Robot Warehouse Cycle Time Estimation Method Based on Dynamic Priority Queuing Network

Abstract

The present invention discloses a method for estimating the cycle time of a robotic warehouse based on a dynamic priority queuing network. The steps include: S1. Establish a coordinate system for the robotic warehouse system; S2. Calculate the travel time of the autonomous transfer robot from the stopping point to the target shelf; S3. Calculate the travel time of the autonomous transfer robot from the target shelf to the picking wall; S4. Calculate the picking time of the autonomous transfer robot; S5. Calculate the throughput rate of the queuing network and the expected waiting time for the autonomous transfer robot to transport the container to the front of the picking wall for unloading based on the approximate average value estimation method; S6. Calculate the total time for the automatic transfer robot to serve one order; S7. Synchronous steady-state analysis; S8. Analysis of the expected waiting time of the dynamic priority queue; S9. Calculate the cycle time of an order of category k. Through the above steps, the present invention can be effectively used to evaluate the cycle time of different types of orders in the robotic warehouse system.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic warehouse systems, and particularly to a method for estimating the cycle time of a robotic warehouse based on a dynamic priority queuing network. Background Art

[0002] In a robotic warehouse system, orders have different delivery time requirements. Some robotic warehouse systems offer multiple delivery options, each with a promised delivery time and corresponding price to meet the needs of different customers.

[0003] Due to the existence of different customer categories, the service system usually adopts the priority principle. Compared with static priorities, dynamic priorities can meet different types of orders within the promised cycle time, highlighting the importance of service fairness.

[0004] It should be noted that in a robotic warehouse system with a dynamic priority policy, it is particularly important to evaluate the cycle time of different types of orders. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for estimating the cycle time of a robotic warehouse based on a dynamic priority queuing network, which can effectively be used to evaluate the cycle time of different types of orders in a robotic warehouse system.

[0006] To achieve the above object, the present invention is implemented through the following technical solutions.

[0007] A method for estimating the cycle time of a robotic warehouse based on a dynamic priority queuing network, which is applied to a robotic warehouse system. The robotic warehouse system includes a picking wall, shelves arranged in rows, and autonomous mobile robots for picking and transporting containers.

[0008] The autonomous mobile robot includes a mobile platform, a lift installed on the mobile platform, and a picking manipulator installed at the driving end of the lift.

[0009] The method for estimating the cycle time of a robotic warehouse based on a dynamic priority queuing network includes the following steps, specifically:

[0010] S1. Establish a coordinate system for the robotic warehouse system. The coordinates of the stop point of the autonomous mobile robot are (x dp , y dp ), and the coordinates of the target shelf are (x tr , y tr ). All shelf positions are represented by a coordinate set C, specifically:

[0011]

[0012] where n ω = 1, 2, … N ω , n l = 1, 2, …, N l , n ωu = 1, 2, n lu = 1, 2, … 5, n ω represents the position of the n-th column shelf in the robotic warehouse system, N ω represents the number of columns of shelves in the robotic warehouse system, n ω represents the position of the n-th row shelf in the robotic warehouse system, N l represents the number of rows of shelves in the robotic warehouse system, (n l , n l ) is the relative coordinate of a storage position in the shelf, S ωu , n lu ) is the relative coordinate of a storage position in the shelf, S a is the width of the longitudinal lane in the robotic warehouse system, S c represents the width of the transverse lane in the robotic warehouse system, W u represents the width of the storage position on the shelf in the robotic warehouse system, L u represents the length of the storage position on the shelf in the robotic warehouse system, W r represents the width of the shelf in the robotic warehouse system, L r represents the length of the shelf in the robotic warehouse system;

[0013] Since the autonomous handling robot only passes in front of the picking wall, the width of the picking wall is ignored, that is, the coordinates of the picking wall are

[0014] S2. Calculate the travel time T of the autonomous handling robot from the stop point to the target shelf dp,tr , v r is the travel speed of the autonomous handling robot;

[0015] The first moment of the travel time T of the autonomous handling robot from the stop point to the target shelf dp,tr is:

[0016]

[0017] The second moment of the travel time T of the autonomous handling robot from the stop point to the target shelf dp,tr is:

[0018]

[0019] S3. Calculate the travel time T of the autonomous handling robot from the target shelf to the picking wall tr,pwThe first moment of

[0020]

[0021] Calculate the travel time T of the autonomous mobile robot from the target shelf to the picking wall tr,pw The second moment of

[0022]

[0023] Among them, the travel time T of the autonomous mobile robot from the target shelf to the picking wall tr,pw is equal to the travel time T of the autonomous mobile robot from the picking wall to the target shelf pw,tr ;

[0024] S4. Calculate the picking time of the autonomous mobile robot:

[0025] The picking time t lr represents the time for the autonomous mobile robot to load or unload the container on the target shelf. The picking time t lp represents the time for the autonomous mobile robot to load or unload the container on the picking wall;

[0026] The lifting speed of the elevator of the autonomous mobile robot is represented by v l ; when the picking manipulator of the autonomous mobile robot reaches the target height, the lateral clamping time of the picking manipulator is ignored;

[0027] t lr The first moment of

[0028] t lr The second moment of

[0029] t lp The first moment of

[0030] t lp The second moment of

[0031] Among them, H r represents the height of the shelf, and H p represents the height of the picking wall;

[0032] S5. Calculate and determine TH(N) and W based on the approximate average value estimation method bp , where TH(N) represents the throughput of the queuing network, and W bp represents the expected waiting time for the autonomous mobile robot to transport the container to wait for unloading in front of the picking wall;

[0033] Dynamic priority is considered when the order is in the external order queue, and the order transportation process follows the first-come, first-served principle, that is, the throughput THC(N) of the semi-open queuing network representing the order transportation process and the expected waiting time W for unloading in front of the picking wall bp are both independent of the order category. Therefore, orders of different categories are regarded as orders of the same category, and the original multi-category semi-open queuing network is transformed into a single-category semi-open queuing network to evaluate THC(N) and W bp ;

[0034] Combined with THC(N) and based on the approximate average value estimation method, determine the network throughput THC(n) when the number n of automatic guided vehicles changes from 1 to N. N represents the number of automatic guided vehicles in the robot warehouse system, and n = 1, 2,... N;

[0035] S6. Calculate the total time T for an automatic guided vehicle to serve an order trans :

[0036] T trans = T dp,tr + t lr + T tr,pw + W bp + t lp ;

[0037] S7. Synchronous steady-state analysis:

[0038] Use the continuous-time Markov chain model of the semi-open queuing network to calculate the steady state of the synchronous station. In the continuous-time Markov chain model, use the unary variable z to define the state space variable, where z = i - j, i represents the number of orders waiting in the order queue, and j represents the number of available vehicles in the automatic guided vehicle queue; i and j cannot both exceed 0, that is, if i > 0, then j = 0; vice versa, if j > 0, then i = 0;

[0039] The total number of automatic guided vehicles in the entire robot warehouse system is N. When the value of the state space variable is -N, it means that N vehicles are available, and when i > 0, it means that there are waiting orders in the order queue and all automatic guided vehicles are busy;

[0040] The total arrival rate of the network is λ = λ1 + λ2 +... + λ K , and the system transfers from one state to another at a rate of λ; when i ≤ N, the system transfers from state X(-N + i) to state X(-N + i - 1) at a rate of THC(i); when i > N, since the maximum number of vehicles is N, the transfer from state X(i) to X(i - 1) occurs at a rate of THC(N);

[0041] π zDenote the steady-state probability of state z in a continuous-time Markov chain. Then, the steady-state probability of any state can be calculated, and the steady-state probabilities π -N 、π0 and π z are respectively:

[0042]

[0043] S8. Analysis of the expected waiting time of the dynamic priority queue:

[0044] Due to different cumulative priority rates, the expected waiting times of different categories of orders are not equal. This means that orders with a higher cumulative priority rate will have a shorter waiting time than orders with a lower cumulative priority rate;

[0045] Orders of category k accumulate priority at a rate of b k starting from the arrival time, where b1 ≥ b2 ≥ … ≥ b K ≥ 0, and K is the total number of order categories; in the order queue of the queuing network, the expected average waiting time of orders of category k in the external order queue

[0046]

[0047] where ρ = λ / THC(N), ρ i = λ i / THC(N), W0 is the average remaining service time of the orders in service, and W0 = 1 / THC(N); M i is the expected waiting time of orders of category i;

[0048] S9. Calculate the cycle time of orders of category k

[0049]

[0050] where the method for estimating the cycle time of the robot warehouse based on the dynamic priority queuing network further includes:

[0051] S10. Calculate the flow time T of the order on the picking wall p and the total cycle time THT of orders of category k k :

[0052]

[0053] where M represents the total number of pickers at the picking wall, and μ p represents the picking service rate of the pickers.

[0054] Among them, the method for estimating the cycle time of a robot warehouse based on a dynamic priority queuing network further includes:

[0055] S11. Calculate the utilization rate ρ of the autonomous transfer robot N , where the utilization rate ρ of the autonomous transfer robot N is the ratio of the order throughput rate to the robot production capacity, and the robot production capacity refers to the maximum number of items that the autonomous transfer robot can transport per unit time;

[0056] The robot production capacity C r = N / (T trans + t lp + T pw,tr + t lr ), the throughput rate of the order is TH(N), that is, the utilization rate of the autonomous transfer robot

[0057] Among them, in the robot warehouse system, both the longitudinal lane and the transverse lane have one-way lanes in two opposite directions, and the shortest path between the starting point and the ending point on the driving path of the autonomous transfer robot is equal to the Manhattan distance.

[0058] Among them, when the autonomous transfer robot transports the cargo box, each autonomous transfer robot can only transport one cargo box at a time.

[0059] Compared with the prior art, the beneficial effects of the present invention are as follows: The method for estimating the cycle time of a robot warehouse based on a dynamic priority queuing network of the present invention is applied to a robot warehouse system, and the robot warehouse system includes a picking wall, shelves arranged in rows, and autonomous transfer robots for picking and transporting cargo boxes; the autonomous transfer robot includes a mobile platform, a lift, and a picking manipulator; the method for estimating the cycle time of a robot warehouse based on a dynamic priority queuing network includes the following steps: S1. Establish a coordinate system for the robot warehouse system; S2. Calculate the driving time of the autonomous transfer robot from the stopping point to the target shelf; S3. Calculate the driving time of the autonomous transfer robot from the target shelf to the picking wall; S4. Calculate the picking time of the autonomous transfer robot; S5. Calculate and determine TH(N) and W bp , where TH(N) represents the throughput rate of the queuing network, and W bp represents the expected waiting time for the autonomous transfer robot to transport the cargo box to the front of the picking wall and wait for unloading; S6. Calculate the total time for the automatic transfer robot to serve one order; S7. Synchronous steady-state analysis; S8. Analysis of the expected waiting time of the dynamic priority queue; S9. Calculate the cycle time of the order of category k. Through the above steps, the method for estimating the cycle time of a robot warehouse based on a dynamic priority queuing network of the present invention can be effectively used to evaluate the cycle time of different types of orders in the robot warehouse system. Description of the Drawings

[0060] The present invention will be described below with reference to the accompanying drawings, but the embodiments in the drawings do not constitute a limitation to the present invention.

[0061] Figure 1 It is a layout schematic diagram of the robotic warehouse system of the invention.

[0062] Figure 2 It is a partial schematic diagram of the robotic warehouse system of the invention.

[0063] Figure 3 It is a schematic diagram of calculating the steady-state probability of the synchronization station by the Markov chain model of the present invention.

[0064] Figure 4 It is a structural schematic diagram of the autonomous transport robot of the present invention. Detailed implementation manners

[0065] The present invention will be described in detail below in conjunction with specific embodiments.

[0066] Embodiment 1, a method for estimating the cycle time of a robotic warehouse based on a dynamic priority queuing network. The method for estimating the cycle time of a robotic warehouse based on a dynamic priority queuing network is applied to a robotic warehouse system, as Figure 1 and Figure 2 shown. The robotic warehouse system includes a picking wall, shelves arranged in rows, and autonomous transport robots for picking and transporting containers.

[0067] Specifically, as Figure 4 shown, the autonomous transport robot includes a mobile platform, a lift installed on the mobile platform, and a picking manipulator installed on the driving end of the lift.

[0068] It should be noted that the method for estimating the cycle time of a robotic warehouse based on a dynamic priority queuing network in this Embodiment 1 includes the following steps, specifically:

[0069] S1. Establish a coordinate system for the robotic warehouse system. The coordinates of the stop point of the autonomous transport robot are (x dp , y dp ), and the coordinates of the target shelf are (x tr , y tr ). All shelf positions are represented by a coordinate set C, specifically:

[0070]

[0071] wherein, n ω = 1, 2, … N ω , n l = 1, 2, …, N l , n ωu= 1, 2, …, n lu = 1, 2, …, 5, n ω represents the position of the nth column shelf in the robotic warehouse system, and N ω represents the number of columns of the shelves in the robotic warehouse system, and n ω represents the position of the nth row shelf in the robotic warehouse system, and N l represents the position of the nth row shelf in the robotic warehouse system l and N l represents the number of rows of the shelves in the robotic warehouse system, (n ωu , n lu ) is the relative coordinate of a storage position in the shelf, and S a is the width of the longitudinal lane in the robotic warehouse system, and S c represents the width of the transverse lane in the robotic warehouse system, and W u represents the width of the storage position on the shelf in the robotic warehouse system, and L u represents the length of the storage position on the shelf in the robotic warehouse system, and W r represents the width of the shelf in the robotic warehouse system, and L r represents the length of the shelf in the robotic warehouse system;

[0072] Since the autonomous handling robot only passes in front of the picking wall, the width of the picking wall is ignored, that is, the coordinates of the picking wall are

[0073] S2. Calculate the travel time T of the autonomous handling robot from the stop point to the target shelf dp,tr , v r is the travel speed of the autonomous handling robot;

[0074] The first moment of the travel time T of the autonomous handling robot from the stop point to the target shelf dp,tr is:

[0075]

[0076] The second moment of the travel time T of the autonomous handling robot from the stop point to the target shelf dp,tr is:

[0077]

[0078] S3. Calculate the travel time T of the autonomous handling robot from the target shelf to the picking wall tr,pw The first moment of which is:

[0079]

[0080] Calculate the travel time T of the autonomous handling robot from the target shelf to the picking wall tr,pwThe second moment of is:

[0081]

[0082] Among them, the travel time T of the autonomous transfer robot from the target shelf to the picking wall tr,pw is equal to the travel time T of the autonomous transfer robot from the picking wall to the target shelf pw,tr ;

[0083] S4. Calculate the picking time of the autonomous transfer robot:

[0084] The picking time t lr represents the time for the autonomous transfer robot to load the container from the target shelf or unload the container onto the target shelf. The picking time t lp represents the time for the autonomous transfer robot to load the container from the picking wall or unload the container onto the picking wall;

[0085] The lifting speed of the elevator of the autonomous transfer robot is represented by v l ; when the picking manipulator of the autonomous transfer robot reaches the target height, the lateral clamping time of the picking manipulator is negligible;

[0086] t lr The first moment of is:

[0087] t lr The second moment of is:

[0088] t lp The first moment of is:

[0089] t lp The second moment of is:

[0090] Among them, H r represents the height of the shelf, and H p represents the height of the picking wall;

[0091] S5. Calculate and determine TH(N) and W based on the approximate average value estimation method bp , where TH(N) represents the throughput of the queuing network, and W bp represents the expected waiting time for the autonomous transfer robot to transport the container to the front of the picking wall and wait for unloading;

[0092] When the order is in the external order queue, dynamic priority is considered, and the order transportation process follows the first-come-first-served principle, that is, the throughput TH(N) of the semi-open queuing network representing the order transportation process and the expected waiting time W for unloading in front of the picking wall bpThey are all independent of the order category. Therefore, orders of different categories are regarded as orders of the same category, and the original multi-category semi-open queuing network is transformed into a single-category semi-open queuing network to evaluate TH(N) and W. bp ;

[0093] Combined with TH(N) and based on the approximate average value estimation method, determine the network throughput THC(n) when the number n of automatic guided vehicles changes from 1 to N. N represents the number of automatic guided vehicles in the robotic warehouse system, and n = 1, 2, …, N.

[0094] S6. Calculate the total time T for an automatic guided vehicle to serve an order. trans :

[0095] T trans = T dp,tr + t lr + T tr,pw + W bp + t lp ;

[0096] S7. Synchronization station steady-state analysis:

[0097] Use the continuous-time Markov chain model of the semi-open queuing network to calculate the steady state of the synchronization station. In the continuous-time Markov chain model, use the single-variable z to define the state space variable, where z = i - j. i represents the number of orders waiting in the order queue, and j represents the number of available vehicles in the automatic guided vehicle queue; i and j cannot both exceed 0, that is, if i > 0, then j = 0; conversely, if j > 0, then i = 0.

[0098] The total number of automatic guided vehicles in the entire robotic warehouse system is N. When the value of the state space variable is -N, it means that N vehicles are available, and when i > 0, it means that there are orders waiting in the order queue and all automatic guided vehicles are busy.

[0099] The total arrival rate of the network is λ = λ1 + λ2 + … + λ K , and the system transfers from one state to another at a rate of λ; when i ≤ N, the system transfers from state X(-N + i) to state X(-N + i - 1) at a rate of THC(i); when i > N, since the maximum number of vehicles is N, the transfer from state X(i) to X(i - 1) occurs at a rate of THC(N).

[0100] π z represents the steady-state probability of state z in the continuous-time Markov chain. Then, the steady-state probability of any state can be calculated, and the steady-state probabilities π -N , π0, and π z are respectively:

[0101]

[0102] S8. Analysis of the expected waiting time of the dynamic priority queue:

[0103] Due to different cumulative priority rates, the expected waiting times of orders in different categories are not equal, which means that orders with a higher cumulative priority rate will have a shorter waiting time than orders with a lower cumulative priority rate.

[0104] An order of category k starts accumulating priority at a rate of b from the arrival time k where b1 ≥ b2 ≥ … ≥ b K ≥ 0, and K is the total number of order categories; in the order queue of the queuing network, the expected average waiting time of an order of category k in the external order queue

[0105]

[0106] where ρ = λ / THC(N), ρ i = λ i / THC(N), W0 is the average remaining service time of the orders in service, and W0 = 1 / THC(N); M i is the expected waiting time of an order of category i.

[0107] S9. Calculate the cycle time of an order of category k

[0108]

[0109] It should be noted that there are K types of orders in the robotic warehouse system, and the arrival rate of orders of category k follows a Poisson distribution; when an order arrives, an order of category k starts accumulating priority at a rate of b k where b1 ≥ b2 ≥ … ≥ b K ≥ 0; if an order of category k arrives at time t and is still in the system at a later time t0 > t (there are orders waiting), this order has a cumulative dynamic priority represented by the linear function b k (t0 - t) at time t0. At the instant of service completion, the order with the highest cumulative dynamic priority in the order queue is selected. When orders of different categories arrive simultaneously at time t = t0 (there are no orders waiting) and at least one robot is available, the order with the highest cumulative rate b k is selected for service.

[0110] Through the above steps S1 - S9, the cycle time estimation method for a robot warehouse based on a dynamic priority queuing network in the first embodiment can effectively calculate the cycle time of an order of category k in the robot warehouse system, that is, the cycle time estimation method for a robot warehouse based on a dynamic priority queuing network in the first embodiment can be effectively used to evaluate the cycle time of different types of orders in the robot warehouse system.

[0111] Embodiment 2, the difference between this Embodiment 2 and Embodiment 1 is that: the cycle time estimation method for a robot warehouse based on a dynamic priority queuing network further includes:

[0112] S10. Calculate the flow time T of the order on the picking wall p and the total cycle time THT of an order of category k k :

[0113]

[0114] where M represents the total number of pickers at the picking wall, and μ p represents the picking service rate of the picker.

[0115] Embodiment 3, the difference between this Embodiment 3 and Embodiment 1 is that: the cycle time estimation method for a robot warehouse based on a dynamic priority queuing network further includes:

[0116] S11. Calculate the utilization rate ρ of the autonomous guided vehicle N , the utilization rate ρ of the autonomous guided vehicle N is the ratio of the order throughput rate to the robot production capacity, and the robot production capacity refers to the maximum number of items that the autonomous guided vehicle can transport per unit time;

[0117] The robot production capacity C r = N / (T trans + t lp + T pw,tr + t lr ), the throughput rate of the order is TH(N), that is, the utilization rate of the autonomous guided vehicle

[0118] Embodiment 4, the difference between this Embodiment 4 and Embodiment 1 is that: both the longitudinal lane and the transverse lane in the robot warehouse system have one - way lanes in two opposite directions, and the shortest path between the starting point and the ending point on the driving path of the autonomous guided vehicle is equal to the Manhattan distance.

[0119] Embodiment 5, the difference between this Embodiment 5 and Embodiment 1 is that: when the autonomous guided vehicle transports the cargo box, each autonomous guided vehicle can only transport one cargo box at a time.

[0120] The above content is only a preferred embodiment of the present invention. For those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. The content of this specification should not be construed as a limitation to the present invention.

Claims

1. A robot warehouse cycle time estimation method based on a dynamic priority queuing network, which is applied to a robot warehouse system, which includes a picking wall, arranged shelves, and autonomous handling robots for picking and handling boxes; The robot includes a mobile platform, an elevator installed on the mobile platform, and a picking manipulator installed on the driving end of the elevator; It is characterized in that The method includes the following steps, specifically: S1. Establish the robot warehouse system coordinate system. The coordinates of the robot stop point are (x dp ,y dp ), the coordinates of the target shelf are (x tr ,y tr ), and all shelf locations are represented by a coordinate set C, specifically: Among them, n ω =1,2,…N ω , n l =1,2,…,N l , n ωu =1,2,n lu =1,2,…5,n ω Indicates the nth ω Row shelves, N ω Indicates the number of rows of shelves, n l Indicates the nth l Row rack, N l Indicates the number of rows of shelves, (n ωu ,n lu ) is the relative coordinate of a storage location in the shelf, S a is the width of the longitudinal lane, S c Indicates the width of the cross lane, W u Indicates the width of the storage location on the shelf, L u Represents the length of the storage location on the shelf, W r Indicates the width of the shelf, L r Indicates the length of the shelf; The coordinates of the picking wall are (x pw ,y pw )={((W+S a ) / 2,0)}; S2. Calculate the driving time T of the robot from the stop point to the target shelf dp,tr , v r is the driving speed of the robot; T dp,tr The first moment of is: T dp,tr The second moment of is: S3, calculate the driving time T of the robot from the target shelf to the picking wall tr,pw The first moment of is: T tr,pw The second moment of is: S4. Calculate the robot's picking time: Picking time t lr It represents the time when the robot loads the box from the target shelf or unloads the box to the target shelf, and the picking time t lp Indicates the time when the robot loads a box from the picking wall or unloads a box on the picking wall; The lifting speed of the robot's lift is expressed in v l express; t lr The first moment of is: t lr The second moment of is: t lp The first moment of is: t lp The second moment of is: Among them, H r Indicates the height of the shelf, H p Indicates the height of the picking wall; S5. Calculate and determine TH(N) and W based on the approximate average value estimation method bp , TH(N) represents the throughput of the queuing network, W bp represents the expected waiting time for the robot to deliver the box to the picking wall before unloading; The dynamic priority is considered when the order is in the external order queue. The order transportation process follows the first-come-first-served principle. The original multi-class semi-open queue network is transformed into a single-class semi-open queue network to evaluate TH(N) and W. bp ; Combined with TH(N) and based on the approximate average estimation method, the network throughput THC(n) is determined when the number of robots n changes from 1 to N, where N represents the number of robots, n = 1, 2, ... N; S6. Calculate the total time T that the robot takes to serve an order trans : T trans =T dp,tr +t lr +T tr,pw +W bp +t lp ; S7. Synchronous station steady-state analysis: The steady state of the synchronization stations is calculated using a continuous-time Markov chain model of a semi-open queueing network; S8. Analysis of expected waiting time of dynamic priority queue: Orders of category k start arriving at a rate b. k Cumulative priority, where b1≥b2≥…≥b K ≥0, K is the total number of order categories; in the order queue of the queuing network, the expected average waiting time of orders of category k in the external order queue Where, ρ = λ / THC(N), ρ c =λ c / THC(N), W0 is the average remaining service time of the orders being served, and W0 = 1 / THC(N); M c is the expected waiting time for orders of category c; π -N represents the steady-state probability when N robots are available, and λ represents the total arrival rate of the network; S9. Calculate the cycle time of orders of category k 2. The method for estimating cycle time of a robot warehouse based on a dynamic priority queuing network according to claim 1, characterized in that: The robot's travel time from the target shelf to the picking wall is T tr,pw Equal to the robot's travel time T from the picking wall to the target shelf pw,tr .

3. The robot warehouse cycle time estimation method based on dynamic priority queuing network according to claim 1 is characterized in that: The method also includes: S10. Calculate the flow time T of the order on the picking wall p and the total cycle time THT for orders of category k k : Where M represents the total number of pickers at the picking wall, μ p Indicates the picking service rate of the picker.

4. The method for estimating cycle time of a robot warehouse based on a dynamic priority queuing network according to claim 2, characterized in that: The method also includes: S11. Calculate the robot utilization rate ρ N , the utilization rate of the robot ρ N is the ratio of order throughput to robot capacity. Robot capacity refers to the maximum number of items that a robot can transport per unit time. Robot production capacity C r =N / (T trans +t lp +T pw,tr +t lr ), the order throughput is TH(N), which is the utilization rate of the robot 5. The method for estimating cycle time of a robot warehouse based on a dynamic priority queuing network according to claim 1, characterized in that: The longitudinal lanes and transverse lanes in the robot warehouse system have two one-way lanes in opposite directions, and the shortest path between the starting point and the end point on the robot's driving path is equal to the Manhattan distance.

6. The method for estimating cycle time of a robot warehouse based on a dynamic priority queuing network according to claim 1, characterized in that: When the robots are transporting boxes, each robot can only transport one box at a time.

7. The robot warehouse cycle time estimation method based on dynamic priority queuing network according to claim 1 is characterized in that: In step S7, in the continuous-time Markov chain model, a tuple variable z is used to define a state space variable, where z=ij, i represents the number of orders waiting in the order queue, and j represents the number of robots available in the robot queue; i and j cannot exceed 0 at the same time, that is, if i>0, then j=0; Vice versa, if j>0, then i=0; The total number of robots in the entire robot warehouse system is N. When the state space variable value is -N, it means that N robots are available, and when i>0, it means that there are waiting orders in the order queue and all autonomous handling robots are busy; The total arrival rate of the network is λ=λ1+λ2+…+λ K , the system transfers from one state to another at rate THC(i); when i≤N, the system transfers from state X(-N+i) to state X(-N+i-1) at rate THC(i); when i>N, since the maximum number of robots is N, the transfer from state X(i) to X(i-1) occurs at rate THC(N); π z represents the steady-state probability of state z in the continuous-time Markov chain, then the steady-state probability of any state is calculated, and the steady-state probability π -N ,π0 and π z They are:

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