A performance evaluation method for robotic sorting systems based on regional congestion control

Abstract

This invention relates to a performance evaluation method for robotic sorting systems that considers regional congestion control. This method divides the system's grids into zones, controls the number of robots admitted to each zone, and establishes a queuing network model for the robotic sorting system. This queuing network model is then analyzed to quickly and accurately determine the throughput of a system of a given scale. This proposed method for evaluating robotic sorting system performance based on regional congestion control provides a new theoretical approach and practical tool for evaluating the operational efficiency of complex robotic sorting systems, ensuring that the design of robotic sorting systems meets practical application requirements.

Description

Technical Field

[0001] The present invention belongs to the technical field of logistics equipment control systems, and in particular to a performance evaluation method for a robot sorting system based on regional congestion control. Background Art

[0002] With the rapid development of e-commerce, the volume of parcel sorting operations continues to increase. Efficiently and accurately completing the logistics sorting and delivery of massive quantities of parcels has become a core concern for logistics companies. In recent years, with the rapid development of robotics technology, companies both domestically and internationally have begun to introduce and deploy robotic equipment on a large scale for parcel sorting. Compared to traditional cross-conveyor sorting systems consisting of conveyor lines and sorting machines, mobile robots offer numerous advantages, including accurate sorting, flexible throughput, rapid and easy deployment, low cost, reduced labor intensity, improved warehouse automation, and enhanced system operational efficiency. However, these systems also have some drawbacks. For example, they require expensive robots and complex control software to control numerous robots moving within a small area and avoid system deadlock or excessive congestion. Currently, faced with a large number of mobile robots within their systems, many logistics companies still struggle with congestion control and performance evaluation. Considering congestion control, conducting rapid and accurate performance evaluation during the design phase of robotic sorting systems is a critical step in ensuring successful deployment and efficient operation. Summary of the Invention

[0003] In order to solve the above technical problems, the present invention provides a performance evaluation method for a robot sorting system based on regional congestion control, which can quickly and accurately evaluate the system sorting efficiency and other performance, ensuring that the design of the robot sorting system meets the actual application requirements.

[0004] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0005] A performance evaluation method for a robot sorting system based on regional congestion control includes the following steps:

[0006] Step S1: Establishing a queuing network model of a robot sorting system based on regional congestion control;

[0007] Step S2: Calculate the expected service time and transfer probability of the task at each service node in the queuing network model;

[0008] Step S3: Calculate the throughput of the robot sorting system queuing network model based on the expected service time and the transition probability.

[0009] Furthermore, the step S1 includes a regional congestion control design and a robot sorting system queuing network model module; the regional congestion control divides the regions according to the total number of system slots, requiring that the number of slots in each region is equal and the region shape is the same (for example, , indicating that there are 9 grid openings in the area, with 3 grid openings in each row and column); after the system area division is obtained, regional congestion control is set to achieve regional congestion control by limiting the maximum number of robots (threshold) that can enter each area at the same time;

[0010] Furthermore, the queuing network model of the robot sorting system is established according to the specific process of package sorting operation in the robot sorting system:

[0011] The parcel sorting operation process of the robot sorting system is as follows: ① The robot receives the parcel to be sorted at the loading platform and obtains the target grid and operation path of the parcel by scanning; ② The robot transports the parcel to the area containing its target grid along the operation path planned by the central control system; ③ After arriving at the target area, the robot determines whether it can enter based on the number of loaded robots in the area. If the current number of loaded robots is lower than the admission threshold, the robot enters; otherwise, it needs to wait; ④ After entering the target area, the robot continues to move to the corresponding target grid and places the parcel into the grid. The parcel slides into the lower bag through the chute; ⑤ The robot returns from the current grid to the next loading platform and waits for the next parcel to be sorted.

[0012] The queuing network model of the robot sorting system is a semi-open semi-closed queuing network model (SOQN): ① The package is placed with the robot in the first The matching model of the loading station is a synchronization station ;② The process of placing the package from the loading platform to the robot tray is modeled as a delayed process, with a service rate of Unlimited First Service Node ③ The process of the robot moving from the loading platform to the boundary of the target area is modeled as a delay process, with a service rate of Unlimited Second Service Nodes ④ The process of the robot entering the target area, moving to the target grid and dropping the package is modeled as The third server node of the server (where each server has a homogeneous service rate ), which means that the maximum number of payload robots that can move simultaneously in this area is ⑤ The movement process of the robot returning from the grid to the next synchronization station after completing the package delivery is modeled as a service rate of Unlimited Fourth Service Node .

[0013] The queuing network model of the robot sorting system is further elaborated as follows: Synchronous station The queue of parcels waiting to be sorted that arrives at the station , and the queue of robots waiting to be served arriving at the station Composition, where the package queue capacity is limited, set After completing the package delivery, the idle robot will go to and join the queue .address The parcel arrival robot sorting system follows a Poisson arrival process with an arrival rate of , and enter randomly One of the synchronization stations. When there is at least one robot in The first package in the queue will be assigned to the first robot in the queue; otherwise, the package must wait for an idle robot to arrive. Once the robot is matched with the package at the synchronization station, the robot will visit the service node in turn. 、 、 、 .

[0014] Furthermore, in step S2, the specific method for calculating the expected service time and access rate of each service node in the queuing network model is as follows.

[0015] Assumption 1. All lanes in the aisles and cross-aisles of the robotic sorting system are unidirectional, and each aisle and cross-aisle contains two lanes running in opposite directions. Robots can move in any direction within the aisle by following the correct lane.

[0016] Assumption 2. Each loading platform faces a channel or cross channel. The east and west loading platforms face the right and left cross channels, respectively; the north and south loading platforms face the upward and downward channels, respectively.

[0017] Assumption 3. The time it takes to place a package on the robot tray at the loading station is constant. .

[0018] Assumption 4. The delivery time of the package at the grid is constant. .

[0019] Assumption 5. Address The parcel arrival robot sorting system follows a Poisson arrival process with an arrival rate of , and enter randomly One of the synchronization stations.

[0020] Assumption 6. There are multiple one-way lanes between adjacent areas, and the congestion of robots in lanes outside the area is negligible.

[0021] Assumption 7. The robot moves at a constant speed. .

[0022] The first service node Expected service time .

[0023] The second service node The expected service time depends on the travel time of the robot from the loading platform to the region boundary, which is expressed as the travel time from the loading platform to the region center minus the travel time from the region boundary to the region center. , where Indicates the total number of loading stations. Indicates the total number of regions, Indicates the area the robot is heading to The probability of Indicates that from The first platform to The Manhattan distance of the regional center, Indicates the distance from the region boundary to the region center.

[0024] The third service node The expected service time includes the travel time of the robot from the area boundary to the corresponding grid and the time to deliver the package. Due to the homogeneity assumption, , where Indicates the number of cells per row in the area. Represents the number of slots in each column in the area, Indicates that the robot goes to the Rank The probability of the column mouth, From the regional center to the Rank Manhattan distance from Legge.

[0025] The fourth service node The expected service time represents the expected travel time for the robot to return to the loading platform after completing the package delivery. This method uses the continuous travel time from the regional center to the next loading platform to approximate. , where Indicates return to the loading platform probability.

[0026] The transfer probability of each service node in the queuing network model of the robot sorting system represents the probability that the task will be transferred to the next node after the task of a node in the queuing network model is completed. According to the queuing model in step S1, after the robot matches the package, it will visit the service nodes in turn. 、 、 、 , with probabilities of 1, 1, , 1, and Return to loading platform Probability Depends on the allocation relationship between package addresses and slots in the system, , where Is a binary value, if the address Assigned to area Takes 1, otherwise 0. Probability Depends on the scheduling strategy of idle robots in the system to return to the loading platform.

[0027] Furthermore, the throughput calculation method of the queuing network model of the robot sorting system in step S3 includes compacting the initial model and solving the throughput of the compacted queuing network model;

[0028] The compactification of the initial model is an approximation method adopted because there is no analytical expression for the system throughput caused by multiple synchronization stations in the model. First, a closed queueing network model (CQN) is formed by eliminating the synchronization stations in the SOQN. Then, all service nodes in the CQN are integrated into an equivalent composite service node with a throughput of ,in represents the number of robots in CQN, Indicates that when there is robot-hour throughput, Indicates the total number of robots in the system. When the number of robots is changed in CQN , and is obtained using the convolution algorithm; when When , the service rate of the empty CQN is zero, that is, Then, the composite service node is used to approximate the SOQN that does not include The subnetwork of synchronization stations is constructed and substituted into the original SOQN model. Therefore, SQON is reconstructed into a compactified SOQN.

[0029] The compactified queuing network model includes Synchronization stations are configured. The present invention adopts a continuous-time Markov chain (CTMC) to represent the state transition rate of the compactified SOQN, thereby obtaining the generating matrix of the CTMC and solving the steady-state probability of each state in the compactified queuing network model. Finally, based on the steady-state probability of the state, the system throughput, the average queuing time of robots at the loading station, the average queuing time of packages at the loading station and other key system performance indicators are calculated.

[0030] Furthermore, the compactified SOQN state space is defined as , in Indicates the system status, represented by -dimensional vector representation, the first The value of the element represents the difference between the number of waiting packages at the i-th loading station and the number of waiting robots. and the total number of robots in the system It can be seen that and , and define the state space. The state transition rate: First, define Indicates the The value of elements is 1, and the rest are 0 -dimensional vector. Then, when Current Status Transfer to state The rate is , and the current state Transfer to state The rate is .

[0031] The generator matrix of the CTMC It can be calculated based on the state transition rate. Definition represents the steady-state probability of all states, then the steady-state probability of each state can be solved by get.

[0032] The system throughput is calculated by the formula Available.

[0033] The beneficial effects of the present invention are:

[0034] The present invention divides the area based on the system grid layout and controls the number of robots that enter the system at the same time, which can effectively control regional congestion. The method is simple in principle and easy to implement.

[0035] This method constructs a queuing network model based on the system's operational flow, constructing an analytical model that aligns with actual system operations and enables rapid calculation of system throughput. Simulation experiments have verified that the throughput values ​​calculated by this model are consistent with experimental results. This also demonstrates that during the design phase of a robotic sorting system, the method presented in this paper can rapidly assess system performance, ensuring successful deployment and efficient operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of the layout and area of ​​the robot sorting system in the method of the present invention;

[0037] Figure 2 This is a queuing network model diagram of the robot sorting system in the method of the present invention;

[0038] Figure 3 is a diagram of a compact queuing network model in the method of the present invention;

[0039] Figure 4 is a flow chart of a calculation method for performance evaluation of a robot sorting system based on regional congestion control according to the present invention;

[0040] Figure 5 It is an implementation effect diagram based on the method of the present invention. DETAILED DESCRIPTION

[0041] The technical solution of the present invention is described clearly and completely below in conjunction with the accompanying drawings and embodiments. Obviously, the embodiments described are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments in the present invention, for ordinary technicians in the field, other different forms of changes or modifications can be made on the basis of the above description. It is not necessary and impossible to list all the implementation methods here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the claims of the present invention.

[0042] This embodiment provides a performance evaluation method for a robotic sorting system based on regional congestion control. The evaluation method for throughput analysis of the robotic sorting system introduces a regional control strategy, characterizes a general queuing network model of the system operation, and focuses on the analysis of the queuing network model.

[0043] According to an embodiment of the present invention, see Figure 1 and Figure 4 The robotic sorting system includes a loading platform, robots, slots, aisles, and transverse aisles. The slots are grouped into zones, and regional congestion control is achieved by limiting the number of load-carrying robots that can enter the zones simultaneously. The robotic sorting system performance evaluation method includes the following steps: Step S1: Establishing a queuing network model for the robotic sorting system based on regional congestion control; Step S2: Calculating the expected service time and transition probability of tasks at each service node in the queuing network model; Step S3: Calculating the throughput of the robotic sorting system queuing network model based on the expected service time and transition probability.

[0044] According to an embodiment of the present invention, the process of robot sorting packages in the robot sorting system includes: ① The robot receives the package to be sorted at the loading platform, and obtains the target grid and running path of the package by scanning; ② The robot transports the package to the area containing its target grid along the running path planned by the central control system; ③ After arriving at the target area, it determines whether it can enter based on the number of loaded robots in the area. If the current number of loaded robots is lower than the entry threshold, it enters, otherwise it needs to wait; ④ After entering the target area, the robot continues to move to the corresponding target grid and puts the package into the grid. The package slides into the lower bag through the chute; ⑤ The robot returns from the current grid to the next loading platform, waiting for the next package to be sorted.

[0045] According to an embodiment of the present invention, see Figure 2 The robot sorting system queue network model (SOQN) includes: ① Modeling the matching of the package and the robot at the i-th loading station as a synchronization station ;② The process of placing the package from the loading platform to the robot tray is modeled as a delayed process, with a service rate of Unlimited First Service Node ③ The process of the robot moving from the loading platform to the boundary of the target area is modeled as a delay process, with a service rate of Unlimited Second Service Nodes ④ The process of the robot entering the target area, moving to the target grid and dropping the package is modeled as The third server node of the server (where each server has a homogeneous service rate ), which means that the maximum number of payload robots that can move simultaneously in this area is ⑤ The movement process of the robot returning from the grid to the next synchronization station after completing the package delivery is modeled as a service rate of Unlimited Fourth Service Node .

[0046] The SOQN is further elaborated as follows: Synchronous Station The queue of parcels waiting to be sorted that arrive at the station from ① , and ② the queue of robots waiting to be served arriving at the station Composition, where the package queue capacity is limited, set After completing the package delivery, the idle robot will go to and join the queue .address The parcel arrival robot sorting system follows a Poisson arrival process with an arrival rate of , and enter randomly One of the synchronization stations. When there is at least one robot in The first package in the queue will be assigned to the first robot in the queue; otherwise, the package must wait for an idle robot to arrive. Once the robot completes the matching with the package at the synchronization station, the robot will visit the first to fourth service nodes in turn. 、 、 、 .

[0047] According to an embodiment of the present invention, see Figure 5 , a top view of a small-scale robotic sorting system, illustrating the expected service time and transition probability of each service node in the queuing network model of the present invention, as follows:

[0048] described Figure 5 The robot sorting system consists of 2 loading platforms and 4 slots, which are divided into 2 areas. There are 3 channels and 3 cross channels. The channel width is 1.2 m. The slots are square with a side length of 0.6 m. There are 5 robots in the system. , responsible for sorting parcels from 3 addresses. Among them, the capacity of the Taichung parcel queue , robot control threshold of the region .

[0049] Assumption 1. All lanes in the aisles and cross-aisles of the robotic sorting system are unidirectional, and each aisle and cross-aisle contains two lanes running in opposite directions. Robots can move in any direction within the aisle by following the correct lane.

[0050] Assumption 2. Each loading platform faces a channel or cross channel. The east and west loading platforms face the right and left cross channels, respectively; the north and south loading platforms face the upward and downward channels, respectively.

[0051] Assumption 3. The time it takes to place a package on the robot tray at the loading station is constant. 1 s.

[0052] Assumption 4. The delivery time of the package at the grid is constant. s.

[0053] Assumption 5. Address The parcel arrival robot sorting system follows a Poisson arrival process, and the arrival rates are pcs / s, and enter randomly One of the synchronization stations.

[0054] Assumption 6. There are multiple one-way lanes between adjacent areas, and the congestion of robots in lanes outside the area is negligible.

[0055] Assumption 7. The robot moves at a constant speed. m / s.

[0056] The first service node Expected service time ;

[0057] The second service node The expected service time depends on the travel time of the robot from the loading platform to the region boundary. This method uses the continuous travel time to approximate, and adjusts the travel time from the region boundary to the region center based on the travel time from the loading platform to the region center. , where the total number of units loaded is , total number of regions , represents the probability that the robot goes to area j, represents the Manhattan distance from the i-th platform to the center of region j, Indicates the distance from the region boundary to the region center.

[0058] The third service node The expected service time includes the travel time of the robot from the area boundary to the corresponding grid and the time to deliver the package. Due to the homogeneity assumption, , where the number of cells per row in the region is , the number of ports in each column in the area , Indicates that the robot goes to the Rank The probability of the column mouth, From the regional center to the Rank Manhattan distance from Legge.

[0059] The fourth service node The expected service time represents the expected travel time for the robot to return to the loading platform after completing the package delivery. This method uses the continuous travel time from the regional center to the next loading platform to approximate. , where Indicates the probability of returning the i-th item station.

[0060] The transfer probability of each service node in the queuing network model of the robot sorting system represents the probability that the task will be transferred to the next node after the task of a node in the queuing network model is completed. According to the queuing model in step S1, after the robot matches the package, it will visit the service nodes in turn. 、 、 、 , with probabilities of 1, 1, , 1, and Returns the i-th item on the platform. Probability Depends on the allocation relationship between package addresses and slots in the system, , where Is a binary value, if the address Assigned to area Take 1, otherwise it is 0. Randomly go to area 1 or area 2. Probability It depends on the scheduling strategy of the idle robots in the system to return to the loading platform. In this embodiment, a random strategy is adopted. .

[0061] According to an embodiment of the present invention, see Figure 3 ,The throughput solution of the robotic sorting system includes the ,compactness of the initial model and the throughput solution of the ,compactness model;

[0062] The compactification of the initial model is an approximation method adopted because there is no analytical expression for the system throughput caused by multiple synchronization stations in the model. First, a closed queueing network model (CQN) is formed by eliminating the synchronization stations in the SOQN. Then, all service nodes in the CQN are integrated into an equivalent composite service node with a throughput of ,in represents the number of robots in CQN, Indicates the total number of robots in the system. When the number of robots is changed in CQN , and is obtained using the convolution algorithm; when When , the service rate of the empty CQN is zero, that is, Then, the composite service node is used to approximate the SOQN that does not include The subnetwork of synchronization stations is constructed and substituted into the original SOQN model. Therefore, SQON is reconstructed into a compactified SOQN.

[0063] The compact queuing network model has Synchronization stations are configured. The present invention adopts a continuous-time Markov chain (CTMC) to represent the state transition rate of the compactified SOQN, thereby obtaining the generating matrix of the CTMC and solving the steady-state probability of each state in the compactified queuing network model. Finally, based on the steady-state probability of the state, the system throughput, the average queuing time of robots at the loading station, the average queuing time of packages at the loading station and other key system performance indicators are calculated.

[0064] Furthermore, the compactified SOQN state space is defined as , in Indicates the system status, represented by -dimensional vector representation, the first The value of the element represents the difference between the number of waiting packages at the i-th loading station and the number of waiting robots. and the total number of robots in the system It can be seen that and , and define the state space, we know that the state space The specific status is shown in Table 1 below:

[0065] Table 1

[0066]

[0067] The state transition rate: First, define Indicates the The value of elements is 1, and the rest are 0 -dimensional vector. Then, when Current Status Transfer to state The rate is , and the current state Transfer to state The rate is The state transition probability is shown in Table 2. Based on Figure 3 (2) The compactified queueing network represented by the state transition has two types: (1) the package arrives at the system; (2) the robot completes the package sorting and joins the synchronization station. Among them, based on the number of packages waiting at the synchronization station type 1, it can be subdivided into four specific cases: 1a: the number of packages waiting at the first synchronization station and the second synchronization station has reached their respective maximum capacity At this time, even if the package arrives, it cannot enter the system, and the next state is still the current state , the transfer rate is ; 1b: The number of packages waiting at the first synchronization station has reached the maximum capacity The number of packages waiting at the second synchronization station is less than the maximum capacity At this time, if the package arrives at the first synchronization station, it cannot enter the system, and the next state is still the current state. , the transfer rate is At this time, if the package arrives at the second synchronization station, it will be added to the second synchronization station package queue. The next state is , the transfer rate is ; 1c: The number of waiting packages at the first synchronization station is less than the maximum capacity The number of packages waiting at the second synchronization station has reached the maximum capacity At this time, if the package arrives at the first synchronization station and joins the first synchronization station package queue, the transfer rate is , the next state is At this time, if the package arrives at the second synchronization station, it cannot enter the system and the next state is still the current state. , the transfer rate is 1d: The number of waiting packages at the first and second synchronization stations is less than their respective maximum capacity. At this time, if the package arrives at the first synchronization station and joins the first synchronization station package queue, the transfer rate is , the next state is At this time, if the package arrives at the second synchronization station, it will be added to the second synchronization station package queue. The next state is , the transfer rate is When the type is 2, it means that the robot has completed the parcel sorting task and joined the synchronization station. , indicating that the number of busy robots in the system is greater than 0, Indicates the rate at which the system completes parcel sorting, represents the probability that the robot will join the ith synchronization station after completing the parcel sorting task, so from the current state Transfer to state The rate is .

[0068] Table 2

[0069]

[0070] The generator matrix of the CTMC Can be calculated based on the state transition rate.

[0071] definition represents the steady-state probability of all states, then the steady-state probability of each state can be solved by get.

[0072] The system throughput is calculated by the formula Therefore, in this embodiment, the throughput of the robotic sorting system is an average of 1706.4 packages that can be sorted per hour.

[0073] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A performance evaluation method for a robot sorting system based on regional congestion control, characterized in that: Follow these steps to achieve this: Step S1: Establishing a queuing network model of a robot sorting system based on regional congestion control; Step S2: Calculate the expected service time and transfer probability of tasks at each service node in the queuing network model of the robot sorting system; Step S3: Calculating the throughput of the robot sorting system queuing network model based on the expected service time and the transition probability; wherein, step S2 includes: Step S21: The process of placing the package from the loading platform onto the robot tray is modeled as a delay process, with a service rate of First service node Indicates that the first service node Expected service time , Indicates the time when the package is placed on the robot tray at the loading station; The process of the robot moving from the loading platform to the boundary of the target area is modeled as a delay process, with a service rate of Second service node To indicate that the second service node Expected service time Depends on the travel time of the robot from the loading platform to the area boundary, that is, the travel time from the loading platform to the area center minus the travel time from the area boundary to the area center: ， In the formula Indicates the total number of loading stations. Indicates the total number of regions, Indicates the robot goes to The probability of a region, Indicates that from The first platform to The Manhattan distance of the regional center, represents the distance from the region boundary to the region center; The process of the robot entering the target area, moving to the target grid and dropping the package is modeled as The third service node of the server , the third service node Expected service time This includes the travel time of the robot from the area boundary to the corresponding grid and the time to deliver the package: , In the formula Indicates the number of cells per row in the area. Indicates the number of slots in each column in the area, Indicates that the robot goes to the Rank The probability of the column mouth, From the regional center to the Rank Manhattan distance of the column mouth, Indicates the delivery time of the package at the grid; The movement process of the robot returning from the grid to the next synchronization station after the package delivery is modeled as a service rate of Fourth service node , the fourth service node Expected service time Indicates the expected travel time for the robot to return to the loading platform after completing the package delivery: ， In the formula Indicates return The probability of loading a piece of equipment; Step S22: The transfer probability of the first to fourth service nodes in the queuing network model of the robot sorting system represents the probability that a task will be transferred to the next service node after a service node completes the task in the queuing network model. According to the queuing model in step S12, after the robot matches the package, it will visit the first to fourth service nodes in sequence. 、 、 、 , with probabilities of 1, 1, , 1, and with probability Return to Loading stations, among which, ， In the formula It is a binary value, indicating that if the address Assigned to the jth region takes 1, otherwise it is 0, the probability Depends on the scheduling strategy of idle robots returning to the loading platform in the system, is the arrival rate, indicating that the address is The process of packages arriving at the robotic sorting system follows a Poisson arrival process; The step S3 comprises: Step S31: Model the matching of the package and the robot at the i-th loading station as a synchronization station , a closed queuing network model is formed by eliminating the synchronization station in the robot sorting system queuing network model, and then all service nodes in the closed queuing network model are integrated into an equivalent composite service node with a throughput rate of ,in represents the number of robots in the closed queuing network model, Indicates that when the number of robots in the closed queuing network model is The throughput rate, Represents the total number of robots in the system, and then uses composite service nodes to approximate the robot sorting system queuing network model does not contain The sub-network of the synchronization station is substituted into the original robot sorting system queue network model and reconstructed into a compactified queue network model; Step S32: The specific method for calculating the throughput of the compacted queuing network model is as follows: Synchronous stations are constructed, and a continuous-time Markov chain is used to represent the state transition rate of the compactified queuing network model. The generator matrix of the continuous-time Markov chain is obtained, and the steady-state probability of each state in the compactified queuing network model is solved. Based on the steady-state probability of each state, the throughput of the system, the average queuing time of robots at the loading station, and the average queuing time of packages at the loading station are calculated.

2. A method for evaluating the performance of a robot sorting system based on regional congestion control according to claim 1, characterized in that: The step S1 comprises: Step S11: Construct a regional congestion control strategy, divide the regions according to the total number of system slots, ensure that the number of slots in each region is equal and the region shape is the same, and implement regional congestion control by limiting the maximum number of robots that can enter each region at the same time; Step S12: A queuing network model of the robot sorting system is established according to the package sorting operation process of the robot sorting system. The package sorting operation process of the robot sorting system is as follows: the robot receives the package to be sorted at the loading platform, scans and obtains the target grid and operation path of the package; the robot transports the package to the target area containing its target grid along the operation path planned by the central control system; after arriving at the target area, the robot determines whether it can enter the target area based on the number of loaded robots in the target area. If the current number of loaded robots is lower than the maximum number of robots, the robot enters; otherwise, it needs to wait; after entering the target area, the robot continues to move to the corresponding target grid and puts the package into the grid; the robot returns from the target grid to the next loading platform, waiting for the next package to be sorted.

Images