Analysis method and system for key parameters of annular rail type shuttle vehicle model

Abstract

The invention relates to a key parameter analysis method and system for an annular rail type shuttle vehicle model, and belongs to the technical field of logistics automation. Comprising the steps of constructing a queuing system model, and determining a waiting mechanism, a mixing mechanism, a first evaluation index and a second evaluation index of the model; according to the number of service objects and a mechanism of the queuing system model, determining a waiting-system queuing system and a mixed-system queuing system, and establishing a shuttle vehicle number calculation model, a cache position size evaluation model and a queuing system throughput evaluation model in combination with a first evaluation index calculation method and a first evaluation index calculation method; inputting the logistics parameters into a shuttle vehicle number calculation model to obtain an optimal shuttle vehicle number; inputting the logistics parameters and the optimal number of shuttle vehicles into a cache location size evaluation model to obtain an optimal cache location size; and inputting the logistics parameters, the optimal shuttle vehicle number and the optimal cache bit size into the throughput evaluation model to obtain the optimal warehousing rate. According to the invention, the carrying efficiency and throughput of the logistics system are improved, and the average waiting time of goods is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of logistics automation, and in particular to a method and system for analyzing key parameters of a circular track shuttle model. Background Art

[0002] With the continuous advancement of automation technology, shuttle vehicles have occupied an important position in modern automated logistics systems with their high-speed and stable operation, high reliability and low cost advantages. They can easily achieve automated docking with other logistics components, such as warehouse management systems, buffer stations, various conveyors, lifting platforms and robots, etc., and ensure the efficient flow of materials according to plan through precise scheduling and collaborative operations. At the same time, shuttle vehicles optimize the material transfer path between different workstations, making the entire conveyor line layout more compact and reasonable, and effectively improving the efficiency and smoothness of logistics operations. In addition, in heavy-load transportation and complex industrial scenes, shuttle vehicles have become indispensable key equipment on these production lines with their powerful load-bearing capacity, excellent safety performance and good adaptability to changing environments. Its stable and reliable performance not only ensures the continuous and efficient operation of the production line, but also reduces operating costs for enterprises and improves overall competitiveness.

[0003] However, traditional logistics systems often use empirical values ​​to set operating parameters, which may directly lead to a decrease in system handling efficiency and a reduction in task throughput due to improper parameter selection. At the same time, the automatic handling process may also cause the shuttle's handling efficiency to not match the amount of goods being handled, resulting in a decrease in logistics system resource utilization, an increase in the average waiting time for goods, and a decrease in overall handling efficiency. Summary of the invention

[0004] To this end, the technical problem to be solved by the present invention is to overcome the problems of decreased handling efficiency, reduced task throughput, decreased resource utilization and prolonged average waiting time of goods caused by improper selection of logistics system parameters in the prior art, and provide a key parameter analysis method and system for a circular track shuttle model, which obtains the optimal logistics system parameters through queuing theory models and scientific formula calculations, improves the overall handling efficiency and task throughput of the logistics system, and reduces the average waiting time of goods. At the same time, each resource is fully utilized.

[0005] In a first aspect, in order to solve the above technical problems, the present invention provides a method for analyzing key parameters of a circular track shuttle model, comprising:

[0006] Constructing a queuing system model, and determining a processing mechanism and an evaluation index of the queuing system model; wherein the queuing system model includes a service object, the processing mechanism includes a waiting mechanism and a mixed mechanism, and the evaluation index includes a first evaluation index and a second evaluation index;

[0007] Determine a waiting queuing system according to the number of service objects and the waiting mechanism; establish a circular track shuttle quantity calculation model according to the waiting queuing system and the calculation method of the first evaluation index; determine a hybrid queuing system according to the number of service objects and the hybrid mechanism; establish a cache size evaluation model and a queuing system throughput evaluation model according to the hybrid queuing system and the calculation method of the second evaluation index;

[0008] Obtain a logistics system to be analyzed; input the logistics parameters of the logistics system into the circular track shuttle number calculation model to obtain the optimal number of shuttles; input the logistics parameters and the optimal number of shuttles into the cache size evaluation model to obtain the optimal cache size; input the logistics parameters, the optimal number of shuttles and the optimal cache size into the queuing system throughput evaluation model to obtain the optimal warehousing rate.

[0009] In one embodiment of the present invention, the first evaluation index includes an average service intensity, and the average service intensity is obtained according to the probability distribution of the cargo arrival process and the cargo arrival time interval in the queuing system, and the calculation formula is:

[0010]

[0011] Among them, λ is the probability of a cargo arriving per unit time, μ is the number of cargo that can be transported per unit time, and c is the number of shuttles; ρ s <1 is a sufficient condition for the queuing system to be stable.

[0012] In one embodiment of the present invention, the method for obtaining the probability distribution of the cargo arrival process and the cargo arrival time interval in the queuing system is:

[0013] The formula for calculating the probability of n cargoes arriving in the time interval [t1, t2) is:

[0014] P n (t1,t2)=P{N(t2)-N(t1)=n};

[0015] Where n is the number of goods and n≥0, N(t1) is the number of goods arriving at the queuing system within time [0, t1], N(t2) is the number of goods arriving at the queuing system within time [0, t2], and t2>t1; for task time t k >t k-1 >t k-2 >…>t1≥0, determine the change in the quantity of goods N(t k )-N(t k-1 ),N(tk-1 )-N(t k-2 ),…,N(t2)-N(t1) are independent of each other;

[0016] In the time interval [t, t+Δt), for sufficiently small Δt, the probability of one cargo arriving is calculated using the calculation formula for the probability of n cargo arriving:

[0017] P1(t,t+Δt)=λΔt+ο(Δt);

[0018] Among them, when Δt→0, ο(Δt) is a high-order infinitesimal about Δt, and λ is the probability of a cargo arriving per unit time;

[0019] In the time interval [t, t+Δt), for sufficiently small Δt, using the calculation formula for the probability of n cargo arrivals, the probability of at least two cargoes arriving is calculated as:

[0020]

[0021] According to the mutual independence of the changes in the quantity of the goods, the probability of the arrival of one goods and the probability of the arrival of at least two goods, it is obtained that the arrival process of the goods obeys Poisson distribution and the time interval of the arrival of the goods obeys a negative exponential distribution with a parameter λ.

[0022] In one embodiment of the present invention, the first evaluation index further includes average queue length, average queue length, average stay time and average waiting time, and the average queue length, average queue length, average stay time and average waiting time are calculated as follows:

[0023] Calculate the average number of shuttles being transported using the formula:

[0024]

[0025] Calculate the probability P of n goods arriving n , the calculation formula is:

[0026]

[0027] Calculate the probability P0 that no goods arrive, the calculation formula is:

[0028]

[0029] Calculate the average queue length E(L q ), the calculation formula is:

[0030]

[0031] Calculate the average length E(L s), the calculation formula is:

[0032] E(L s )=E(L q )+c s ;

[0033] According to the average queue length, the average waiting time E(W q ), the calculation formula is:

[0034]

[0035] According to the average length of the captain, the average stay time E(W s ), the calculation formula is:

[0036]

[0037] Among them, L q is the number of goods waiting in line, L s is the quantity of goods in the logistics system, W q W is the time interval from the goods entering the queuing system to being transported, s is the time interval from the goods entering the queuing system to the goods leaving the queuing system after the service is completed, c s is the average number of shuttles, c is the number of shuttles, n is the number of goods, P n is the probability of n goods arriving, ρ is the transportation service intensity, ρ s is the average service intensity, P0 is the probability that no goods arrive, λ is the probability that one goods arrive per unit time, and μ is the number of goods that can be transported per unit time.

[0038] In one embodiment of the present invention, the second evaluation index includes a system blocking probability, and the system blocking probability calculation formula is:

[0039]

[0040] Among them, c is the number of shuttles, r is the maximum queue length, ρ is the handling service intensity, P n is the probability of n goods arriving, P0 is the probability of no goods arriving; P n The calculation formula is:

[0041]

[0042] The calculation formula of P0 is:

[0043]

[0044] Where N = c + r, and N > c, N is the maximum number of goods in the logistics system, n is the number of goods, ρs The average service intensity.

[0045] In one embodiment of the present invention, the processing mechanism further includes an abandonment mechanism.

[0046] In one embodiment of the present invention, the queuing system model uses symbols to represent parameters under different processing mechanisms; the symbols include: X representing the time interval distribution of cargo arrival at the system, Y representing the transportation time distribution of shuttle vehicles, Z representing the number of shuttle vehicles, A representing the maximum cargo capacity allowed in the queuing system, B representing the number of cargo in the cargo source, and C representing queuing rules.

[0047] In one embodiment of the present invention, the queuing rule of the waiting queuing system is that goods arrive continuously and are independent of each other.

[0048] In one embodiment of the present invention, the service principle of the queuing system model is a first-come, first-served principle.

[0049] In a second aspect, in order to solve the above technical problems, the present invention provides a key parameter analysis system for a circular track shuttle model, comprising:

[0050] A queuing system model building module is used to build a queuing system model and determine the processing mechanism and evaluation index of the queuing system model; wherein the queuing system model includes a service object, the processing mechanism includes a waiting mechanism and a mixed mechanism, and the evaluation index includes a first evaluation index and a second evaluation index;

[0051] A model building module is used to determine a waiting queuing system according to the number of service objects and the waiting mechanism; establish a circular track shuttle number calculation model according to the waiting queuing system and the calculation method of the first evaluation index; determine a mixed queuing system according to the number of service objects and the mixed mechanism; establish a cache size evaluation model and a queuing system throughput evaluation model according to the mixed queuing system and the calculation method of the second evaluation index;

[0052] The optimal parameter acquisition module is used to acquire the logistics system to be analyzed; input the logistics parameters of the logistics system into the circular track shuttle number calculation model to obtain the optimal number of shuttles; input the logistics parameters and the optimal number of shuttles into the cache size evaluation model to obtain the optimal cache size; input the logistics parameters, the optimal number of shuttles and the optimal cache size into the queuing system throughput evaluation model to obtain the optimal storage rate;

[0053] The UI interface includes a simulation result display area and a user operation area. The simulation result display area includes a queue type structure diagram, a cargo arrival time and system blocking rate simulation diagram, a service time and system blocking rate simulation diagram, a simulation diagram of different customer numbers and system blocking rate, and a simulation diagram of different numbers of shuttle vehicles for system blocking rate; the user operation area includes a single queue and a single service desk, a single queue and multiple service desks, and multiple queues and multiple service desks.

[0054] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0055] The key parameter analysis method and system of the circular track shuttle model described in the present invention can determine the optimal configuration of the number of shuttles and cache bits in the logistics system by calculating the key parameters of the circular track shuttle model based on queuing theory modeling, so that each resource can be fully utilized. Reducing the configuration of invalid resources avoids the waste of system investment and meets the requirements of the logistics system for efficient operation. The optimization of resource allocation not only makes the logistics system more economical, but also provides a good foundation for further expansion and upgrading. Among them, the calculation process is relatively concise and clear, easy to understand and implement. Using modern computing tools and programming languages, the simulation and optimization of the performance of the logistics system can be quickly realized, greatly shortening the time for setting and adjusting parameters. In addition, the UI interface can more intuitively and accurately display the algorithm results, making the system more adaptable to different similar problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

[0057] Figure 1 This is a flow chart of a key parameter analysis method for a circular track shuttle model in a preferred embodiment of the present invention;

[0058] Figure 2 This is a flow chart of the transportation of the circular track shuttle in the preferred embodiment of the present invention;

[0059] Figure 3 It is a schematic diagram of the working scene layout of the circular track shuttle in the preferred embodiment of the present invention;

[0060] Figure 4 This is a graph showing the effect of different numbers of shuttle vehicles on average service intensity and average waiting time in a preferred embodiment of the present invention;

[0061] Figure 5 This is a graph showing the effect of different cache bit sizes on system blocking rate in a preferred embodiment of the present invention;

[0062] Figure 6This is a graph showing the effect of different storage efficiencies on the average service intensity of shuttle vehicles in a preferred embodiment of the present invention;

[0063] Figure 7 This is a UI interactive interface diagram of a key parameter analysis system for a circular track shuttle model in a preferred embodiment of the present invention;

[0064] Figure 8 This is an example result diagram of the UI interaction interface of a key parameter analysis system for a circular track shuttle model in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0065] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0066] Embodiment 1

[0067] Reference Figure 1 As shown, a method for analyzing key parameters of a circular track shuttle model provided by an embodiment of the present invention includes:

[0068] Construct a queuing system model and determine the processing mechanism and evaluation index of the queuing system model; wherein the queuing system model includes a service object, the processing mechanism includes a waiting mechanism and a mixed mechanism, and the evaluation index includes a first evaluation index and a second evaluation index;

[0069] According to the number of service objects and the waiting mechanism, a waiting queuing system is determined; according to the waiting queuing system and the calculation method of the first evaluation index, a circular track shuttle number calculation model is established; according to the number of service objects and the mixed mechanism, a mixed queuing system is determined; according to the mixed queuing system and the calculation method of the second evaluation index, a cache size evaluation model and a queuing system throughput evaluation model are established;

[0070] Obtain the logistics system to be analyzed; input the logistics parameters of the logistics system into the circular track shuttle number calculation model to obtain the optimal number of shuttles; input the logistics parameters and the optimal number of shuttles into the cache size evaluation model to obtain the optimal cache size; input the logistics parameters, the optimal number of shuttles and the optimal cache size into the queuing system throughput evaluation model to obtain the optimal warehousing rate.

[0071] A method for analyzing key parameters of a circular rail shuttle model provided by an embodiment of the present invention can be used to analyze logistics systems of different types and sizes. Whether it is a small internal conveying system of a production line or a large automated warehousing system, it can be applied and provide an effective optimization solution. At the same time, the circular rail shuttle number calculation model, the cache size evaluation model and the queuing system throughput evaluation model calculate the required number of shuttles, the cache size, and the performance of the system under different parameter settings through formulas. This avoids the problem that the parameter setting of the traditional logistics system relies solely on empirical values, and greatly improves the rationality and scientificity of the design. It is specifically manifested in reducing the average waiting time of goods in the logistics system, improving the utilization rate of shuttles, and optimizing the throughput of the system. For example, by scientifically setting the number of shuttles and caches, congestion caused by unreasonable resource allocation can be avoided or reduced, and the fluidity of the system can be improved.

[0072] Specifically, a queuing system model is constructed, and the key parameters include the service station and the service object, where the service station is a shuttle, which can also be called a rail guide vehicle (RGV), and the service object is the goods to be transported. The shuttle is used to transport the arrived goods. When all the shuttles are busy, the goods that arrive later will be processed according to the processing mechanism of the queuing system, which includes a waiting mechanism, a abandonment mechanism, and a mixed mechanism. Among them, the waiting mechanism is that the goods choose to enter the queuing system and wait until there is an available shuttle for transportation; the abandonment mechanism is that the goods choose not to wait and directly exit the queuing system; the mixed mechanism combines the waiting mechanism and the abandonment mechanism. The goods queue according to the waiting mechanism, but after the waiting time exceeds a certain limit, the goods will leave the queuing system.

[0073] Under different processing mechanisms, there are different solution models. For different solution models, the queuing system will have different variations to cope with different scenarios. This embodiment preferably uses symbolic formulas to define different types of queuing systems. Specifically, the queuing system model uses symbols to represent parameters under different processing mechanisms, and the symbols include: X representing the time interval distribution of the arrival of goods in the system, Y representing the transportation time distribution of the shuttle, Z representing the number of shuttles, A representing the maximum cargo capacity allowed in the queuing system, B representing the number of goods in the cargo source, and C representing the queuing rules.

[0074] According to the distribution of the time intervals of the goods arriving at the queuing system, the time interval distribution can be: fixed length distribution (D), exponential distribution or Poisson distribution (M), K-order Erlang distribution (E rk ), independent arrival time interval distribution (GI) and general time interval distribution (G).

[0075] In the queuing system model, when goods are waiting in accordance with specific queuing rules, the service mode can be first-come, first-served (FCFS), last-come, first-served (LCFS), random service (ROS) and priority service (PR). In this embodiment, the service principle of the queuing system model is preferably the first-come, first-carried principle. In addition, the configuration of the queuing queue can be set according to the actual application scenario, which can be a single queue model or a multi-queue model. The queuing system model also includes evaluation indicators. The preferred evaluation indicators in this embodiment include: Captain L s 、Queue leader L q , duration of stay s , waiting time W q , service intensity ρ and system blocking rate P jam Specifically, Captain L s Represents the quantity of goods in the logistics system, and the queue length L q Indicates the number of goods waiting in line; where the queue leader = queue length + number of goods being transported. Stay time W s It represents the time interval from when the goods enter the queuing system until the service is completed and they leave the queuing system. The waiting time W q It represents the time interval from the goods entering the queuing system to the time they are transported; where the stay time = waiting time + transport time. Service intensity ρ is an important indicator to measure the service efficiency of the shuttle (i.e., the service desk), and it is also an important indicator that affects the team leader. System blocking rate P jam is the probability of system congestion when the number of goods exceeds the maximum cargo capacity of the queuing system.

[0076] Specifically, a complete cargo queuing process can be referred to Figure 2 The cargo source sends the cargo according to the time interval distribution of the cargo arriving at the queuing system. The cargo arriving at the logistics system will enter the queuing system and queue according to the queuing rules, which can be a single queue or multiple queues. When there is an available shuttle, the shuttle transports the cargo and delivers it to the designated location, thereby completing a cargo transportation task. The number of available shuttles may be single or multiple.

[0077] Next, according to the handling characteristics of the circular track shuttle and combined with relevant queuing theory, the queuing system is determined to be a waiting queuing system, and a circular track shuttle quantity calculation model is established in combination with the calculation method of the first evaluation index.

[0078] 1 Calculation model of the number of circular rail shuttles

[0079] 1.1 Waiting Queue System

[0080] Specifically, the working warehouse layout of the circular rail shuttle-cargo queuing model of the embodiment of the present invention is as follows: Figure 3Specifically, the shuttle runs in the same fixed direction, transporting the goods from the input / output station (I / O) to the inbound conveyor, and then the stacker stores the inbound goods in the designated cargo position and returns to the conveyor, thus completing the inbound transportation task of the goods.

[0081] In the circular track shuttle-cargo queuing model of this embodiment, it is assumed that the pallets on the warehousing platform arrive continuously. At this time, the model is equivalent to the "cargo waiting for shuttle" model, which is hereinafter referred to as the first model. Since there are multiple shuttles responsible for handling tasks in the waiting queuing system, the model can be regarded as a multi-service station queuing system. Further analysis shows that different goods are queued at multiple warehousing platforms waiting for warehousing. Each platform is independent and does not affect each other. If the pallets are evenly distributed at each platform, the multi-platform queuing model can be equivalent to a single-platform queuing model. That is, multiple platform queues are merged into a single queue, and its maximum cache number is the sum of the cache numbers of all platforms. For this reason, the first model can be equivalent to a single-queue and multi-service station queuing system.

[0082] Furthermore, the probability distribution of the cargo arrival process and the cargo arrival time interval in the queuing system is obtained as follows:

[0083] The calculation formula for the probability of n (n ≥ 0) cargoes arriving in the time interval [t1, t2) is:

[0084] P n (t1,t2)=P{N(t2)-N(t1)=n}.

[0085] Where n is the number of goods and n≥0, N(t1) is the number of goods arriving at the queuing system within time [0, t1], N(t2) is the number of goods arriving at the queuing system within time [0, t2], and t2>t1.

[0086] For the first model, the following conditions S301, S302, and S303 are satisfied:

[0087] Condition S301: In non-overlapping time intervals, the quantity of goods arriving is independent of each other, that is, it has increment independence. Specifically, for the task time t k >t k-1 >t k-2 >…>t1≥0, determine the change in the quantity of goods N(t k )-N(t k-1 ),N(t k-1 )-N(t k-2 ),…,N(t2)-N(t1) are independent of each other.

[0088] Condition S302: In the time interval [t, t+Δt), for sufficiently small Δt, the probability of a cargo arriving is independent of t, but is approximately proportional to the length of the interval Δt. Using the calculation formula for the probability of n cargo arrivals, the probability of one cargo arriving is calculated as: P1(t, t+Δt) = λΔt + ο(Δt). Among them, when Δt→0, ο(Δt) is a high-order infinitesimal with respect to Δt. The parameter λ is the probability of a cargo arriving per unit time, which can also be called the average cargo arrival rate.

[0089] Condition S303: In the time interval [t, t+Δt), for sufficiently small Δt, the probability of two or more goods arriving is substantially 0. Therefore, according to the calculation formula for the probability of n goods arriving, the probability of at least two goods arriving is calculated as:

[0090]

[0091] According to the independent changes in the quantity of goods in condition S301, the probability of one cargo arriving in condition S302 and the probability of at least two cargoes arriving in condition S303, it is obtained that the cargo arrival process obeys Poisson distribution and the cargo arrival time interval obeys negative exponential distribution with parameter λ.

[0092] Furthermore, in the queuing rules, if the goods in the queuing system arrive continuously and are independent of each other, each shuttle has only one pallet to be transported, and the other pallets of goods are waiting in line, and the shuttles do not interfere with each other, then it is determined to be a waiting queuing system.

[0093] Furthermore, in the service process, the service principle of the shuttle bus in this embodiment is preferably the first-come-first-served principle. In addition, according to the cargo arrival process obeying the Poisson distribution, the cargo arrival time interval obeying the negative exponential distribution with parameter λ, the queuing rules and the service process, it can be determined that the queuing system is the M / M / c / ∞ / ∞ / FCFS waiting queuing system.

[0094] 1.2 Derivation of calculation formula

[0095] Specifically, the first evaluation index includes the average service intensity, which is obtained according to the probability distribution of the cargo arrival process and the cargo arrival time interval in the queuing system. The specific steps are:

[0096] According to conditions S301 and S302, we can get:

[0097] P0(t,t+Δt)=P0(t)P0(Δt), (2-1)

[0098]

[0099] According to conditions S302 and S303, we can get:

[0100] P0(Δt)=1-λΔt+ο(Δt); (2-3)

[0101] Combining equations (2-1), (2-2) and (2-3) we get:

[0102]

[0103] The solution is:

[0104]

[0105] Therefore, we get the service intensity ρ and average service intensity ρ of the waiting queue system. s , the formula is:

[0106]

[0107] Among them, P n (t) is P n (0, t), λ is the probability of a cargo arriving per unit time, μ is the number of cargoes that can be transported per unit time, and c is the number of shuttles; ρ s <1 is a sufficient condition for the stability of the queuing system. Of course, the calculation formula of average service intensity can be appropriately modified according to the needs of the actual application scenario. For example, in the scenario where multiple shuttles are running on the same track, the transportation efficiency will inevitably be reduced due to path interference between vehicles. At this time, the operating efficiency η under the multi-shuttle mode is introduced, and the calculation formula of average service intensity is modified to:

[0108]

[0109] Specifically, the first evaluation index also includes the average length of the queue, the average queue length, the average stay time and the average waiting time. The calculation method of the average length of the queue, the average queue length, the average stay time and the average waiting time is:

[0110] According to the corresponding relationship between the number of goods and the number of shuttles, the state equation can be obtained as follows:

[0111]

[0112] Solving the difference equation, we get:

[0113]

[0114] Among them, P n is the probability of n goods arriving, and P0 is the probability of no goods arriving.

[0115] Furthermore, according to equations (2-4) and (2-5), the average queue length, average queue length, average stay time and average waiting time can be solved.

[0116] Average Captain E(L s ) and the average queue length E(L q ) is:

[0117] E(L s )=E(L q )+c s . (2-6)

[0118] Calculate the average number of shuttles being transported c s , the calculation formula is:

[0119]

[0120] Combining equations (2-5) and (2-7), we get:

[0121]

[0122] For the average queue length E(L q ), the calculation formula is:

[0123]

[0124] Combining equations (2-6), (2-8) and (2-9), we get the average length E(L s ) is calculated as:

[0125]

[0126] Furthermore, the average stay time and the average waiting time are calculated. Assume that the cargo waiting time W q In [0, t) (t>0), define W q The distribution function of is calculated as:

[0127]

[0128] Among them, P{W q =0} means that there is no need to queue, that is, the number of goods is less than the number of shuttles. The calculation formula is:

[0129]

[0130] P{0<W q <t} means the quantity of goods is greater than the number of shuttle vehicles. The calculation formula is:

[0131]

[0132] Combining equations (2-11), (2-12) and (2-13), we can get The derivative of The calculation formula is:

[0133]

[0134] Among them, δ(t) is the Dirac function, which has three properties:

[0135] ① δ(t)=δ(-t), ② ③

[0136] Therefore, the average waiting time E(W q ) is calculated as:

[0137]

[0138] The average stay time is equal to the sum of the queuing time and the handling time. The handling time is from the time when the pallet cargo is handed over to the shuttle vehicle until the unloading is completed. s ) is calculated as:

[0139]

[0140] Among them, L q is the number of goods waiting in line, L s is the quantity of goods in the logistics system, W q W is the time interval from the goods entering the queuing system to being transported, s is the time interval from the goods entering the queuing system to the goods leaving the queuing system after the service is completed, c s is the average number of shuttles, c is the number of shuttles, n is the number of goods, P n is the probability of n goods arriving, ρ is the transportation service intensity, ρ s is the average service intensity, P0 is the probability that no goods arrive, λ is the probability that one goods arrive per unit time, and μ is the number of goods that can be transported per unit time.

[0141] From formulas (2-15) and (2-16), it can be concluded that the average waiting time can be calculated based on the average queue length, and the average stay time can be calculated based on the average queue length.

[0142] 1.3 Solution and analysis

[0143] According to the formula derivation in 1.2, this embodiment is based on the actual transportation scenario to establish a circular track shuttle-cargo queuing model. The relevant parameters of the model are shown in Table 2-1.

[0144] Table 2-1 Model parameter table

[0145]

[0146] From the parameters in Table 2-1, we can see that the average storage time for each pallet of cargo is:

[0147]

[0148] The shuttle vehicle completes one handling service time:

[0149]

[0150] According to the cargo arrival process following Poisson distribution and the cargo arrival time interval following negative exponential distribution with parameter λ, we calculated that: λ=1 / W=0.05; μ=1 / T=0.016.

[0151] Since there is a path interference problem between vehicles when multiple shuttles are running on the same track, it is inevitable to reduce the handling efficiency. Therefore, the operation efficiency η and the average service intensity ρ under the multi-shuttle mode are introduced. s The formula is modified to:

[0152]

[0153] According to the circular track shuttle-cargo queuing model and calculation method, the results of the first evaluation index are shown in Table 2-2. The impact of the number of shuttles on the average service intensity and average waiting time, refer to Figure 4 .

[0154] Table 2-2 The impact of the number of shuttle vehicles on the key indicators of the system

[0155]

[0156]

[0157] Refer to Table 2-2 and Figure 4 , when the number of shuttles is less than 5, the average service intensity ρ s>1, this means that the existing number of shuttles in the system cannot meet the transportation demand, which will lead to a backlog of platform pallet cargo and affect system efficiency. As the number of shuttles increases, the average service intensity gradually decreases, and the average queue length and average queue length also gradually decrease. When the number of shuttles is 5, the logistics system achieves a good balance between supply and demand and can better complete the transportation of platform pallet cargo. When the number of shuttles continues to increase, although it can also meet the transportation needs of the system, it also causes an increase in costs and greatly increases the probability of congestion between shuttles. Therefore, under the condition of supply and demand balance, when there are 5 shuttles, the average waiting time is 45.1977 seconds, which is lower than the time it takes for the shuttle to complete a transportation task (62.5 seconds), which will significantly improve the system's transportation efficiency.

[0158] Furthermore, the total number of goods in the queuing system model is restricted, the queuing system is determined to be a mixed queuing system, and a cache size evaluation model and a queuing system throughput evaluation model are established in combination with the calculation method of the second evaluation index.

[0159] 2 Cache size evaluation model and queuing system throughput evaluation model

[0160] 2.1 Hybrid Queuing System

[0161] Limit the cargo capacity in the circular track shuttle-cargo queuing model (i.e., the first model) of the waiting queuing system in 1.1, and obtain a new circular track shuttle-cargo queuing model, referred to as the second model. In actual scenarios, it is impossible for cargo to be continuously available. Therefore, when the number of cargo in the queuing system exceeds the maximum number of cargo allowed by the system, the system will temporarily prevent new cargo from arriving. The probability of this event occurring at this time is called the system blocking probability, where the second evaluation index includes the system blocking probability. According to the similar analysis method in Section 1.1, it can be concluded that the queuing system is a mixed queuing system of M / M / c / N / ∞ / FCFS, where N represents the maximum number of cargo in the system, and N>c; it is stipulated that: N=c+r, where r represents the maximum queue length. The repeated parts in the analysis method will not be repeated here.

[0162] 2.2 Derivation of relevant formulas

[0163] The equation in the second model is:

[0164]

[0165] The probability P of n goods arriving n , the calculation formula is:

[0166]

[0167] The probability that no goods arrive, P0, is calculated as:

[0168]

[0169] Among them, P n The distribution of and P0 can be called the state stationary distribution of the second model, and the calculation formula of the system blocking probability is:

[0170]

[0171] Next, the influence of the buffer size of the transmission line on the performance of the second model is solved and analyzed through the relevant formulas, and the system throughput is calculated.

[0172] 2.3 Solution and analysis

[0173] According to the solution and analysis in 1.3, when supply and demand are balanced, c = 5, ρ s =0.8333, the relationship between the system blocking probability and the cache bit size can be obtained. The results can be found in Table 3-1. The effect of different cache bit sizes on the system blocking rate can be found in Figure 5 .

[0174] Table 3-1 System blocking rate and cache bit size relationship results

[0175]

[0176]

[0177] Refer to Table 3-1 and Figure 5 It can be seen that the probability of system congestion decreases with the increase of cache positions, and the rate of change gradually decreases and tends to be stable. For the probability that all shuttles are idle, no matter how the cache positions change, its value always remains at about 3%. For a system with 7 conveyor lines, when the cache position is 7 (that is, 1 cache position for each conveyor line), the probability of congestion is 0.31%. When the cache position is 14 (that is, 2 cache positions for each conveyor line), the probability of congestion is only about 0.01%, and the congestion probability does not change much. Insufficient cache positions will increase the probability of congestion when the system tasks surge, reducing the system handling efficiency. Too many cache positions will increase costs. According to the results in Table 3-1, the cache positions for each conveyor line can be set to 2, that is, a total of 14 as the maximum number of caches for the system.

[0178] 2.4 Solution and analysis in the queuing system throughput evaluation model

[0179] Furthermore, according to the results obtained in 1.3 and 2.3, the number of shuttles is selected as 5 and the cache size is set to 14. The influence of the system storage efficiency Q1 on the system blocking rate is further studied. The results can be found in Table 4-1. The influence of different storage efficiencies on the average service intensity of shuttles can be found in Table 4-1. Figure 6 .

[0180] Table 4-1 The impact of system storage efficiency on average service intensity and blocking rate

[0181]

[0182] Refer to Table 4-1 and Figure 6 It can be seen that with the increase of the system's warehousing efficiency, the average service intensity of the shuttle and the probability of system congestion also gradually increase. When the number of pallets entering the warehouse per hour is no more than 210, the system will basically not be blocked, but the average service intensity of the shuttle is relatively large. When the number of pallets entering the warehouse per hour reaches 220, the average service intensity of the shuttle is greater than 1, indicating that the current number of vehicles will no longer meet the current throughput of the system. At the same time, the probability of system congestion reaches 0.11%. Therefore, under this system, in order to meet the service intensity requirements of the system, the warehousing capacity should be controlled below 210 pallets.

[0183] Based on the output results of the calculation model of the number of circular rail shuttles, the platform cache size evaluation model, and the system throughput evaluation model, it can be concluded that the current logistics system can select 5 shuttles, set the cache size to 14, and control the storage capacity below 210 pallets, which can achieve the optimal state. In addition, this embodiment uses MATLAB software to calculate the results many times to verify the effectiveness of the key parameter analysis method of the circular rail shuttle model provided in this embodiment.

[0184] The key parameter analysis method of the circular track shuttle model provided by the embodiment of the present invention has a concise and clear calculation process, which is easy to understand and implement. By scientifically setting the number of shuttles and cache bits, congestion caused by unreasonable resource allocation can be avoided or reduced, thereby improving the fluidity of the system.

[0185] Embodiment 2

[0186] Based on the same inventive concept, this embodiment provides a circular track shuttle model key parameter analysis system, and its principle of solving the problem is similar to the circular track shuttle model key parameter analysis method provided in Example 1, and the repeated parts will not be repeated.

[0187] An embodiment of the present invention provides a key parameter analysis system for a circular track shuttle model, comprising:

[0188] A queuing system model building module is used to build a queuing system model and determine the processing mechanism and evaluation index of the queuing system model; wherein the queuing system model includes a service object, the processing mechanism includes a waiting mechanism and a mixed mechanism, and the evaluation index includes a first evaluation index and a second evaluation index;

[0189] The model building module is used to determine the waiting queuing system according to the number of service objects and the waiting mechanism; establish a circular track shuttle number calculation model according to the waiting queuing system and the calculation method of the first evaluation index; determine the mixed queuing system according to the number of service objects and the mixed mechanism; establish a cache size evaluation model and a queuing system throughput evaluation model according to the mixed queuing system and the calculation method of the second evaluation index;

[0190] The optimal parameter acquisition module is used to obtain the logistics system to be analyzed; input the logistics parameters of the logistics system into the circular track shuttle number calculation model to obtain the optimal number of shuttles; input the logistics parameters and the optimal number of shuttles into the cache size evaluation model to obtain the optimal cache size; input the logistics parameters, the optimal number of shuttles and the optimal cache size into the queuing system throughput evaluation model to obtain the optimal storage rate;

[0191] The UI interface includes a simulation result display area and a user operation area. The simulation result display area includes a queue type structure diagram, a simulation diagram of cargo arrival time and system blocking rate, a simulation diagram of service time and system blocking rate, a simulation diagram of different numbers of customers and system blocking rate, and a simulation diagram of different numbers of shuttle vehicles for system blocking rate; the user operation area includes a single queue and a single service desk, a single queue and multiple service desks, and multiple queues and multiple service desks.

[0192] Specifically, the UI interface in this embodiment can refer to Figure 7 It mainly consists of two parts: the queuing theory algorithm simulation result display area and the user operation area. The user operation area can select different queuing modes according to different problem types. After selecting the corresponding queuing mode, you can enter the real parameters in different parameter columns for simulation calculation according to the actual situation. The simulation result graph will be displayed in the simulation result display area. The UI simulation interactive program can visualize the algorithm results and output data for subsequent verification and analysis.

[0193] Specifically, the optimal number of shuttles, the optimal cache size, and the optimal storage rate can be obtained according to the above example 1. In the UI interface, select the single queue and multiple service desks queue type, enter the number of service desks as 5, the average service time as 62.5, the total number of customers as 2000, and the average arrival time as 20 in the 1 queue N service desk parameter column. The simulation results refer to Figure 8 The built-in algorithm of the UI interface will select the required parameters according to different simulation diagrams. The simulation conclusion of this example is basically consistent with the conclusion analyzed in the above embodiment 1.

[0194] The embodiment of the present invention provides a key parameter analysis system for a circular rail shuttle model, which can quickly simulate and optimize the performance of a logistics system using modern computing tools and programming languages, greatly shortening the time for setting and adjusting parameters. At the same time, the UI interface can more intuitively and accurately display the algorithm results, making the system more adaptable to different similar problems.

[0195] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0196] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0197] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0198] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0199] Obviously, the above embodiments are merely examples for clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived from these are still within the protection scope of the invention.

Claims

1. A method for analyzing key parameters of a circular track shuttle model, characterized in that ,include: Constructing a queuing system model, and determining a processing mechanism and an evaluation index of the queuing system model; wherein the queuing system model includes a service object, the processing mechanism includes a waiting mechanism and a mixed mechanism, and the evaluation index includes a first evaluation index and a second evaluation index; Determine a waiting queuing system according to the number of service objects and the waiting mechanism; establish a circular track shuttle quantity calculation model according to the waiting queuing system and the calculation method of the first evaluation index; determine a hybrid queuing system according to the number of service objects and the hybrid mechanism; establish a cache size evaluation model and a queuing system throughput evaluation model according to the hybrid queuing system and the calculation method of the second evaluation index; Obtain a logistics system to be analyzed; input the logistics parameters of the logistics system into the circular track shuttle number calculation model to obtain the optimal number of shuttles; input the logistics parameters and the optimal number of shuttles into the cache size evaluation model to obtain the optimal cache size; input the logistics parameters, the optimal number of shuttles and the optimal cache size into the queuing system throughput evaluation model to obtain the optimal warehousing rate.

2. A method for analyzing key parameters of a circular track shuttle model according to claim 1, characterized in that: The first evaluation index includes average service intensity, which is obtained according to the probability distribution of the cargo arrival process and the cargo arrival time interval in the queuing system, and is calculated as follows: Among them, λ is the probability of a cargo arriving per unit time, μ is the number of cargo that can be transported per unit time, and c is the number of shuttles; ρ s <1 is a sufficient condition for the queuing system to be stable.

3. A method for analyzing key parameters of a circular track shuttle model according to claim 2, characterized in that: The method for obtaining the probability distribution of the cargo arrival process and the cargo arrival time interval in the queuing system is as follows: The formula for calculating the probability of n cargoes arriving in the time interval [t1, t2) is: P n (t1,t2)=P{N(t2)-N(t1)=n}; Where n is the number of goods and n≥0, N(t1) is the number of goods arriving at the queuing system within time [0, t1], N(t2) is the number of goods arriving at the queuing system within time [0, t2], and t2>t1; for task time t k >t k-1 >t k-2 >…>t1≥0, determine the change in the quantity of goods N(t k )-N(t k-1 ),N(t k-1 )-N(t k-2 ),…,N(t2)-N(t1) are independent of each other; In the time interval [t, t+Δt), for sufficiently small Δt, the probability of one cargo arriving is calculated using the calculation formula for the probability of n cargo arriving: P1(t,t+Δt)=λΔt+ο(Δt); Among them, when Δt→0, ο(Δt) is a high-order infinitesimal about Δt, and λ is the probability of a cargo arriving per unit time; In the time interval [t, t+Δt), for sufficiently small Δt, using the calculation formula for the probability of n cargo arrivals, the probability of at least two cargoes arriving is calculated as: According to the mutual independence of the changes in the quantity of the goods, the probability of the arrival of one goods and the probability of the arrival of at least two goods, it is obtained that the arrival process of the goods obeys the Poisson distribution and the time interval of the arrival of the goods obeys the negative exponential distribution with parameter λ.

4. The key parameter analysis method of a circular track shuttle model according to claim 1 is characterized in that: The first evaluation index also includes average queue length, average queue length, average stay time and average waiting time. The calculation method of the average queue length, average queue length, average stay time and average waiting time is: Calculate the average number of shuttles being transported using the formula: Calculate the probability P of n goods arriving n , the calculation formula is: Calculate the probability P0 that no goods arrive, the calculation formula is: Calculate the average queue length E(L q ), the calculation formula is: Calculate the average length E(L s ), the calculation formula is: And(L s )=E(L q )+c s ; According to the average queue length, the average waiting time E(W q ), the calculation formula is: According to the average length of the captain, the average stay time E(W s ), the calculation formula is: Among them, L q is the number of goods waiting in line, L s is the quantity of goods in the logistics system, W q W is the time interval from the goods entering the queuing system to being transported, s is the time interval from the goods entering the queuing system to the goods leaving the queuing system after the service is completed, c s is the average number of shuttles, c is the number of shuttles, n is the number of goods, P n is the probability of n goods arriving, ρ is the transportation service intensity, ρ s is the average service intensity, P0 is the probability that no goods arrive, λ is the probability that one goods arrive per unit time, and μ is the number of goods that can be transported per unit time.

5. The key parameter analysis method of a circular track shuttle model according to claim 1 is characterized in that: The second evaluation index includes a system blocking probability, and the system blocking probability calculation formula is: Among them, c is the number of shuttles, r is the maximum queue length, ρ is the handling service intensity, P n is the probability of n goods arriving, P0 is the probability of no goods arriving; P n The calculation formula is: The calculation formula of P0 is: Where N = c + r, and N > c, N is the maximum number of goods in the logistics system, n is the number of goods, ρ s The average service intensity.

6. The method for analyzing key parameters of a circular track shuttle model according to claim 1, characterized in that: The processing mechanism also includes an abandonment mechanism.

7. The method for analyzing key parameters of a circular track shuttle model according to claim 1, characterized in that: The queuing system model uses symbols to represent parameters under different processing mechanisms; the symbols include: X representing the time interval distribution of cargo arrival at the system, Y representing the transportation time distribution of shuttle vehicles, Z representing the number of shuttle vehicles, A representing the maximum cargo capacity allowed in the queuing system, B representing the number of cargo in the cargo source, and C representing the queuing rules.

8. The method for analyzing key parameters of a circular track shuttle model according to claim 1, characterized in that: The queuing rule of the waiting queuing system is that the goods arrive continuously and are independent of each other.

9. The method for analyzing key parameters of a circular track shuttle model according to claim 1, characterized in that: The service principle of the queuing system model is the first-come, first-served principle.

10. A key parameter analysis system for a circular track shuttle model, characterized in that: include: A queuing system model building module is used to build a queuing system model and determine the processing mechanism and evaluation index of the queuing system model; wherein the queuing system model includes a service object, the processing mechanism includes a waiting mechanism and a mixed mechanism, and the evaluation index includes a first evaluation index and a second evaluation index; A model building module is used to determine a waiting queuing system according to the number of service objects and the waiting mechanism; establish a circular track shuttle number calculation model according to the waiting queuing system and the calculation method of the first evaluation index; determine a mixed queuing system according to the number of service objects and the mixed mechanism; establish a cache size evaluation model and a queuing system throughput evaluation model according to the mixed queuing system and the calculation method of the second evaluation index; The optimal parameter acquisition module is used to acquire the logistics system to be analyzed; input the logistics parameters of the logistics system into the circular track shuttle number calculation model to obtain the optimal number of shuttles; input the logistics parameters and the optimal number of shuttles into the cache size evaluation model to obtain the optimal cache size; input the logistics parameters, the optimal number of shuttles and the optimal cache size into the queuing system throughput evaluation model to obtain the optimal storage rate; The UI interface includes a simulation result display area and a user operation area. The simulation result display area includes a queue type structure diagram, a cargo arrival time and system blocking rate simulation diagram, a service time and system blocking rate simulation diagram, a simulation diagram of different customer numbers and system blocking rate, and a simulation diagram of different numbers of shuttle vehicles for system blocking rate; the user operation area includes a single queue and a single service desk, a single queue and multiple service desks, and multiple queues and multiple service desks.

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