailing or passenger side. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0047] Figure 1 This is a step diagram of a method for simulating and optimizing a pick-up area for online ride-hailing vehicles at a transportation hub based on double-ended queuing theory according to an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of matching online ride-hailing vehicles and passengers at a transportation hub according to an embodiment of the present invention;

[0049] Figure 3 This is a flow chart of a double-ended single-queue parallel multi-server queuing algorithm according to an embodiment of the present invention;

[0050] Figure 4 A diagram showing the birth and death process of a Markov chain according to an embodiment of the present invention;

[0051] Figure 5 This is a geometric interpretation diagram of Lyapunov stability according to an embodiment of the present invention. DETAILED DESCRIPTION

[0052] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0053] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0054] To address the aforementioned technical issues, the present invention provides a simulation and optimization method for ride-hailing pickup areas at transportation hubs based on double-ended queuing theory. This method considers the overall operational status of the transportation hub and fully utilizes lane resources in the ride-hailing area, reducing overall vehicle delays and improving passenger satisfaction. The system provided by the present invention can determine the optimal ride-hailing pickup area optimization solution that meets the needs of the transportation hub. Specifically, it dynamically schedules the arrival rates of ride-hailing vehicles and passengers based on time series.

[0055] The present invention relates to the technical field of traffic organization optimization at transportation hubs, and specifically discloses a simulation and optimization method for online car-hailing boarding areas at transportation hubs based on double-ended queuing theory. In response to the problems of imbalance in the dynamic matching between berth resources and passenger demand, double-ended queue congestion during peak hours, and insufficient system stability in the prior art, the present invention proposes the following innovative solutions: First, a two-dimensional continuous-time Markov model based on double-ended collaborative queuing theory is constructed to characterize the dynamic matching mechanism between passengers and online car-hailing vehicles through the birth and death process, and to quantify the double-ended service intensity to evaluate the system load; secondly, the joint optimization objective function of the average waiting time of the two queues is derived in combination with the improved Little formula, and a mixed integer programming algorithm is designed to dynamically control the number of service desks and the matching rate; further, the Lyapunov stability theory is introduced to construct the double-ended joint queue energy function to ensure the strong stability of the system under time-varying arrival rates; finally, hysteresis control is used to prevent the system from experiencing oscillation effects and avoid instantaneous overload. The present invention realizes the efficient allocation of resources in the online ride-hailing boarding area of ​​transportation hubs, solves the imbalance problem of vehicle detention and passenger waiting caused by the traditional "first come, first served" rule, significantly reduces the delay time at both ends, and provides a breakthrough solution for dynamic optimization and risk warning for the online ride-hailing dispatching system of intelligent transportation hubs.

[0056] This patent creatively proposes a simulation and optimization method for intelligent control of online car-hailing boarding areas based on the double-end collaborative queuing theory: for the first time, the passenger-vehicle matching process is defined as a two-dimensional continuous-time Markov process with capacity constraints, and establishes Two-ended state transfer model (where represents the passenger dimension, Representing the ride-hailing dimension, this approach accurately characterizes the birth-death relationship. By quantifying service intensity on both ends and adopting appropriate control strategies, the system maintains stable operation without overload. Furthermore, based on the improved Little formula, a joint optimization objective function for the average waiting time of both queues is derived. This, combined with a mixed integer programming algorithm, solves an optimal solution for ride-hailing pickup areas that minimizes delays. This provides a breakthrough technical path for the intelligent upgrade of ride-hailing dispatching systems at high-speed rail hubs.

[0057] To achieve the above objectives, the technical solutions adopted by the present invention are as follows:

[0058] The present invention provides a method for simulating and optimizing a pick-up area for online ride-hailing vehicles at a transportation hub based on double-ended queuing theory, the method comprising:

[0059] S1: Obtain passenger arrival information, ride-hailing vehicle arrival information, and the number of available service counters at the ride-hailing vehicle pickup area at the transportation hub.

[0060] S2: Based on the Markov chain, the number of effective service stations and the number of actual active service stations are derived according to the birth and death process, and the steady-state probability distribution is obtained by combining the global equilibrium equation and the equilibrium condition. The parameter space is a three-dimensional discrete state space composed of the following parameters: passenger arrival rate ; Vehicle arrival rate ;time The number of passengers waiting to be matched (passenger queue length) ;time Number of ride-hailing vehicles waiting to be matched (vehicle queue length) ;time Number of active service desks (maximum parallel matching capacity) The matching rule is: matching is triggered only when the passenger and the vehicle are present at the same service desk at the same time, and the unilateral arrival enters the queue and waits; after the matching is successful, the vehicle immediately leaves the parking space, the passenger completes the ride, and the service desk is released.

[0061] S3: Solve the key performance indicators of the double-ended single queue parallel multi-server model and obtain the average queue length of online ride-hailing vehicles and passengers. The formula further derives the average waiting time for ride-hailing vehicles and passengers. The formula is defined as follows:

[0062]

[0063] The effective reach rate is defined as:

[0064]

[0065] in and They represent the state of no waiting vehicles and the state of no waiting passengers respectively.

[0066] S4: Jointly quantify the passenger arrival rate and the online car-hailing arrival rate, define the service intensity index of both ends, and adopt different control strategies according to the current load level of the system.

[0067] Furthermore, the control strategy objective function of the service station is:

[0068]

[0069] in, is the real-time arrival rate of passengers; The arrival rate for online ride-hailing services; is the service rate; definition is a rounding function, which ensures that the number of service stations is an integer. Since the above three items are used to calculate the minimum number of service stations required in the objective function, when When set to this value, each term divided by the number of service desks (i.e., service intensity) is less than 1. Therefore, the first term in the formula can ensure that the system load is less than 1; the second term can ensure the service intensity of the passenger side. The third item can ensure the service intensity of the vehicle side .

[0070] Furthermore, the control strategy objective function of the service rate is:

[0071]

[0072] in, is the number of service desks. According to the system load level, the above two control schemes can be reasonably selected.

[0073] S5: Use Lyapunov stability theory to ensure the stability of double-ended queues and ensure that there will be no imbalance on one side. Construct the energy function of the double-ended joint queue based on Lyapunov function:

[0074]

[0075] in, For the moment The passenger queue length (number of passengers waiting to be matched); For the moment The length of the ride-hailing queue (the number of ride-hailing vehicles waiting to be matched); is the coupling coefficient, and the optimization strategy is controlled by gradient descent.

[0076] Furthermore, we can obtain the service station quantity constraint and service rate compensation constraint:

[0077]

[0078] S6: For dynamic control strategies, since frequent switching of service desks may cause shock effects, hysteresis control needs to be added. The upper and lower thresholds form a buffer zone. When the activation threshold is reached, the number of service desks is increased; when the release threshold is reached, the number of service desks is reduced.

[0079] The above technical solution is described in detail:

[0080] The optimization problem of the online car-hailing boarding area at a transportation hub can be described as follows: the passenger arrival rate in the waiting hall of the online car-hailing boarding area at a transportation hub is The arrival rate of vehicles arriving at the dedicated parking lot for online car-hailing is , at this time, passengers and online ride-hailing vehicles are queued at both ends in a non-first-come-first-served manner, and the matching efficiency (i.e., the service rate of the system) is In this case, ride-hailing vehicles and passengers are considered to be single queues in both time and space, and the number of lanes in the dedicated ride-hailing parking lot (actually, one lane corresponds to two train spaces) is considered the number of service stations. Due to travel time constraints, peak passenger arrivals and peak ride-hailing arrivals will inevitably lead to earlier or later arrivals. Therefore, the number of service stations and service rates in the dedicated ride-hailing parking lot must be regulated based on the real-time arrival rates of both parties to ensure that the system load does not exceed the upper limit. At the same time, the stability of the double-ended queuing system must be maintained to avoid imbalance in the queuing system.

[0081] When solving this problem, we need to make the following assumptions:

[0082] (1) One online-hailing car can only use one parking space, and one parking space can only accommodate one online-hailing car at a time;

[0083] (2) All parking spaces are available for normal use;

[0084] (3) When the service counter (channel) is in an inactive state, online ride-hailing vehicles are prohibited from entering the parking spaces of the channel;

[0085] (4) When the online ride-hailing vehicle is parked in the designated parking space, the passenger can find the reserved online ride-hailing vehicle smoothly without any mismatching.

[0086] (5) Initially, there is no vehicle in any parking space;

[0087] Specifically, such as Figure 1 As shown, the present invention provides a simulation and optimization method for a ride-hailing boarding area in a transportation hub based on the double-ended queuing theory, comprising the following steps S1 to S5:

[0088] S1: Obtain the real-time passenger arrival rate at the transportation hub, the real-time arrival rate of online ride-hailing vehicles, the number of service counters (lanes) in the dedicated parking lot for online ride-hailing vehicles, and the number of parking spaces on both sides of each lane. Then calibrate the service rate of the double-ended queuing system based on simulation. Then set dynamic parameters to define the vehicle arrival rate. , passenger arrival rate , service rate , the number of service desks currently enabled , and define the system state variables: vehicle queue length , passenger queue length .

[0089] The arrival rate is the number of arrivals per unit time, and the service rate is the number of groups of passengers and vehicles matched per unit time.

[0090] Then calculate the system load and perform end-to-end calculations, taking capacity limitations into account:

[0091]

[0092] in Represents vehicle end load; Represents the passenger side load; Represents the number of active service desks at the current moment. Due to the split-end calculation method, when the sum of the two is less than 1, the system is considered stable.

[0093] Furthermore, in actual operation, each service desk and the parking space corresponding to the service desk are limited, such as Figure 2 As shown in the diagram of matching online ride-hailing and passengers at the transportation hub, limited parking capacity is introduced. , for the state space, the number of parking spaces is constrained as follows: .

[0094] like Figure 3 As shown, the overall process steps of the double-ended single-queue parallel multi-server queuing algorithm of the present invention are as follows:

[0095] Step 1: The queuing system collects real-time data, including the number of service desks, passenger arrival rate, and ride-hailing arrival rate;

[0096] Step 2: Calculate the service intensity based on the real-time service rate. When the service intensity is greater than The system enters the warning state;

[0097] Step 3: When the system enters the warning state, the strategy is executed based on the current number of service desks. If the number of currently enabled service desks is less than the total number of service desks in the system, capacity expansion is performed; when the number of enabled service desks reaches the maximum capacity, the service rate is adjusted;

[0098] Step 4: The current system state is tested for stability using the Lyapunov function, and new constraints are established to maintain the stability of the system.

[0099] Step 5: To address the oscillation effect in the dynamic control of the number of service desks, hysteresis control is used to avoid system disorder caused by frequent state switching;

[0100] Step 6: Output the new service rate and number of consoles, combine them with the new real-time arrival rate, and repeat the above steps.

[0101] S2: Based on the Markov chain, derive the birth and death process of a double-ended queue with multiple servers in parallel, and define the state transition rate of the birth process (arrival):

[0102]

[0103]

[0104] in, is the passenger arrival state transition rate; is the vehicle arrival state transition rate; It is a binary indicator function, whose logic is that if the condition is met, the function output is 1, and if the condition is not met, the function output is 0; and They represent the number of online ride-hailing vehicles that are not matched by the system at the current moment and the number of online ride-hailing vehicles that are not matched by the system at the next moment respectively; and They represent the number of unmatched passengers in the system at the current moment and the number of unmatched passengers in the system at the next moment, respectively.

[0105] Furthermore, the death process (matching) is defined:

[0106]

[0107] The process of birth and death is like Figure 4 The Markov chain birth and death process is shown in the process diagram, where the vertical connecting lines represent the arrival of vehicles and the horizontal connecting lines represent the arrival of passengers. Since it is not a first-come, first-served policy, the queuing system will continue to expand. The diagonal connections are matching services, representing the state transition of the system.

[0108] Furthermore, the equilibrium equation is derived. For the global equilibrium equation, any state that the system may be in is considered. Assume that the system enters the state within a period of time and leave state Since arrivals and departures occur alternately, the average occurrence rates of these two events are considered equal, that is, the inflow is equal to the outflow under statistical equilibrium. According to this principle, the equilibrium equation is as follows:

[0109]

[0110] in: is the actual number of active service desks, expressed as: ; Indicates that the system is in state after running for a long time. When the system runs for a long enough time, the state probability distribution tends to be stable. It no longer changes with time. This formula directly reflects the distribution probability of each queue length in the steady state of the system.

[0111] Furthermore, we need to Establish the equation. According to the normalization condition, the sum of all state probabilities is 1, and we have the following formula:

[0112]

[0113] Furthermore, for the stationary distribution analysis, the effective number of service stations is defined as:

[0114]

[0115] The actual number of active service desks is:

[0116]

[0117] Furthermore, according to the stationary distribution expression:

[0118]

[0119] Among them, i and j represent the index variables of the passenger dimension and vehicle dimension in the state space respectively, and the probability distribution of the steady state can be obtained.

[0120] S3: Solve the key performance indicators. For the double-ended single queue parallel multi-server model, it is assumed that passengers and vehicles form independent queues and share When a service station is idle, it will pick one from each of the passenger queue and vehicle queue for matching. Therefore, based on the above-mentioned steady-state distribution , calculate the expectation by summing:

[0121]

[0122] Introducing double-ended queues into coupled queuing theory and combining The classic result of , correcting the additional queue effect caused by double-ended synchronization, can get the average length of the queue:

[0123]

[0124] in, is the average queue length of passengers; is the average queue length of vehicles; It is the number of service desks that can currently work simultaneously in the system.

[0125] Furthermore, according to the basic theorem in queuing theory The formula is defined as follows:

[0126]

[0127] The effective reach rate is defined as:

[0128]

[0129] in and They represent the state of no waiting vehicles and the state of no waiting passengers, respectively, indicating that both the online car-hailing vehicle and the passenger must exist at the same time to trigger the matching service.

[0130] Since passengers and vehicles form independent queues, the arrival process follows a Poisson distribution, and the rates are and , and the service desk , each service desk can handle the task of matching one passenger with one vehicle at the same time, so the average queuing time can be obtained as:

[0131]

[0132] in, is the average waiting time for passengers; is the average queuing time of vehicles. From this indicator, we can know the corresponding queuing time and provide an indicator feedback.

[0133] S4: Quantify the service intensity of both ends to avoid system overload. First, define the service intensity of both ends. In a two-end queuing system, the arrival rates of passengers and vehicles need to be jointly quantified to represent the overall business load. Introduce the two-end service intensity index , which is defined as the product of the ratio of passenger and vehicle arrival rates to service capacity:

[0134]

[0135] According to the expression of the dual-end integrated service intensity index, it is believed that when When , the system is in a light load, the arrival rate at both ends is balanced with the service capacity, and the queue is stable; when , the system enters an overloaded state, and the queue length at at least one end increases infinitely. In this case, if the time step reaches the set threshold, the control strategy needs to be triggered.

[0136] Furthermore, in order to achieve stability conditions, the number of service desks needs to be adjusted dynamically. Matching rate The specific strategies are as follows: First, the number of service desks According to the actual situation and the actual operation logic of the online car-hailing area, the parking spaces and passages in the passenger area will not be fully open when the flow of people is low. This is beneficial to management and reduces management costs. On the other hand, it is helpful for passengers to quickly find the location of the online car-hailing area and improve the service rate. Therefore, based on the above logic, the number of service desks can be capped and optimized in real time. According to the dynamic real-time arrival rate, and , dynamic adjustment Value:

[0137]

[0138] in Defined as a rounding function, this ensures that the number of service desks is an integer. The first term in the formula can guarantee the service intensity. ; The second item can ensure the passenger side load , the third item can ensure the vehicle end load .

[0139] Furthermore, if the number of service desks Due to hardware limitations, if the upper limit is reached and further adjustments cannot be made, the matching algorithm can be optimized to improve Specifically, this method can trigger dynamic capacity expansion by calling or requesting the cloud server cluster on the platform side to limit the access rate of new requests from passengers or vehicles, as shown in the following formula:

[0140]

[0141] Furthermore, in order to fine-tune the control, the system load state is divided into three levels: , maintain the current and , the system only needs to monitor and no optimization measures are needed; when When , we believe that the system has entered the early warning state, and at this time we will perform pre-calculation by dynamically adjusting the k value, prepare for resource expansion, and open a new service desk; when When the system is considered to be overloaded, dynamic capacity expansion is triggered immediately.

[0142] S5: To ensure system stability in dual-source queues, we use Lyapunov stability theory to demonstrate the decay (negative definite drift) of this function and derive the stability conditions for the system. Therefore, this method is effective for analyzing the joint stability of passenger and vehicle queues in dual-source queues. First, based on the previously defined state variables, we have the following queue dynamic equations:

[0143]

[0144] in: Representative Moment The passenger queue length (number of passengers waiting to be matched) is different from that in S3. The values ​​remain consistent; Representative Moment The length of the vehicle queue (the number of vehicles waiting to be matched) is different from that in S3. The values ​​remain consistent; Represents the number of dynamically adjusted service desks; Represents the dynamically adjusted matching rate. The above formula shows that when the matching rate is limited to the smaller value of the queue length, it reflects the coupling of the dual input source queues. When a queue section is empty, the matching rate is 0, avoiding resource waste.

[0145] Furthermore, based on the construction of the Lyapunov function, the dual-input source joint queue energy function is defined as the sum of the squares of the passenger and vehicle queue lengths:

[0146]

[0147] in, Quantify the congestion energy of the system, where a larger value indicates a more severe queue accumulation; is the coupling coefficient, and the control strategy is optimized by gradient descent. Decreasing over time (negative drift), stability conditions can be derived.

[0148] Furthermore, the single-step Lyapunov drift is calculated :

[0149]

[0150] Substitute it into the queue dynamics equation, expand and simplify (ignore high-order small quantities):

[0151]

[0152] in, is the dual input source matching efficiency factor.

[0153] Furthermore, in order to ensure system stability (i.e. ), must meet the following requirements:

[0154]

[0155] Further simplification can yield the stability condition:

[0156]

[0157] By moving the items, we can obtain the service station quantity constraint and service rate compensation constraint:

[0158]

[0159] The compensation constraint is used to set an upper limit on the number of dynamically adjusted enabled service desks and service rates, where: 、 Indicates the upper limit of the compensation constraint for enabling the service desk and the service rate.

[0160] The above formula converts the Lyapunov drift minimization into an explicit control formula for the number of service stations and the matching rate. It can be proved that the queue length is bounded in the expected sense (weak stability) or converges to a steady-state distribution (strong stability). It is applicable to time-varying arrival rates and non-first-come-first-served matching strategies. Figure 5 As shown, the surface exhibits parabolic characteristics. The origin (0,0) corresponds to the system's stable state (the lowest energy point). The color map represents energy intensity, with warmer areas corresponding to high queuing risk. The spiraling downward trajectory indicates the system's asymptotic stability under Lyapunov control. The orange plane divides the state space into a stable region (lower) and a potentially unstable region (upper). When the trajectory crosses the plane and enters the stable region, the system enters a self-equilibrium state.

[0161] S6: To address the oscillation effect in the dynamic regulation of the number of service desks, hysteresis control is used. First, a double-threshold hysteresis zone design is performed to define the regulation threshold interval, i.e., the business intensity. The upper and lower thresholds are: upper limit and lower limit , the expression is:

[0162]

[0163] in, The number of service desks enabled at the last moment; The state retention time is set according to actual needs. When a new service desk is added, set the service desk activation delay and reserve During the preparation time, the number of service desks will be processed according to the previous moment to avoid instantaneous overload; when the closing command is issued, the matched vehicles are allowed to complete the passenger boarding.

[0164] Furthermore, the single adjustment range is limited to 4 per hour to avoid sudden large passenger flows causing system instability. The following constraints are added:

[0165]

[0166] Furthermore, the gradient sensitivity is adjusted. Rate of change When the threshold is exceeded, the hysteresis interval is automatically widened, so the following constraints are added:

[0167]

[0168]

[0169] in, is the sensitivity coefficient, which is calibrated in real time through simulation.

[0170] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A simulation and optimization method for the online car-hailing boarding area at a transportation hub based on the double-ended queuing theory, characterized by: include: Obtain dynamic parameters of ride-hailing pickup areas at transportation hubs, including passenger arrival rate, vehicle arrival rate, service rate, and the number of activated service stations. Based on the passenger arrival rate and vehicle arrival rate, the Markov chain is used to simulate the ride-hailing pick-up area of ​​the transportation hub to obtain a steady-state probability distribution; According to the steady-state probability distribution, the average queue length of vehicles and the average queue length of passengers are calculated; Calculate service intensity based on dynamic parameters, judge service intensity, and adjust service rate and number of activated service desks based on the judgment results; Constrain the adjusted service rate and the number of activated service desks based on the passenger arrival rate and vehicle arrival rate; A threshold judgment is made on the service intensity, and based on the threshold judgment result, a hysteresis control is performed on the number of activated service stations after the constraint, so as to realize the simulation optimization of the online car-hailing boarding area in the transportation hub.

2. The method according to claim 1, characterized in that The steady-state probability distribution is: in, is the distribution probability of each queue length in steady state, represents the passenger arrival rate, represents the arrival rate of online ride-hailing vehicles, represents the service rate, i and j represent the index variables of the passenger dimension and vehicle dimension in the state space respectively, Indicates time The number of passengers waiting to be matched, Indicates time The number of ride-hailing vehicles waiting to be matched.

3. The method according to claim 1, characterized in that The calculation process of the average queue length of vehicles and the average queue length of passengers is: ； in, is the average queue length of passengers; is the average queue length of vehicles; is the number of service desks that can currently work simultaneously in the system, Represents vehicle end load; Represents the passenger side load.

4. The method according to claim 3, characterized in that The calculation process of the vehicle-side load and the passenger-side load is as follows: in Represents vehicle end load; Represents the passenger side load; Represents the number of service desks currently enabled. represents the vehicle arrival rate, represents the passenger arrival rate, Represents service rate.

5. The method according to claim 4, characterized in that The calculation process of the service intensity includes: ； in, Indicates service intensity.

6. The method according to claim 1, characterized in that The process for adjusting service rates and the number of active service desks includes: The service intensity is judged, wherein when the service intensity is higher than a first threshold and lower than a second threshold, the number of enabled service stations is adjusted: ； When the service intensity is higher than the second threshold, the service rate is adjusted: 。 7. The method according to claim 1, characterized in that The process of constraining the adjusted service rate and the number of active service desks includes: 。 8. The method according to claim 1, characterized in that The process of performing hysteresis control on the number of enabled service desks after the constraint includes: A threshold value is determined for the service intensity, and based on the threshold value determination result, the number of activated service stations after the constraint is gradually hysteresis-controlled: in, is the lower limit of service intensity, is the upper limit of server strength, is the state holding time, k(t - ) indicates the number of enabled service desks at the previous moment.

9. The method according to claim 8, characterized in that The hysteresis control of the number of enabled service desks after the constraint also includes: To constrain the number of enabled service desks in hysteresis control: 。 10. The method according to claim 8, characterized in that The upper and lower limits of the service intensity are constrained: in, is the sensitivity coefficient.

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