Modeling and performance analysis method for electric motor truck and barge synchronous operation system

Abstract

The application discloses a kind of electric truck tractor and shell synchronous operation system modeling and performance analysis method, comprising: constructing the semi-open queuing network model of electric truck tractor and shell synchronous operation with charging station;The original model is decomposed into first closed queuing network and second closed queuing network by decomposition algorithm, and the matrix geometric method is used to solve system steady-state probability distribution, and then the system performance index is calculated;Based on system performance index, the annual total cost minimization model is constructed, and the annual total cost minimization model is solved, to obtain the optimal configuration scheme of electric truck tractor, spare battery and charger.The present application can accurately depict the random interaction behavior of electric truck tractor in loading and unloading operation and charging process, effectively balance operation efficiency and investment cost, and provide decision support for resource allocation of port electric truck tractor and shell synchronous operation system.

Description

Technical Field

[0001] This invention relates to the field of port logistics modeling and optimization, and in particular to a method for modeling and performance analysis of a synchronous operation system for electric container trucks. Background Technology

[0002] In recent years, with the continuous development of global trade and the increasing volume of container shipping, higher demands have been placed on the operational capacity and efficiency of container terminals. Traditional fuel-powered trucks pose serious air pollution and greenhouse gas emissions problems, and are no longer suitable for the green development concept of ports in the new era. Under the guidance of the national green and low-carbon strategy, electric trucks, with their advantages of low carbon emissions, low noise, high energy efficiency, and low operating costs, are gradually replacing traditional fuel-powered trucks and becoming an inevitable trend in the future development of ports.

[0003] Simultaneous loading and unloading of containers is an efficient container terminal operation method. By changing the quay crane operation sequence, it enables trucks to achieve full-load detouring and full-load return in a complete operation process, effectively improving truck utilization and reducing empty-load driving and downtime. The combination of electric trucks and simultaneous loading and unloading can bring significant economic and environmental benefits to terminal operations.

[0004] However, due to limitations in battery range and charging technology, electric container trucks require periodic charging and battery swapping during operation, which makes the system's workflow more complex. In the synchronous operation system of electric container trucks, different links such as quay crane loading and unloading, yard crane loading and unloading, container truck transportation, and charging and battery swapping are mutually influential and coupled, which is a typical complex stochastic service system. Local optimization of a single link cannot achieve the overall system optimization. It is necessary to perform integrated modeling and analysis of the system from a global perspective.

[0005] Existing research has the following main shortcomings: In terms of modeling methods, simulation methods or simplified mathematical programming models are mostly used. The former has high computational cost and it is difficult to give analytical expressions, while the latter is difficult to accurately characterize the stochastic coupling characteristics between various links; In terms of research scope, existing research on terminal systems based on queuing networks mainly focuses on traditional fuel trucks and does not fully consider the impact of charging and battery swapping constraints of electric trucks on system performance; In terms of optimization perspective, there is a lack of systematic methods that incorporate loading and unloading operations and charging and battery swapping processes into a unified framework for analytical performance evaluation. Summary of the Invention

[0006] This invention provides a modeling and performance analysis method for a synchronous operation system of electric trucks, which overcomes the problems of high computational cost and difficulty in accurately characterizing the random coupling characteristics between various links in the prior art, as well as the problem of not fully considering the impact of the charging and swapping constraints of electric trucks on system performance.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A method for modeling and performance analysis of a synchronous operation system for electric container trucks includes: S1. Construct a semi-open queuing network for simultaneous operation of electric trucks with charging and battery swapping stations; S2. Based on the semi-open queuing network of electric trucks with charging and swapping stations operating synchronously, the first closed queuing network and the second closed queuing network are obtained through a decomposition algorithm; and the steady-state probability distribution of the system is obtained by solving the matrix geometry method; and the system performance index is calculated based on the steady-state probability distribution. S3. Based on system performance indicators, construct an annual total cost minimization model and solve the annual total cost minimization model to obtain the optimal configuration scheme of electric trucks, backup batteries and chargers.

[0008] Furthermore, the semi-open queuing network for simultaneous operation of electric trucks with charging and battery swapping stations includes: a semi-open queuing network for simultaneous operation of electric trucks and a nested semi-open queuing network for charging and battery swapping stations; the specific steps for constructing the semi-open queuing network for simultaneous operation of electric trucks and the nested semi-open queuing network for charging and battery swapping stations are as follows: S11. Establish a two-dimensional rectangular coordinate system for the synchronous loading and unloading operation area of ​​electric trucks and obtain the coordinate positions of each facility; based on the coordinate positions of each facility, obtain the first two moments of the facility service time. S12. Define service nodes based on the coordinates of each facility; S13. Based on the first two moments of service nodes and facility service time, and the synchronous loading and unloading operation process of electric trucks in the same container, construct a semi-open queuing network for synchronous operation of electric trucks in the same container; based on service nodes and electric truck charging and swapping process, construct a nested semi-open queuing network of charging and swapping stations; based on the semi-open queuing network for synchronous operation of electric trucks in the same container and the nested semi-open queuing network of charging and swapping stations, obtain a semi-open queuing network for synchronous operation of electric trucks in the same container with charging and swapping stations.

[0009] Furthermore, the coordinate positions of each facility include the complete coordinate set of the loading and unloading area, the coordinates of the charging and battery swapping station at the maximum boundary of the x-axis coordinate of the electric truck synchronous operation area, and the coordinates of the charging and battery swapping station at the bottom of the electric truck synchronous operation area; the specific steps to obtain the coordinate positions of each facility include: S111. Take the corner point of the minimum x-axis coordinate and the minimum y-axis coordinate in the synchronous operation area of ​​electric trucks as the origin and construct a two-dimensional rectangular coordinate system for the synchronous operation area of ​​electric trucks. S112. Based on the two-dimensional rectangular coordinate system of the electric container truck synchronous operation area, establish the coordinate set of the location of the shore loading and unloading area, expressed as:

[0010]

[0011] In the formula, The coordinate set for the working positions of electric container trucks in the shore loading and unloading area; This refers to the lateral offset parameter for the shoreline loading and unloading area. The width of the shore-side loading and unloading area; For the working positions of electric container trucks in the shore loading and unloading area Axis coordinates; The longitudinal offset parameter for the bottom of the shore loading and unloading area; The length of the shore-side loading and unloading area; For the working positions of electric container trucks in the shore loading and unloading area Axis coordinates; The length of the area for synchronous operation of electric container trucks; S113. Based on the two-dimensional rectangular coordinate system of the synchronous operation area of ​​electric container trucks, establish the coordinate set of the import and export container loading and unloading area, expressed as:

[0012] In the formula, A coordinate set for the working positions of electric container trucks in the import and export container loading and unloading area; The width of the area for loading and unloading import and export containers; The width of the passageway between the import / export container loading / unloading area and the shore loading / unloading area; For import and export container loading and unloading areas Axis coordinates; Electric container truck working positions in the import and export container loading and unloading area Axis coordinates; Electric container truck working positions in the import and export container loading and unloading area Axis coordinates; S114. Add the coordinate set of the quayside loading and unloading area to the coordinate set of the import and export container loading and unloading area to obtain the complete coordinate set of the loading and unloading area. The expression is:

[0013] In the formula, S For the complete coordinate set of the loading and unloading area; S115. Based on the two-dimensional rectangular coordinate system of the electric truck synchronous operation area, establish the electric truck synchronous operation area. The coordinates of the charging / swapping station at the maximum boundary of the axis coordinate system are expressed as follows:

[0014] In the formula, For electric container trucks to operate synchronously in the same area The charging and swapping station at the maximum boundary of the axis coordinate. Axis coordinates; For electric container trucks to operate synchronously in the same area The charging and swapping station at the maximum boundary of the axis coordinate. Axis coordinates; The width of the area for simultaneous operation of electric container trucks; For electric container trucks to operate synchronously in the same area Index of charging / swapping station numbers at the maximum boundary of the axis coordinate system; For electric container trucks to operate synchronously in the same area The number of charging and battery swapping stations at the maximum boundary of the axis coordinate; S116. Based on the two-dimensional rectangular coordinate system of the electric truck synchronous operation area, establish the coordinates of the charging and battery swapping station at the bottom of the electric truck synchronous operation area, expressed as:

[0015] In the formula, The charging and battery swapping station at the bottom of the synchronous operation area for electric container trucks. Axis coordinates; The charging and battery swapping station at the bottom of the synchronous operation area for electric container trucks. Axis coordinates.

[0016] Furthermore, the first two moments of the service time include the first two moments of the travel time from the electric truck's parking point to the working position, the first two moments of the travel time from the electric truck's parking point to the charging and battery swapping station, and the first two moments of the charging time of the electric truck. The expressions for the first two moments of the travel time from the electric truck's resting point to its working position are as follows:

[0017] In the formula, It is the average travel time from the electric truck's docking point to its working position, which is the first moment of the travel time from the electric truck's docking point to its working position. Number of areas for loading and unloading import / export containers; Coordinates of the electric truck's parking point; The coordinates are the locations of the loading and unloading areas for electric container trucks; It is the square of the coefficient of variation of the travel time from the electric truck's resting point to its working position, which is the second moment of the travel time from the electric truck's resting point to its working position. Let be the expected value of the square of the travel time from the electric truck's docking point to its working position; The expressions for the first two moments of the travel time from the electric truck's parking point to the charging / battery swapping station are as follows:

[0018] In the formula, It is the average travel time from the electric truck's parking point to the charging and battery swapping station, which is the first moment of the travel time from the electric truck's parking point to the charging and battery swapping station. It is the square of the coefficient of variation of the travel time from the electric truck's parking point to the charging and battery swapping station, which is the second moment of the travel time from the electric truck's parking point to the charging and battery swapping station. The expected value of the square of the travel time from the electric truck's parking point to the charging and battery swapping station;

[0019] The expressions for the first two moments of the charging time of the electric truck are:

[0020]

[0021] In the formula, For electric container trucks to operate synchronously in the same area as electric container trucks The average charging time of the charging and battery swapping station at the maximum boundary of the axis coordinate, i.e., the time for electric trucks to operate synchronously with other electric trucks in the same area. The first moment of the charging time at the charging and swapping station at the maximum boundary of the axial coordinate system; For electric container trucks to operate synchronously in the same area as electric container trucks The square of the coefficient of variation of the charging time of the charging and battery swapping station at the maximum boundary of the axial coordinate, i.e., the electric truck in the synchronous operation area of ​​the electric truck. The second moment of the charging time of the charging and swapping station at the maximum boundary of the axial coordinate; For electric container trucks to operate synchronously in the same area as electric container trucks The lower bound of the uniform distribution of service time of charging and swapping stations at the maximum boundary of the axis coordinate; For electric container trucks to operate synchronously in the same area as electric container trucks The upper bound of the uniform distribution of service time of charging and swapping stations at the maximum boundary of the axis coordinate; It is the average charging time of electric trucks at the charging and battery swapping stations at the bottom of the electric truck synchronous operation area, that is, the first moment of the charging time of electric trucks at the charging and battery swapping stations at the bottom of the electric truck synchronous operation area. It is the square of the coefficient of variation of the charging time of electric trucks at the charging and battery swapping station at the bottom of the electric truck synchronous operation area, which is the second moment of the charging time of electric trucks at the charging and battery swapping station at the bottom of the electric truck synchronous operation area. The lower bound for the uniform distribution of service time of charging and battery swapping stations at the bottom of the synchronous operation area of ​​electric trucks; This is the upper bound of the uniform distribution of service time for charging and battery swapping stations at the bottom of the synchronous operation area of ​​electric trucks.

[0022] Furthermore, step S2 specifically includes: S21. Set the arrival rate of packing transactions and the arrival rate of unpacking transactions, and aggregate the arrival rates of packing transactions and unpacking transactions into the total arrival rate; S22. Based on the first two moments of the service time, a single-class semi-open queuing network is obtained by weighting the arrival rates of packing transactions, unpacking transactions, and total arrival rates. S23. Short-circuit the loading and unloading transaction paths in the single-type semi-open queuing network to obtain the first closed queuing network containing the target work location service node, the work service node, and the storage node. S24. Short-circuit the charging and swapping service paths in the single-type semi-open queuing network to obtain a second closed queuing network that includes charging station service nodes, swapping station service nodes, battery charging service nodes, and return dwell point service nodes. S25. Solve the first closed queuing network and the second closed queuing network respectively by the approximate mean value analysis method to obtain the service rate of the first closed queuing network and the service rate of the second closed queuing network. S26. Based on the service rates of the first closed queuing network and the second closed queuing network, the steady-state probability distribution of the system is obtained by solving the problem using the matrix geometry method.

[0023] Furthermore, the annual total cost minimization model aims to minimize the cost of the electric truck synchronous operation system, and is constrained by the throughput time constraint of the packing transaction and the constraint that the number of spare batteries is equal to the number of chargers. The objective function of the annual total cost minimization model is expressed as follows:

[0024] In the formula, Total annual cost; This refers to the number of electric container trucks; The number of backup battery chargers at the battery swapping station; This refers to the number of spare batteries; Annual cost of electric trucks; Annual cost for a single backup battery charger; Annual cost for a single backup battery; The expression for the bin packing transaction throughput time constraint is:

[0025] In the formula, For the throughput time of packing transactions; This is the preset throughput time threshold for packing transactions; The expression for the constraint that the number of backup batteries is equal to the number of chargers is: .

[0026] Beneficial effects: The modeling and performance analysis method of the electric truck synchronous operation system of the present invention, by constructing a semi-open queuing network for electric truck synchronous operation with charging and battery swapping stations, can truly reflect the random interaction characteristics of electric trucks in multiple stages such as loading and unloading, waiting, charging and battery swapping. It overcomes the limitation of traditional models that ignore energy supply constraints and fully depicts the random coupling characteristics of loading and unloading process and charging and battery swapping process under a unified framework. By using a decomposition algorithm to transform the complex semi-open network into two closed queuing networks, and combining matrix geometry methods to solve the steady-state probability distribution, the complexity of model solving is significantly reduced while ensuring computational accuracy. This enables the rapid acquisition of key performance indicators such as system throughput, average waiting time, and utilization rate of charging and swapping facilities. Based on system performance indicators, an annual total cost minimization model is constructed, which simultaneously optimizes the number of electric trucks, spare batteries, and chargers. This breaks through the limitations of previous independent or experience-based configurations and can provide the optimal configuration solution from a global economic perspective, effectively balancing equipment investment and operating waiting costs. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart illustrating the system modeling and performance analysis method of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] This embodiment provides a method for modeling and performance analysis of a synchronous operation system for electric container trucks, such as... Figure 1 As shown, it includes: S1. Construct a semi-open queuing network for simultaneous operation of electric trucks with charging and battery swapping stations; Specifically, this embodiment describes a complete container terminal system that uses pure electric trucks as horizontal transport vehicles and employs synchronous loading and unloading technology to perform container loading and unloading operations as well as charging and battery swapping processes for electric trucks. In this system, electric trucks can move within the system's internal channels and reach their operating positions to complete loading and unloading operations. Charging stations are located at the system's boundaries to facilitate charging and battery swapping for electric trucks. The channels are arranged along the x and y axes, allowing electric trucks to move and perform loading and unloading tasks within the channels. When container ships arrive at the port, electric trucks need to perform container transportation tasks between the quay, the import container area, the export container area, and the charging and battery swapping station. Electric trucks perform container loading tasks at the quay, then transport imported containers to the import container area, where they unload them. They then drive empty to the export container area to perform container loading operations. They transport export containers to the quay, and then perform unloading operations. If the electric truck runs out of power during the entire loading and unloading process, it is guided to the electric truck charging and battery swapping station to replenish its energy before returning to the entire loading and unloading process. Given that different operational processes in the electric container truck synchronous operation system influence each other, it is a complex stochastic service system. The improvement of the system efficiency depends on the effective coordination between each link. The configuration and scheduling of electric container trucks directly affect the loading and unloading efficiency of quay cranes and yard cranes. In this embodiment, a semi-open queuing network (SOQN) is established to evaluate and analyze the system performance. The charging process of electric container trucks is modeled as a single queue, and the battery exchange process of electric container trucks is modeled as a nested SOQN. The transactions in the electric container truck synchronous loading and unloading system include container loading and unloading transactions; the container loading and unloading process, i.e., the electric container truck synchronous loading and unloading operation process, includes the following steps: Expected waiting time for a transaction to wait in an external queue for an available electric truck. This embodiment assumes that the arrival of both loading and unloading transactions follows a Poisson process; and that the allocation of electric trucks to transactions follows a random rule, i.e., if all electric trucks are in a transaction or charging process, the system will allocate the first available truck to the transaction; otherwise, the system will randomly allocate an idle node to the transaction; or the electric truck closest to the workstation can be allocated to the transaction to complete the work in a timely manner. (b) The electric truck moves from its station to the target working position, where the loading and unloading operations will take place, in a time period of [time missing]. This embodiment considers the acceleration and deceleration of the electric truck; the electric truck will move to the destination via the designated shortest path; the electric truck will move to the target location to perform the designated loading and unloading operations. One workstation is dedicated to the packing operation. Each workstation is dedicated to unloading operations; the travel times are respectively... and The working positions of electric container trucks can be changed to loading and unloading positions according to specific business needs; the allocation of loading and unloading operations follows random rules. (c) If the yard crane and quay crane are busy, the electric trucks will queue at their working positions; for loading positions, the waiting time for the electric trucks is [time period missing]. For the unloading work position, the waiting time for the electric container truck is... ; (d) During the container loading service, the yard crane and quay crane will place the designated container on the ship or inside the yard onto the corresponding electric truck; during the container unloading service, the yard crane and quay crane will unload the container transported by the electric truck and place it on the ship or in the designated location in the yard. (e) After completing its work, the electric container truck will move to the storage location to await new tasks (i.e., work completion); the movement time is the time required for the packing task. And unloading affairs This embodiment adopts a Point Service Complete (POSC) residence strategy, whereby the electric truck will reside at the location where the transaction is completed. (f) In this system, regarding the charging problem of electric trucks, this embodiment considers a charging and battery swapping strategy. After the electric truck completes a transaction, the system checks its battery level and guides the depleted electric truck to a charging and battery swapping station for energy replenishment; the probability of the electric truck being depleted upon completion of a transaction is expressed as... The travel time for an electric truck with depleted battery to reach a charging station is When the battery is fully restored, the electric truck will take approximately [time] to move to the resting point. ; In the electric truck synchronous loading and unloading operation system, the electric truck charging and battery swapping station consists of three components: a battery charger, a spare battery inventory, and a battery exchange mechanism. A depleted electric truck is guided to the charging and battery swapping station, where its battery is replaced. If the spare battery is exhausted, the electric truck will queue up until a battery becomes available. It is assumed that the battery swapping time follows a uniform distribution U[3600,4200] seconds and is added to the spare battery inventory. This embodiment assumes that the battery exchange mechanism has sufficient capacity. Spare batteries and battery chargers are the main resources affecting the efficiency and cost of the charging and battery swapping station. The electric truck charging and battery swapping station is located at the system boundary. This embodiment assumes that there is sufficient space for waiting electric trucks.

[0031] Preferably, the semi-open queuing network for simultaneous operation of electric trucks with charging and battery swapping stations includes: a semi-open queuing network for simultaneous operation of electric trucks and a nested semi-open queuing network for charging and battery swapping stations; the specific steps for constructing the semi-open queuing network for simultaneous operation of electric trucks and the nested semi-open queuing network for charging and battery swapping stations are as follows: S11. Establish a two-dimensional rectangular coordinate system for the synchronous loading and unloading operation area of ​​electric trucks and obtain the coordinate positions of each facility; based on the coordinate positions of each facility, obtain the first two moments of the facility service time. Preferably, the coordinate positions of each facility include the complete coordinate set of the loading and unloading area, the coordinates of the charging and battery swapping station at the maximum boundary of the x-axis coordinate of the electric truck synchronous operation area, and the coordinates of the charging and battery swapping station at the bottom of the electric truck synchronous operation area; the specific steps to obtain the coordinate positions of each facility include: S111. Take the corner point of the minimum x-axis coordinate and the minimum y-axis coordinate in the synchronous operation area of ​​electric trucks as the origin and construct a two-dimensional rectangular coordinate system for the synchronous operation area of ​​electric trucks. In this embodiment, the rectangular area covered by the two-dimensional rectangular coordinate system is referred to as the system operation area; S112. Based on the two-dimensional rectangular coordinate system of the electric container truck synchronous operation area, establish the coordinate set of the location of the shore loading and unloading area, expressed as:

[0032]

[0033] In the formula, The coordinate set for the working positions of electric container trucks in the shore loading and unloading area; This refers to the lateral offset parameter for the shoreline loading and unloading area. The width of the shore-side loading and unloading area; For the working positions of electric container trucks in the shore loading and unloading area Axis coordinates; The longitudinal offset parameter for the bottom of the shore loading and unloading area; The length of the shore-side loading and unloading area; For the working positions of electric container trucks in the shore loading and unloading area Axis coordinates; The length of the area for synchronous operation of electric container trucks; S113. Based on the two-dimensional rectangular coordinate system of the synchronous operation area of ​​electric container trucks, establish the coordinate set of the import and export container loading and unloading area, expressed as:

[0034] In the formula, A coordinate set for the working positions of electric container trucks in the import and export container loading and unloading area; The width of the import and export container loading and unloading area; The width of the passageway between the import / export container loading / unloading area and the shore loading / unloading area; For import and export container loading and unloading areas Axis coordinates; Electric container truck working positions in the import and export container loading and unloading area Axis coordinates; Electric container truck working positions in the import and export container loading and unloading area Axis coordinates; S114. Add the coordinate set of the quayside loading and unloading area to the coordinate set of the import and export container loading and unloading area to obtain the complete coordinate set of the loading and unloading area. The expression is:

[0035] In the formula, S For the complete coordinate set of the loading and unloading area; S115. Based on the two-dimensional rectangular coordinate system of the electric truck synchronous operation area, establish the electric truck synchronous operation area. The coordinates of the charging / swapping station at the maximum boundary of the axis coordinate system are expressed as follows:

[0036] In the formula, For electric container trucks to operate synchronously in the same area The charging and swapping station at the maximum boundary of the axis coordinate. Axis coordinates; For electric container trucks to operate synchronously in the same area The charging and swapping station at the maximum boundary of the axis coordinate. Axis coordinates; The width of the area for simultaneous operation of electric container trucks; For electric container trucks to operate synchronously in the same area Index of charging / swapping station numbers at the maximum boundary of the axis coordinate system; For electric container trucks to operate synchronously in the same area The number of charging and battery swapping stations at the maximum boundary of the axis coordinate; S116. Based on the two-dimensional rectangular coordinate system of the electric truck synchronous operation area, establish the coordinates of the charging and battery swapping station at the bottom of the electric truck synchronous operation area, expressed as:

[0037] In the formula, The charging and battery swapping station at the bottom of the synchronous operation area for electric container trucks. Axis coordinates; The charging and battery swapping station at the bottom of the synchronous operation area for electric container trucks. Axis coordinates.

[0038] S12. Define service nodes based on the coordinates of each facility; Specifically, the process of defining a service node is as follows: When a loading / unloading process is required, an available electric truck will be declared, corresponding to a synchronization node consisting of two queues, which are transaction queues. and electric truck queue If electric truck queue If there are electric container trucks, they will be randomly selected from the electric container truck queue according to random rules. The system will accept an electric truck and leave the synchronization node; otherwise, it will leave the transaction queue. The first available electric truck waiting in the waiting area is claimed; then, the electric truck moves from its station to the target working position to carry out loading and unloading operations. Once the electric container truck moves to the loading position, the coordinates of that position are set as the service node. This is used to represent a packing transaction; if an unpacking operation is performed, the coordinates of this location are set as the service node coordinates. This indicates the unloading process. Electric container trucks are based on probability. Move to the packing work position With probability Move to the unloading work position Once the electric container truck arrives at the designated location, if the quay crane or yard crane is busy, it will queue up at the target location and wait. At the container loading location, quay cranes and yard cranes place containers from the ship or at designated locations in the yard onto corresponding electric trucks; this location is modeled as a service node. At the unloading work location, quay cranes and yard cranes unload containers from electric trucks and place them on the ship or at a designated location in the yard, which is modeled as a service node. ; In the electric container truck queuing network system, a battery charging and swapping strategy is used. The system checks the electric container truck's battery after loading and unloading transactions are completed, and the electric container truck... The probability of running out of power and heading to a charging / swapping station, which is modeled as an infinite number of charging / swapping service nodes, is high. Once the electric truck's battery is fully restored, it will be modeled as a battery swapping service node. and battery charging service nodes The electric truck returns to the previous dwell point and is modeled as an infinitely dwelling service node. Electric container trucks The probability serves the next transaction, corresponding to the entry into the queue. ; S13. Based on the first two moments of service nodes and facility service time, and the synchronous loading and unloading operation process of electric trucks in the same container, construct a semi-open queuing network for synchronous operation of electric trucks in the same container; based on service nodes and electric truck charging and swapping process, construct a nested semi-open queuing network of charging and swapping stations; based on the semi-open queuing network for synchronous operation of electric trucks in the same container and the nested semi-open queuing network of charging and swapping stations, obtain a semi-open queuing network for synchronous operation of electric trucks in the same container with charging and swapping stations.

[0039] Specifically, the semi-open queuing network for simultaneous operation of electric container trucks is defined according to the logic of the simultaneous loading and unloading operation of electric container trucks, with each service link as a node and the container truck flow route as an edge, and the topology of the semi-open queuing network is defined; the topology includes at least synchronization nodes, internal service node chains, service rates of service nodes, and charging and swapping branches; the service rate of each service node is determined by the first two moments of the facility service time. The nested semi-open queuing network of the charging and battery swapping station, with a backup battery queue With the queue of trucks running out of power The system forms a synchronization node. After the truck exhausts its battery and claims a spare battery, it passes through the battery swapping service node and the battery charging service node in sequence to complete the closed-loop process of battery exchange and recycling charging. The backup batteries are additional resources that will be synchronized with the depleted electric trucks; the depleted electric trucks first claim a backup battery at the synchronization node, and this backup battery is then assigned to the backup battery queue. And queue of electric trucks with depleted battery Composition; if If a battery is available, the electric truck that has run out of power will randomly claim one; otherwise, the electric truck will... Waiting in the middle; then, at the battery charging service node The depleted battery is swapped with a backup battery, and the electric truck moves to its previous parking spot; then, the depleted battery moves to the charging process, which is also modeled as having… A single queue for each server.

[0040] Preferably, the first two moments of the service time include the first two moments of the travel time from the electric truck's parking point to the working position, the first two moments of the travel time from the electric truck's parking point to the charging and battery swapping station, and the first two moments of the charging time of the electric truck. The expressions for the first two moments of the travel time from the electric truck's resting point to its working position are as follows:

[0041] In the formula, It is the average travel time from the electric truck's docking point to its working position, which is the first moment of the travel time from the electric truck's docking point to its working position. Number of areas for loading and unloading import / export containers; Coordinates of the electric truck's parking point; The coordinates are the locations of the loading and unloading areas for electric container trucks; It is the square of the coefficient of variation of the travel time from the electric truck's resting point to its working position, which is the second moment of the travel time from the electric truck's resting point to its working position. Let be the expected value of the square of the travel time from the electric truck's docking point to its working position; Specifically, the steps for deriving the first two moments of the travel time from the electric truck's dwell point to its working position are as follows: The electric truck needs to travel along the passage to reach the designated location, so it needs to choose the shortest rectangular path to reach the target location; if the shortest distance is traveled from the upper passage of the system, then the travel distance is:

[0042] In the formula, This represents the distance traveled through the upper passage. electric truck parking points Axis coordinates; electric truck parking points Axis coordinates; This embodiment adopts a POSC residency point strategy. Coordinates of the target working position All are sets The elements in the set have a selection probability of 1. ; If the shortest distance is to travel through the lower passage of the system, then the travel distance is:

[0043] In the formula, This represents the distance traveled in the lower passage. The shortest travel distance is obtained by comparing the distance traveled in the upper passage with the distance traveled in the lower passage. ; Considering the acceleration of the electric truck, the travel time from the parking point to the working position is:

[0044] In the formula, The travel time from the electric truck's parking point to its working position; This refers to the maximum driving speed of the electric container truck. For the acceleration (deceleration) of electric trucks; The first two moments of the travel time from the dwelling point to the working position of the electric truck are obtained by weighted averaging of the squares of the mean and the coefficient of variation over all combinations of dwelling points and target positions in the complete coordinate set S of the loading and unloading area. Travel time of electric container trucks from their resting point to their working location Travel time of electric trucks from their work location to their station The first two moments are the same, that is , ; The expressions for the first two moments of the travel time from the electric truck's parking point to the charging / battery swapping station are as follows:

[0045] In the formula, It is the average travel time from the electric truck's parking point to the charging and battery swapping station, which is the first moment of the travel time from the electric truck's parking point to the charging and battery swapping station. It is the square of the coefficient of variation of the travel time from the electric truck's parking point to the charging and battery swapping station, which is the second moment of the travel time from the electric truck's parking point to the charging and battery swapping station. The expected value of the square of the travel time from the electric truck's parking point to the charging and battery swapping station; Specifically, the steps for deriving the first two moments of the travel time from the electric truck's parking point to the charging / swapping station are as follows: When the electric truck runs out of power, it needs to go to a designated charging and battery swapping station to replenish its energy. Since the charging stations are evenly distributed at the bottom and right side of the system, there are two situations. When the designated charging / swapping station is located at the bottom of the system, the travel distance is:

[0046] In the formula, The travel distance of the bottom charging and battery swapping stations; When the designated charging / swapping station is located on the right side of the system, if the shortest travel distance is via the upper passage, then the distance is:

[0047] In the formula, The distance traveled by the charging and battery swapping station on the right through the upper passage; When the designated charging / swapping station is located on the right side of the system, if the shortest travel distance is via the lower passage, then the distance is:

[0048] In the formula, The distance traveled by the charging and battery swapping station on the right via the lower passage; By comparing the travel distance of the bottom charging / battery swapping station, the travel distance of the right-side charging / battery swapping station via the upper passage, and the travel distance of the right-side charging / battery swapping station via the lower passage, the shortest travel distance was obtained. ; Considering the acceleration of the electric truck, the travel time from the truck's parking point to the charging / battery swapping station is:

[0049] In the formula, The travel time from the electric truck's parking point to its working position; The first two moments of the travel time from the electric truck's parking point to the charging / battery swapping station are obtained by weighting the squares of the mean and the coefficient of variation on the combination of the charging / battery swapping parking point and the target location in the complete coordinate set S of the loading and unloading area. Travel time of electric trucks from their parking location to the charging / battery swapping station Electric trucks return to their parking positions from the charging and battery swapping station. The first two moments of the travel time are the same, that is... , ; The service rates of electric trucks from their parking location to the charging / battery swapping station and from the charging / battery swapping station back to their parking location are respectively and .

[0050] This embodiment assumes that the service time of the right-side charging and swapping station follows... Bottom charging and battery swapping stations obey ; The expressions for the first two moments of the charging time of the electric truck are:

[0051]

[0052] In the formula, For electric container trucks to operate synchronously in the same area as electric container trucks The average charging time of the charging and battery swapping station at the maximum boundary of the axis coordinate, i.e., the time for electric trucks to operate synchronously with other electric trucks in the same area. The first moment of the charging time at the charging and swapping station at the maximum boundary of the axial coordinate system; For electric container trucks to operate synchronously in the same area as electric container trucks The square of the coefficient of variation of the charging time of the charging and battery swapping station at the maximum boundary of the axial coordinate, i.e., the electric truck in the synchronous operation area of ​​the electric truck. The second moment of the charging time of the charging and swapping station at the maximum boundary of the axial coordinate; For electric container trucks to operate synchronously in the same area as electric container trucks The lower bound of the uniform distribution of service time of charging and swapping stations at the maximum boundary of the axis coordinate; For electric container trucks to operate synchronously in the same area as electric container trucks The upper bound of the uniform distribution of service time of charging and swapping stations at the maximum boundary of the axis coordinate; It is the average charging time of electric trucks at the charging and battery swapping stations at the bottom of the electric truck synchronous operation area, that is, the first moment of the charging time of electric trucks at the charging and battery swapping stations at the bottom of the electric truck synchronous operation area. It is the square of the coefficient of variation of the charging time of electric trucks at the charging and battery swapping station at the bottom of the electric truck synchronous operation area, which is the second moment of the charging time of electric trucks at the charging and battery swapping station at the bottom of the electric truck synchronous operation area. The lower bound for the uniform distribution of service time of charging and battery swapping stations at the bottom of the synchronous operation area of ​​electric trucks; This is the upper bound of the uniform distribution of service time for charging and battery swapping stations at the bottom of the synchronous operation area of ​​electric trucks.

[0053] S2. Based on the semi-open queuing network of electric trucks with charging and swapping stations operating synchronously, the first closed queuing network and the second closed queuing network are obtained through a decomposition algorithm; and the steady-state probability distribution of the system is obtained by solving the matrix geometry method; and the system performance index is calculated based on the steady-state probability distribution. Preferably, step S2 specifically includes: S21. Set the arrival rate of packing transactions and the arrival rate of unpacking transactions, and aggregate the arrival rates of packing transactions and unpacking transactions into the total arrival rate; Specifically, the loading and unloading services for electric container trucks will be integrated into one customer's business. The total arrival rate is:

[0054] In the formula, This is the set of arrival rates for packing transactions; For the arrival rate of unloading transactions; S22. Based on the first two moments of the service time, a single-class semi-open queuing network is obtained by weighting the arrival rates of packing transactions, unpacking transactions, and total arrival rates. Specifically, the weighted average of the packing transaction arrival rate, unpacking transaction arrival rate, and total arrival rate can be expressed as:

[0055] In the formula, For transaction type Arrival rate; For service nodes For transaction types Service speed; For service nodes The square of the coefficient of variation of the aggregated service time; For service nodes For transaction types The square of the coefficient of variation of service time; For service nodes The aggregated service rate is the weighted average service rate with the arrival rates of various types of transactions as weights. Wherein, the coefficient of squared variation is Each service node Aggregation reach ,in To access service nodes A collection of transactions.

[0056] S23. Short-circuit the loading and unloading transaction paths in the single-type semi-open queuing network to obtain the first closed queuing network containing the target work location service node, the work service node, and the storage node. Specifically, the transaction portion is short-circuited to construct a separate first closed queuing network (CQN1), serving nodes from the dwell point to the target working location. Work service nodes and target working location to storage node composition; S24. Short-circuit the charging and swapping service paths in the single-type semi-open queuing network to obtain a second closed queuing network that includes charging station service nodes, swapping station service nodes, battery charging service nodes, and return dwell point service nodes. Specifically, the charging and battery swapping process of electric trucks is short-circuited to construct a second closed queuing network (CQN2), from the target location to the charging station service node. Battery swapping nodes Battery charging service nodes Return to the target location with the charging station service node composition; S25. Solve the first closed queuing network and the second closed queuing network respectively by the approximate mean value analysis method to obtain the service rate of the first closed queuing network and the service rate of the second closed queuing network. Specifically, the Approximate Mean Value Analysis (AMVA) method is used to derive the load-related throughput of the first closed queuing network. ,in It is the number of customers aggregated in the first closed queuing network; then, the transaction service part is replaced by composite service nodes with load-related service rates of exponential distribution; the load-related service rate is equal to the throughput of the first closed queuing network under a given number of electric trucks, i.e. ,in, Let the load-related service rate of the first closed queuing network be given the number of electric trucks. The approximate mean analysis method is existing technology and will not be described in detail here. In order to obtain the throughput of the second closed queuing network, this embodiment first independently analyzes the battery exchange and charging process inside the second closed queuing network, and then replaces it with a load-dependent server. Assume that during the battery exchange and charging process within the second closed queuing network, there are... Electric container trucks, when ≤ Define the state variables of the battery exchange and charging process within the second closed queuing network as follows: ,in and Let be the number of electric trucks at the battery swapping node and the charging node, respectively. By solving the Markov chain process at the bottom layer of the battery swapping and charging process within the second closed queuing network, the state probabilities of the battery swapping and charging process within the second closed queuing network can be obtained from the following formula. Throughput related to load :

[0057] In the formula, Let be the number of batteries actually being charged in the charging node under a given state, and ,in, Total number of backup batteries. Index of the current state variable, Number of chargers; The number of customers aggregated in the first closed queuing network; The number of electric trucks in the second closed queuing network; This represents the number of electric trucks involved in the battery exchange and charging process within the second closed queuing network; the subscript numbers correspond one-to-one with the closed subnetwork numbers. , These are all enumerated variables in the AMVA solution process, which are traversed one by one within their respective value ranges and are not fixed parameters specified by humans. In obtaining Subsequently, the battery swapping and charging process within the second closed queuing network is replaced with load-related service rates. The composite service node is then solved using the AMVA method to obtain its load-related throughput. Therefore, the load-related service rate of the first closed queuing network under a given number of electric trucks can be obtained. .

[0058] S26. Based on the service rates of the first closed queuing network and the second closed queuing network, the steady-state probability distribution of the system is obtained by solving the problem using the matrix geometry method.

[0059] Specifically, the steps for solving the problem using matrix geometry methods are as follows: The state variables of the simplified nested semi-open queuing network of charging and swapping stations are defined as follows: ,in, It is an external queue The number of waiting transactions. For the status indicator, the expression is:

[0060] In the formula, The number of customers aggregated in the first closed queuing network; This represents the total number of electric trucks in the system. The number of customers aggregated in the second closed queuing network; set up for The steady-state probability is defined as the steady-state probability vector. and ; Based on the state transition process, the generator matrix Q can be represented as a block tridiagonal structure, and the generator matrix Q has a repeating structure; the recursive relationship of the steady-state probability can be established using the structure of the generator matrix Q as follows:

[0061] In the formula, For the first Layer steady-state probability; For the first Layer steady-state probability; The transition probability matrix; This is the hierarchical number of the steady-state probability vector.

[0062] Where G is the transition probability matrix, satisfying:

[0063] In the formula, external queue The state transition rate submatrix when the number of waiting transactions increases by 1; external queue The state transition rate submatrix when the number of waiting transactions remains constant; external queue The state transition rate submatrix when the number of waiting transactions decreases by 1; all three are generator matrices. Components of a block tri-diagonal repeating structure; in, , It is obtained based on the service rates of the first closed queuing network and the second closed queuing network; when the first closed queuing network is at... The service is completed at a certain speed, allowing an electric truck to leave the first closed queuing network, at which point... Write matrix ; The transition probability matrix is ​​obtained through the following iterative method: Initialize the transition probability matrix to And set the convergence precision ; The transition probability matrix is ​​calculated iteratively, and its expression is: ; The iterative calculation ends when the convergence condition is met; the convergence condition is if... If the result is positive, increment the time by 1 and continue the calculation; otherwise, set the time to zero. And terminate the iteration.

[0064] In this embodiment, the following equation holds when a steady state is reached:

[0065]

[0066] Combining the two equations above, we can obtain the steady-state probability. , ,as well as .

[0067] Specifically, the system performance indicators include the expected waiting time for loading and unloading transactions, the expected waiting time in loading and unloading transactions, the expected waiting time for electric trucks with depleted batteries to the charging station, the utilization rate of electric trucks, the utilization rate of quay cranes and yard cranes, the throughput time, and the battery depletion rate. The expected waiting time and throughput time for the loading and unloading transactions are calculated based on the steady-state probability distribution. The expression for the expected waiting time of the electric container truck loading and unloading transactions is:

[0068] In the formula, Expected waiting time for loading services for electric container trucks; Expected waiting time for unloading containers from electric container trucks; The expected quantity of the packing transaction; The expected number of unloading transactions; in, and The expression is:

[0069]

[0070] In the formula, external queue The expected number of aggregated customers is expressed as: ; The expression for the expected waiting time of the electric container truck in loading and unloading transactions is:

[0071] In the formula, Expected waiting time for loading containers for electric trucks; Expected waiting time for unloading containers from electric container trucks; and The expected number of customers aggregated in the packing and unpacking business queues are respectively calculated by weighted summation of AMVA under different load conditions; The expression for the expected waiting time of the electric truck with depleted battery at the charging station is:

[0072] In the formula, The expected waiting time for the transaction; The number of depleted electric trucks that are expected to wait to enter a charging station for charging. The probability that an electric truck will run out of power after completing a transaction; To aggregate customer reach rates; The expression for the utilization rate of the electric truck is:

[0073] In the formula, To improve the utilization rate of electric trucks; and The expected number of aggregated customers for composite service nodes; This represents the total number of electric trucks; The utilization rate of quay cranes and yard cranes during container loading and unloading operations. and Obtained through AMVA respectively and (i.e., composite business node) have The weighted sum of the probability of busy conditions when quay cranes and yard cranes are handling container loading and unloading for each customer is calculated and the steady-state probability is obtained. The expression for the throughput time is:

[0074]

[0075] In the formula, For the throughput time of packing transactions; For the throughput time of unloading transactions; The expected quantity of the packing transaction; The expected number of unloading transactions; The number of workstations for packing tasks; The number of workstations for unloading containers; For electric truck parking points to the first Average travel time for each packing task location; For electric truck parking points to the first Average travel time for each unloading task location; The expected waiting time in the packing process; The expected waiting time during the unloading process; The power depletion rate is given by assuming the voltage of the electric truck battery is... The battery capacity of the electric truck is Assuming the electric truck's battery has 5% remaining charge, it is considered that the electric truck is depleted. Therefore, the energy a fully charged battery can provide is:

[0076] In the formula, The energy that a fully charged battery can provide; This refers to the voltage of the battery in the electric truck. Battery capacity for electric trucks; During loading or unloading operations, the usage time of electric container truck batteries is used for... express, ,in Let the time consumed by the electric container truck during a single loading and unloading operation be denoted as ; and These represent the energy consumed per second during the operation of a fully loaded electric container truck and an unloaded electric container truck, respectively. The energy consumed during packing and unpacking operations; over a duration of During the cycle, the energy of the electric truck battery decreases. ; Therefore, a fully charged electric truck can perform a total of [number] transactions. Since the average number of transactions completed per hour is Therefore, the maximum operating time of an electric container truck when fully charged is The probability that the electric truck's battery will be depleted after the transaction is completed can be calculated using the following formula: .

[0077] S3. Based on system performance indicators, construct an annual total cost minimization model and solve the annual total cost minimization model to obtain the optimal configuration scheme of electric trucks, backup batteries and chargers.

[0078] In this embodiment, the cost minimization problem of a semi-open queuing network for simultaneous operation of electric container trucks with charging and battery swapping stations is modeled as an annual total cost minimization model; the examined electric container truck simultaneous operation system has a given number of inlet and outlet container areas. A fixed number of quay cranes, yard cranes, and fixed number of electric container truck working positions. Number of fixed electric truck charging and battery swapping stations And the arrival rate of packing and unpacking transactions. and ; Preferably, the annual total cost minimization model aims to minimize the cost of the electric truck synchronous operation system, and is constrained by the throughput time constraint of the packing transaction and the constraint that the number of spare batteries is equal to the number of chargers. The objective function of the annual total cost minimization model is expressed as follows:

[0079] In the formula, Total annual cost; This refers to the number of electric container trucks; The number of backup battery chargers at the battery swapping station; This refers to the number of spare batteries; Annual cost of electric trucks; Annual cost for a single backup battery charger; Annual cost for a single backup battery; The expression for the bin packing transaction throughput time constraint is:

[0080] In the formula, For the throughput time of packing transactions; This is the preset throughput time threshold for packing transactions; The expression for the constraint that the number of backup batteries is equal to the number of chargers is: .

[0081] Specifically, the annual total cost minimization model is solved by using gradient descent or a genetic algorithm to solve the problem based on the number of electric trucks, spare batteries, and chargers. These are existing technologies and will not be described in detail here.

[0082] In this embodiment, the optimal configuration scheme is determined by iteratively optimizing the number of electric trucks, spare batteries, and chargers under the constraint of packing transaction throughput time, using these as decision variables. This minimizes the total annual cost. In the optimal configuration scheme, the ratio of electric trucks to spare batteries and chargers is reasonably balanced, ensuring that the system has neither idle resources nor performance bottlenecks caused by insufficient resources. This achieves a stable and lower total annual cost while meeting the set packing throughput time requirements, thus realizing the optimal balance between operational efficiency and system cost.

[0083] In this embodiment, by surveying actual port operation data and current mainstream electric container truck data, an algorithm constructed using Python is used to analyze and evaluate various indicators of the electric container truck synchronous loading and unloading operation system. To analyze the operational capacity of the electric container truck synchronous system, it is assumed that the service times of quay cranes and yard cranes both follow a negative exponential distribution, and the battery swapping time of electric container trucks follows a uniform distribution U[3600,4200] seconds. Since the service rates of yard cranes in the import and export container yards are not significantly different, the number of yard cranes in the import and export container yards is set to be the same to balance the operational capacity of the import and export container yards. The maximum number of quay cranes deployed in loading and unloading operations is set to 5, and the number of yard cranes in the import container yard is set to 5. The verification objectives include the impact of the number of backup batteries on system throughput time, the impact of the number of electric trucks on system throughput time, the impact of electric truck battery degradation on system throughput time, and optimization of system annual cost. The impact of the number of backup batteries on system throughput time is as follows: assuming the system has a fixed fleet of 80 electric trucks performing transportation tasks, and the number of backup batteries is equal to the number of chargers. The electric truck has an initial battery level of 100%, and the number of backup batteries at the charging and battery swapping station is [number missing]. The number of batteries varied from 5 to 50. The results showed that when the number of electric trucks in the system remained constant and only the number of backup batteries was changed, the waiting time of electric trucks at the charging and battery swapping station decreased as the number of backup batteries increased, and the system gradually reached a stable state. The system performance indicators, throughput and time, no longer changed. The system began to stabilize when the number of backup batteries reached about 30 and basically stabilized when the number of backup batteries reached about 47. The impact of the number of electric trucks on system throughput time is as follows: The number of batteries in the electric truck charging / swapping stations is set to 50, the initial battery level of the electric trucks is 100%, and the number of electric trucks R varies from 0 to 100. The results show that as the number of electric trucks increases, the waiting time of the electric trucks at the quay crane yard gradually decreases, the number of charging / swapping operations decreases, the system throughput gradually decreases, and the system gradually reaches a stable state. The system begins to stabilize when the number of electric trucks reaches approximately 60, and basically stabilizes when the number of electric trucks reaches approximately 76. The impact of electric truck battery degradation on system throughput time was investigated by setting the number of backup batteries at the electric truck charging and swapping stations in the system to 50 and the number of electric trucks to 80. The initial battery charge of the electric trucks was used to represent different degrees of battery degradation, ranging from 10% to 100%. The results showed that the higher the degree of battery degradation (i.e., the lower the initial charge), the longer the system waiting time, and the throughput time variation was basically linear with the degree of battery degradation. The system's annual cost optimization is achieved by calculating the time required for each throughput through numerical experiments. The corresponding minimum cost was used to verify the trade-off between system performance and system cost; the results show that as As the throughput increases, the overall system cost gradually decreases. Based on performance analysis, the optimal system throughput is between 250 and 300 seconds, corresponding to an optimal system cost range of approximately $80,000 to $100,000. By rationally configuring the number of electric trucks, spare batteries, and chargers, a cost-benefit balance can be achieved while ensuring operational efficiency. Based on the verification results, the modeling and performance analysis method in this embodiment constructs a model of a synchronous loading and unloading operation system for electric container trucks based on a semi-open queuing network, realizing integrated modeling and analysis of the charging and swapping process of electric container trucks and the loading and unloading operation process. By combining decomposition and matrix geometry methods, analytical expressions for various performance indicators under steady-state conditions are obtained. Through a cost minimization model, a quantitative optimization scheme for system resource allocation is provided. This invention can effectively simulate real terminal operation scenarios, providing a practical and feasible solution reference for the electrification of port container trucks, and providing theoretical research and decision-making reference for the optimization of multi-equipment resource collaborative operation processes in container terminal loading and unloading operations, showing significant application prospects.

[0084] The present invention has the following beneficial effects: The present invention provides a modeling and performance analysis method for electric truck synchronous operation system. By constructing a semi-open queuing network for electric truck synchronous operation with charging and battery swapping stations, it can realistically reflect the random interaction characteristics of electric trucks in multiple stages such as loading and unloading, waiting, charging and battery swapping. It overcomes the limitation of traditional models that ignore energy supply constraints and fully depicts the random coupling characteristics of loading and unloading process and charging and battery swapping process under a unified framework. By using a decomposition algorithm to transform the complex semi-open network into two closed queuing networks, and combining matrix geometry methods to solve the steady-state probability distribution, the complexity of model solving is significantly reduced while ensuring computational accuracy. This enables the rapid acquisition of key performance indicators such as system throughput, average waiting time, and utilization rate of charging and swapping facilities. Based on system performance indicators, an annual total cost minimization model is constructed, which simultaneously optimizes the number of electric trucks, spare batteries, and chargers. This breaks through the limitations of previous independent or experience-based configurations and can provide the optimal configuration solution from a global economic perspective, effectively balancing equipment investment and operating waiting costs.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for modeling and performance analysis of a synchronous operation system for electric container trucks, characterized in that, include: S1. Construct a semi-open queuing network for simultaneous operation of electric trucks with charging and battery swapping stations; S2. Based on the semi-open queuing network of electric trucks with charging and swapping stations operating synchronously, the first closed queuing network and the second closed queuing network are obtained through a decomposition algorithm; and the steady-state probability distribution of the system is obtained by solving the matrix geometry method; and the system performance index is calculated based on the steady-state probability distribution. S3. Based on system performance indicators, construct an annual total cost minimization model and solve the annual total cost minimization model to obtain the optimal configuration scheme of electric trucks, backup batteries and chargers.

2. The method for modeling and performance analysis of a synchronous operation system for electric container trucks according to claim 1, characterized in that, The semi-open queuing network for simultaneous operation of electric trucks with charging and battery swapping stations includes: a semi-open queuing network for simultaneous operation of electric trucks and a nested semi-open queuing network for charging and battery swapping stations; the specific steps for constructing the semi-open queuing network for simultaneous operation of electric trucks and the nested semi-open queuing network for charging and battery swapping stations are as follows: S11. Establish a two-dimensional rectangular coordinate system for the synchronous loading and unloading operation area of ​​electric trucks and obtain the coordinate positions of each facility; based on the coordinate positions of each facility, obtain the first two moments of the facility service time. S12. Define service nodes based on the coordinates of each facility; S13. Based on the first two moments of service nodes and facility service time, and the synchronous loading and unloading operation process of electric trucks in the same container, construct a semi-open queuing network for synchronous operation of electric trucks in the same container; based on service nodes and electric truck charging and swapping process, construct a nested semi-open queuing network of charging and swapping stations; based on the semi-open queuing network for synchronous operation of electric trucks in the same container and the nested semi-open queuing network of charging and swapping stations, obtain a semi-open queuing network for synchronous operation of electric trucks in the same container with charging and swapping stations.

3. The method for modeling and performance analysis of a synchronous operation system for electric container trucks according to claim 2, characterized in that, The coordinates of each facility include the complete coordinate set of the loading and unloading area, the coordinates of the charging and battery swapping station at the maximum boundary of the electric truck synchronous operation area, and the coordinates of the charging and battery swapping station at the bottom of the electric truck synchronous operation area; the specific steps to obtain the coordinates of each facility include: S111. Take the corner point of the minimum x-axis coordinate and the minimum y-axis coordinate in the synchronous operation area of ​​electric trucks as the origin and construct a two-dimensional rectangular coordinate system for the synchronous operation area of ​​electric trucks. S112. Based on the two-dimensional rectangular coordinate system of the electric container truck synchronous operation area, establish the coordinate set of the location of the shore loading and unloading area, expressed as: In the formula, The coordinate set for the working positions of electric container trucks in the shore loading and unloading area; This refers to the lateral offset parameter for the shoreline loading and unloading area. The width of the shore-side loading and unloading area; For the working positions of electric container trucks in the shore loading and unloading area Axis coordinates; The longitudinal offset parameter for the bottom of the shore loading and unloading area; The length of the shore-side loading and unloading area; For the working positions of electric container trucks in the shore loading and unloading area Axis coordinates; The length of the area for synchronous operation of electric container trucks; S113. Based on the two-dimensional rectangular coordinate system of the synchronous operation area of ​​electric container trucks, establish the coordinate set of the import and export container loading and unloading area, expressed as: In the formula, A coordinate set for the working positions of electric container trucks in the import and export container loading and unloading area; The width of the area for loading and unloading import and export containers; The width of the passageway between the import / export container loading / unloading area and the shore loading / unloading area; For import and export container loading and unloading areas Axis coordinates; Electric container truck working positions in the import and export container loading and unloading area Axis coordinates; Electric container truck working positions in the import and export container loading and unloading area Axis coordinates; S114. Add the coordinate set of the quayside loading and unloading area to the coordinate set of the import and export container loading and unloading area to obtain the complete coordinate set of the loading and unloading area. The expression is: In the formula, S For the complete coordinate set of the loading and unloading area; S115. Based on the two-dimensional rectangular coordinate system of the electric truck synchronous operation area, establish the electric truck synchronous operation area. The coordinates of the charging / swapping station at the maximum boundary of the axis coordinate system are expressed as follows: In the formula, For electric container trucks to operate synchronously in the same area The charging and swapping station at the maximum boundary of the axis coordinate. Axis coordinates; For electric container trucks to operate synchronously in the same area The charging and swapping station at the maximum boundary of the axis coordinate. Axis coordinates; The width of the area for simultaneous operation of electric container trucks; For electric container trucks to operate synchronously in the same area Index of charging / swapping station numbers at the maximum boundary of the axis coordinate system; For electric container trucks to operate synchronously in the same area The number of charging and battery swapping stations at the maximum boundary of the axis coordinate; S116. Based on the two-dimensional rectangular coordinate system of the electric truck synchronous operation area, establish the coordinates of the charging and battery swapping station at the bottom of the electric truck synchronous operation area, expressed as: In the formula, The charging and battery swapping station at the bottom of the synchronous operation area for electric container trucks. Axis coordinates; The charging and battery swapping station at the bottom of the synchronous operation area for electric container trucks. Axis coordinates.

4. A method for modeling and performance analysis of a synchronous operation system for electric container trucks according to claim 2 or 3, characterized in that, The first two moments of the service time include the first two moments of the travel time from the electric truck's parking point to the working position, the first two moments of the travel time from the electric truck's parking point to the charging and battery swapping station, and the first two moments of the electric truck's charging time. The expressions for the first two moments of the travel time from the electric truck's resting point to its working position are as follows: In the formula, It is the average travel time from the electric truck's docking point to its working position, which is the first moment of the travel time from the electric truck's docking point to its working position. Number of areas for loading and unloading import / export containers; Coordinates of the electric truck's parking point; The coordinates are the locations of the loading and unloading areas for electric container trucks; It is the square of the coefficient of variation of the travel time from the electric truck's resting point to its working position, which is the second moment of the travel time from the electric truck's resting point to its working position. Let be the expected value of the square of the travel time from the electric truck's docking point to its working position; The expressions for the first two moments of the travel time from the electric truck's parking point to the charging / battery swapping station are as follows: In the formula, It is the average travel time from the electric truck's parking point to the charging and battery swapping station, which is the first moment of the travel time from the electric truck's parking point to the charging and battery swapping station. It is the square of the coefficient of variation of the travel time from the electric truck's parking point to the charging and battery swapping station, which is the second moment of the travel time from the electric truck's parking point to the charging and battery swapping station. The expected value of the square of the travel time from the electric truck's parking point to the charging and battery swapping station; The expressions for the first two moments of the charging time of the electric truck are: In the formula, For electric container trucks to operate synchronously in the same area as electric container trucks The average charging time of the charging and battery swapping station at the maximum boundary of the axis coordinate, i.e., the time for electric trucks to operate synchronously with other electric trucks in the same area. The first moment of the charging time at the charging and swapping station at the maximum boundary of the axial coordinate system; For electric container trucks to operate synchronously in the same area as electric container trucks The square of the coefficient of variation of the charging time of the charging and battery swapping station at the maximum boundary of the axial coordinate, i.e., the electric truck in the synchronous operation area of ​​the electric truck. The second moment of the charging time of the charging and swapping station at the maximum boundary of the axial coordinate; For electric container trucks to operate synchronously in the same area as electric container trucks The lower bound of the uniform distribution of service time of charging and swapping stations at the maximum boundary of the axis coordinate; For electric container trucks to operate synchronously in the same area as electric container trucks The upper bound of the uniform distribution of service time of charging and swapping stations at the maximum boundary of the axis coordinate; It is the average charging time of electric trucks at the charging and battery swapping stations at the bottom of the electric truck synchronous operation area, that is, the first moment of the charging time of electric trucks at the charging and battery swapping stations at the bottom of the electric truck synchronous operation area. It is the square of the coefficient of variation of the charging time of electric trucks at the charging and battery swapping station at the bottom of the electric truck synchronous operation area, which is the second moment of the charging time of electric trucks at the charging and battery swapping station at the bottom of the electric truck synchronous operation area. The lower bound for the uniform distribution of service time of charging and battery swapping stations at the bottom of the synchronous operation area of ​​electric trucks; This is the upper bound of the uniform distribution of service time for charging and battery swapping stations at the bottom of the synchronous operation area of ​​electric trucks.

5. The method for modeling and performance analysis of a synchronous operation system for electric container trucks according to claim 4, characterized in that, The specific steps of step S2 include: S21. Set the arrival rate of packing transactions and the arrival rate of unpacking transactions, and aggregate the arrival rates of packing transactions and unpacking transactions into the total arrival rate; S22. Based on the first two moments of the service time, a single-class semi-open queuing network is obtained by weighting the arrival rates of packing transactions, unpacking transactions, and total arrival rates. S23. Short-circuit the loading and unloading transaction paths in the single-type semi-open queuing network to obtain the first closed queuing network containing the target work location service node, the work service node, and the storage node. S24. Short-circuit the charging and swapping service paths in the single-type semi-open queuing network to obtain a second closed queuing network that includes charging station service nodes, swapping station service nodes, battery charging service nodes, and return dwell point service nodes. S25. Solve the first closed queuing network and the second closed queuing network respectively by the approximate mean value analysis method to obtain the service rate of the first closed queuing network and the service rate of the second closed queuing network. S26. Based on the service rates of the first closed queuing network and the second closed queuing network, the steady-state probability distribution of the system is obtained by solving the problem using the matrix geometry method.

6. The method for modeling and performance analysis of a synchronous operation system for electric container trucks according to claim 1, characterized in that, The annual total cost minimization model aims to minimize the cost of the electric truck synchronous operation system, and is constrained by the throughput time constraint of the packing transaction and the constraint that the number of spare batteries is equal to the number of chargers. The objective function of the annual total cost minimization model is expressed as follows: In the formula, Total annual cost; This refers to the number of electric container trucks; The number of backup battery chargers at the battery swapping station; This refers to the number of spare batteries; Annual cost of electric trucks; Annual cost for a single backup battery charger; Annual cost for a single backup battery; The expression for the bin packing transaction throughput time constraint is: In the formula, For the throughput time of packing transactions; This is the preset throughput time threshold for packing transactions; The expression for the constraint that the number of backup batteries is equal to the number of chargers is: 。

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