CN115375132B - A multi-level charging and rebalancing joint scheduling method based on queuing theory - Google Patents
A multi-level charging and rebalancing joint scheduling method based on queuing theoryInfo
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Abstract
本发明提供一种基于排队理论的多等级充电与再平衡联合调度方法，涉及按需出行系统的控制技术领域。本发明结合多等级充电调度与基于站点的再平衡策略解决充电延迟和系统失衡问题，并构建乘客等待队列和车辆充电队列，提出一种基于静态平衡的联合调度方案，使系统达到响应时间和运营成本最小化的目标。其中构建的按需出行系统的考虑充电规模的多等级充电调度与基于站点的再平衡策略相结合联合调度模型。考虑了可充电客运站与独立充电站相结合的模型。同时，将充电桩数量作为优化变量，给予最小充电桩的数量的同时以保证充电站服务的效率。
The present invention provides a multi-level charging and rebalancing joint scheduling method based on queuing theory, which relates to the control technology field of on-demand travel systems. The present invention combines multi-level charging scheduling with a site-based rebalancing strategy to solve the problems of charging delay and system imbalance, and constructs a passenger waiting queue and a vehicle charging queue, and proposes a joint scheduling scheme based on static balance, so that the system can achieve the goal of minimizing response time and operating costs. The constructed on-demand travel system combines a multi-level charging scheduling model that considers the charging scale with a site-based rebalancing strategy. A model combining rechargeable passenger stations with independent charging stations is considered. At the same time, the number of charging piles is used as an optimization variable, and the minimum number of charging piles is given while ensuring the efficiency of the charging station service.
Description
Technical Field
The invention relates to the technical field of control of an on-demand travel system, in particular to a multi-level charging and rebalancing combined scheduling method based on a queuing theory.
Background
In recent years, because shared automobiles are widely distributed, customer behaviors are random and unpredictable, so that available vehicles are lack in some stations, and vehicles are excessive due to the fact that other stations are inevitably stacked in a large amount in some stations, the idle vehicles in the system are required to be migrated and scheduled among the stations, and the vehicle utilization rate is improved, namely, a rebalancing process. In addition, considering the protection environment, resources are saved, and the shared vehicle generally adopts an electric automobile, so that the cruising ability is limited, the charging time is long, and the charging schedule is not negligible. However, there is little research on the combined problem of charge scheduling and rebalancing of on-demand travel systems.
Xu et al "G.Guo and T.Xu,"Vehicle rebalancing with charging scheduling in one-way car-sharing systems,"IEEE Transactions on Intelligent Transportation Systems,pp.1–10,2020." propose a joint framework consisting of multi-server M/M/s queuing and fluid models to solve this problem, where the former is used to handle the charge scheduling of vehicles and the latter describes the dynamics of the vehicles and users in the system. M. Kang et al, based on the study of T.xu et al, provide a price-driven customer travel mechanism "G.Guo and M.Kang,"Rebalancing and charging scheduling with price incentives for car sharing systems,"IEEE Transactions on Intelligent Transportation Systems,pp.1–11,2022.", that represents customer ride demand as a linear function of ride price, which allows for more efficient adjustment of customer demand. Zhang et al propose a Model Predictive Control (MPC) based rebalancing and charging joint scheduling scheme "R.Zhang,F.Rossi,and M.Pavone,"Model predictive control of autonomous mobility-on-demand systems,"in proc.IEEE Int.(ICRA),2016,pp.1382–1389.", describing AMoD system operation mechanism and vehicle state of charge variation by state space equations and provide strict stability evidence. The r.icobucci further expands the model "R.Iacobucci,B.Mclellan,and T.Tezuka,"Optimization of shared autonomous electric vehicles operations with charge scheduling and vehicle-to-grid,"Transportation Research Part C:Emerging Technologies,vol.100,no.MAR.,pp.34–52,2019.", to provide a two-layer optimization model for the difference in time scale between transport optimization and charge optimization. Charging is optimized on a longer time scale to minimize latency and power costs. Routing and relocation are optimized on a shorter time scale to minimize latency, with the results of the long time scale optimization as charging constraints, effectively optimizing both aspects of system operation. Belakaria et al propose a multi-stage charge model "S.Belakaria,M.Ammous,L.Smith,S.Sorour,and A.Abdel-Rahim,"Multi-class management with sub-class service for autonomous electric mobility on-demand systems,"IEEE Transactions on Vehicular Technology,vol.68,no.7,pp.7155–7159,2019.", that models vehicles at each stage that can immediately serve waiting passengers, and derives the stability conditions of the system using Lagrangian and KKT conditions. The maximum expected response time of the system is then minimized by optimizing these vehicle service decisions.
Most of the above researches do not consider the problems of charging delay and limited number of charging piles or simply assume that the charging piles are supplied and required, and cannot describe the process of queuing and charging vehicles and solve the problem of overlong charging time. Meanwhile, in the rebalancing scheme of R.Zhang and R.Iacobucci based on model predictive control, the characteristics of the model are limited by a state space method, and the model is only suitable for a small-sized system. The multi-level charge schedule policy "Pavone,M.,Smith,S.L.,Frazzoli,E.,and Rus,D.Robotic load balancing for mobility-on-demand systems.The International Journal of Robotics Research,2012,31(7):839-854.", with sub-level services by belakari et al can effectively reduce computation and charge delays, but does not take into account the imbalance problem between sites.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a multi-level charging and rebalancing combined dispatching method based on queuing theory, solves the problems of charging delay and system unbalance by combining multi-level charging dispatching and station-based rebalancing strategies, constructs a passenger waiting queue and a vehicle charging queue, and provides a combined dispatching scheme based on static balancing, so that the system achieves the aim of minimizing response time and operation cost.
A multi-level charging and rebalancing combined dispatching method based on queuing theory specifically comprises the following steps:
step 1, classifying a vehicle and a passenger into K grades according to the charge state of the vehicle and the travel distance of the passenger;
classifying the vehicles from low to high according to the residual electric quantity of the vehicles, and classifying the passengers from short to long according to the travel distance of the passengers;
step 2, designing an excessively low-power vehicle, namely a 0-level vehicle charging mechanism, and other vehicles, namely a K-level vehicle charging mechanism, wherein K is {0 };
The charging mechanism of the k-level vehicle is as follows:
after the vehicle arrives at the passenger station after finishing the last task, 1) the passenger is directly served without charging 2) Partial charging at a local station and serving passengers3) Partial charging to a charging station for passenger serviceWherein the method comprises the steps ofRepresenting the probability that a class k vehicle is not charged,Representing the probability of the vehicle part of class k charging, o i representing the probability of the vehicle charging at the own station,Representing a probability that a k-level vehicle is charged to a charging station m, wherein part of the charging is that the vehicle is charged from k-level to k+1-level;
The 0-level vehicle charging mechanism is as follows:
if the arriving vehicle is an excessively low-power vehicle, 1) the passenger is served after full vehicle charging is carried out at the site 2) Partial charging at a local station to serve passengers
Step 3, designing a dispatching mechanism of the vehicle which does not need to be charged and a dispatching mechanism of the vehicle which completes the charging task;
The dispatching mechanism without charging the vehicle comprises 1) leaving at the passenger station PS i to provide service o i for passengers at the passenger station, 2) going to PS j station to provide service for passengers at the j station after the vehicle completes the previous task
The scheduling mechanism of the vehicle completing the charging task is 1) the vehicle completing the charging task at the site i is the same as the scheduling mechanism of the vehicle not needing to be charged, 2) the vehicle completing the charging at CS m is required to go to a PS j station with a requirement to provide service h mj for passengers;
Step 4, a charging queue model is built according to a queuing theory, and a queue stability condition is deduced;
The method comprises the steps that a charging queue model is built, namely, whole vehicle charging of a passenger station PS is modeled as an M/M/1/1 queue, partial charging of the passenger station PS is modeled as an M/M/r i/K queue, and partial charging of a charging station CS is modeled as an M/M/r m/K queue;
1) Charging of passenger station PS the process of arrival of a passenger vehicle at a PS i station is modeled as a Poisson process, the expected rate is Then the arrival rate of the k-class passenger vehicles at the PS i stationRepresented asWhere p k represents the probability that the state of charge of the vehicle arriving at the system belongs to the k-level. Vehicle without chargingK-class vehicle that requires charging at the passenger stationSince the class 0 vehicle does not have redundant power to serve passengers and to travel to the nearby charging station CS, the class 0 vehicle can only be charged at the arrival station, and the class 0 vehicle that needs to be charged at the station isWherein the method comprises the steps ofRepresenting the arrival rate of the class-0 passenger vehicles at the station i;
2) Charging station CS charging:
The vehicle arrival rate λ im at station i to the vehicle select CS m for charging is as follows:
where N is the set of passenger stations, i.e { 1..N } and M is the set of charging stations, m.e { 1..M.,M },
The queue stability condition is specifically that the vehicle arrival rate at each charging point must be less than its total service rate to avoid charging delays.
1) Stability condition of passenger station PS i station partial charge queue:
Where p 0 represents the probability of reaching the vehicle as a class 0 vehicle;
2) Stability condition of passenger station PS i station full charge queue:
Mu i g is the charging rate provided by the charging piles of the PS i station, and r i is the number of the charging piles of the PS i station.
3) Charging station CS m station charging queue stability conditions:
where r m is the number of charging piles of charging station m, A charging rate provided for the m-station charging pile;
Step5, designing a service mechanism of the vehicle to passengers, constructing a service queue model, and deducing a system stability condition;
The service mechanism of the vehicle to passengers is as follows:
1) FCFS rules-passenger queues are modeled as M/M/1/K-FCFS queues, the first of the customer queues preferentially allocating vehicles;
2) Peer service and subset service-vehicles with complete charging or k-class vehicles without charging The probability of (2) is that the passenger of level I is served, wherein k is larger than or equal to l;
the service queue model is as follows:
The k-class available vehicle achievement rate lambda i k for the passenger station PS i station includes the vehicle of the passenger station PS i station itself Vehicle with passenger station PS j station rebalancing to passenger station PS i stationVehicle with charging station CS m station distributed to i station
Service rate provided by i station for k-level customers
Where lambda i d represents the class d vehicle available at the i station,Representing the probability that a class d vehicle serves a class k passenger.
The system stability comprises service queue stability and traffic flow stability of each station;
the stability of the service queue is that the service rate provided for passengers is larger than the arrival rate of the passengers:
λi sk>λi ck,k=1,...,K (7)
Wherein the method comprises the steps of K-stage passenger arrival rate for passenger station PS i station.
The maximum response time T of the system is expressed as
Then
The stability of the traffic flow of each station is that the inflow amount of the vehicles of each station is equal to the outflow amount according to the conservation law:
k-stage passenger vehicle arrival rate at passenger station PS i station The following are provided:
the vehicles rebalancing from passenger station PS i station to j station are as follows:
Wherein the method comprises the steps of Probability of rebalancing a vehicle from station i to station j
The traffic flow λ mj scheduled from the charging station CS m station to the passenger station PS j station is as follows:
Passenger station PS i traffic flow stability:
charging station CS m traffic flow stability:
In order to ensure stability and response time limit, the arrival rate lower limit of various vehicles including passenger vehicles and rebalancing vehicles at station i is as follows:
indicating that the i station does not participate in rebalancing, the k-class vehicle arrival rate for directly providing service to the i station passengers, Indicating the k-level vehicle arrival rate rebalancing from station j to station i,Representing a class k vehicle at station m,The arrival rate of the k-stage passenger at the station i is represented.
According to the above formula (6) and formula (8):
Wherein lambda j vcw represents the arrival rate of the w-class passenger vehicles at the j station, Representing the probability of a w-level vehicle selecting portion to charge,Representing the probability that a class w vehicle will choose not to charge,Representing the probability that a class w vehicle serves a class k passenger, p w-1 represents the probability that a class w-1 vehicle is reached,Representing the probability of a selected portion of the w-1 class vehicle being charged, o j representing the probability that the j-station vehicle will not participate in rebalancing to directly service the j-station passenger,Indicating the probability that the j-station vehicle chooses to rebalance to the i-station,Representing the probability that a K-class vehicle serves a K-class passenger,Represents the arrival rate of the j-station K-1 class passenger vehicles,Representing the probability of the K-1 class vehicle selecting a partial charge,Indicating the probability that the j-station vehicle selects to charge to the m-station, h mi indicates the allocation rate of the m-station vehicle to the i-station.
Summing all inequalities in (15) gives:
Equivalent to:
according to The method can obtain:
Step 6, analyzing the equilibrium state of the system, designing a joint scheduling strategy based on site rebalancing, and establishing an optimization model of the multi-objective joint scheduling problem so as to minimize the maximum response time T and the operation cost C of the system;
objective functions in the optimization model of the multi-objective joint scheduling problem comprise a system maximum response time T and a system operation cost C
Maximum response time of system:
the system operation cost comprises vehicle on-road running cost, vehicle charging cost and charging pile maintenance and use cost;
cost of vehicle driving in transit:
Vehicle charging cost:
Charging pile maintenance and use cost:
System operation cost c=c tr+Cch+Cpile (23)
Wherein, C p represents the depreciation cost and the loss cost of the vehicle in unit time, C si represents the charging cost of the vehicle at the PS i charging level 1 point, C sm represents the charging cost of the vehicle at the CS m charging level 1 point, C ri represents the maintenance cost and the use cost of the PS i charging pile, and C rm represents the maintenance cost and the use cost of the CS m charging pile.
The optimization model of the multi-objective joint scheduling problem is:
and 7, deducing an analytic solution lower bound of an optimization model of the multi-objective joint scheduling problem by utilizing Lagrange analysis and KKT conditions.
The simplified symbols A-N are defined as follows:
Using additive variables And ζ mi represents an optimal value in the case where there is a solution to the complete expression. Wherein the method comprises the steps ofAndThe decision vectors for the charging and rebalancing of the vehicles at station i,Is a vehicle service decision vector, h= [ h mi ] is an m-station vehicle allocation decision vector.A lagrangian multiplier representing the inequality associated with the client queue of class i station k,Lagrangian multipliers representing inequalities associated with the i-station and m-station k-level vehicle charge queues respectively,Represents the lagrangian equation multiplier associated with the i station k-level passenger service queue scheduling decision, γ= [ γ K ] represents the lagrangian multiplier associated with the upper bound inequality of the expected response time,And x= [ χ im ] represents the lagrangian multiplier of the equation relating to the i-station and m-station vehicle flows, respectively.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in:
the invention provides a multi-level charging and rebalancing combined scheduling method based on a queuing theory, which has the following advantages:
1) Conventional research on-demand travel systems often defaults to full vehicle charge, or a single study of charging problems. According to the invention, the vehicle and the customer requests are respectively classified according to the SoC and the travel distance, so that a combined optimization framework of multi-level charging, site-based rebalancing and vehicle-customer matching is provided, and unnecessary delay caused by in-transit charging or full-charge charging is avoided.
2) The existing research often takes the benefits of passengers or operators as optimization targets, and the invention takes two contradictory indexes of operation cost and system response time as combined optimization targets to construct a multi-target optimization model. Customer satisfaction is guaranteed, operation cost of the system is minimized, and two aspects of passengers and operators are considered.
3) Aiming at the problem of limited scale of passenger stations and charging stations. A model of a chargeable passenger station in combination with a stand-alone charging station is considered. Meanwhile, the number of the charging piles is used as an optimization variable, and the minimum number of the charging piles is given to ensure the service efficiency of the charging station.
Drawings
FIG. 1 is a general flow chart of a joint scheduling method according to an embodiment of the present invention;
FIG. 2 is a schematic illustration of a vehicle and passenger classification in accordance with an embodiment of the present invention;
wherein, fig. (a) -vehicle classification schematic, fig. (b) -passenger classification schematic;
FIG. 3 is a model of a MoD system including three passenger stations PS and two charging stations CS for use in an embodiment of the invention;
FIG. 4 is a schematic diagram of a rebalancing and charging schedule model of a passenger station PS according to an embodiment of the present invention;
FIG. 5 is a graph showing the maximum response time of a system according to the arrival rate of passengers according to an embodiment of the present invention;
FIG. 6 is a graph showing the maximum response time of a system according to the fleet size according to the embodiment of the present invention;
FIG. 7 is a schematic diagram of the system operation cost according to an embodiment of the present invention;
FIG. 8 is a schematic diagram of a charging cost according to an embodiment of the present invention;
fig. 9 is a schematic diagram of an average charging pile of the passenger station PS i according to an embodiment of the present invention;
fig. 10 is a schematic view of a charging pile of a charging station CS m according to an embodiment of the present invention;
FIG. 11 is a schematic view of waiting passengers at various moments in an embodiment of the present invention;
fig. 12 is a schematic diagram of latency of each station in an embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
As shown in FIG. 1, the method for multi-level charging and rebalancing combined scheduling based on queuing theory in this embodiment is implemented by using LINGO and MATLAB as tool software, and specifically includes the following steps:
Step 1, classifying the vehicle and the passengers into K grades according to the charge state of the vehicle and the travel distance of the passengers, as shown in fig. 2;
classifying the vehicles from low to high according to the residual electric quantity of the vehicles, and classifying the passengers from short to long according to the travel distance of the passengers;
step 2, designing an excessively low-power vehicle, namely a 0-level vehicle charging mechanism, and other vehicles, namely a K-level vehicle charging mechanism, wherein K is {0 };
The charging mechanism of the k-level vehicle is as follows:
after the vehicle arrives at the passenger station after finishing the last task, 1) the passenger is directly served without charging 2) Partial charging at a local station and serving passengers3) Partial charging to a charging station for passenger serviceWherein the method comprises the steps ofRepresenting the probability that a class k vehicle is not charged,Representing the probability of the vehicle part of class k charging, o i representing the probability of the vehicle charging at the own station,Representing a probability that a k-level vehicle is charged to a charging station m, wherein part of the charging is that the vehicle is charged from k-level to k+1-level;
The 0-level vehicle charging mechanism is as follows:
if the arriving vehicle is an excessively low-power vehicle, 1) the passenger is served after full vehicle charging is carried out at the site 2) Partial charging at a local station to serve passengers
FIG. 3 is a model of a MoD system including three passenger stations PS (circular) and two charging stations CS (rectangular) for use in an embodiment of the invention;
step 3, designing a dispatching mechanism of the vehicle which does not need to be charged and a dispatching mechanism of the vehicle which completes the charging task;
The dispatching mechanism without charging the vehicle comprises 1) leaving at the passenger station PS i to provide service o i for passengers at the passenger station, 2) going to PS j station to provide service for passengers at the j station after the vehicle completes the previous task
The scheduling mechanism of the vehicle completing the charging task is 1) the vehicle completing the charging task at the site i is the same as the scheduling mechanism of the vehicle not needing to be charged, 2) the vehicle completing the charging at CS m is required to go to a PS j station with a requirement to provide service h mj for passengers;
Step 4, a charging queue model is built according to a queuing theory, and a queue stability condition is deduced;
The method comprises the steps that a charging queue model is built, namely, whole vehicle charging of a passenger station PS is modeled as an M/M/1/1 queue, partial charging of the passenger station PS is modeled as an M/M/r i/K queue, and partial charging of a charging station CS is modeled as an M/M/r m/K queue;
1) Charging of passenger station PS the process of arrival of a passenger vehicle at a PS i station is modeled as a Poisson process, the expected rate is Then the arrival rate of the k-class passenger vehicles at the PS i stationRepresented asWhere p k represents the probability that the state of charge of the vehicle arriving at the system belongs to the k-level. Vehicle without chargingK-class vehicle that requires charging at the passenger stationSince the class 0 vehicle does not have redundant power to serve passengers and to travel to the nearby charging station CS, the class 0 vehicle can only be charged at the arrival station, and the class 0 vehicle that needs to be charged at the station isWherein the method comprises the steps ofRepresenting the arrival rate of the class-0 passenger vehicles at the station i;
2) Charging at charging station CS, in order to avoid charging delay and to increase charging rate, only partial charging is performed at charging station.
The vehicle arrival rate λ im at station i to the vehicle select CS m for charging is as follows:
where N is the set of passenger stations, i.e { 1..N } and M is the set of charging stations, m.e { 1..M.,M },
The queue stability condition is specifically that the vehicle arrival rate at each charging point must be less than its total service rate to avoid charging delays.
1) Stability condition of passenger station PS i station partial charge queue:
Where p 0 represents the probability of reaching the vehicle as a class 0 vehicle;
2) Stability condition of passenger station PS i station full charge queue:
Mu i g is the charging rate provided by the charging piles of the PS i station, and r i is the number of the charging piles of the PS i station.
3) Charging station CS m station charging queue stability conditions:
where r m is the number of charging piles of charging station m, A charging rate provided for the m-station charging pile;
FIG. 4 is a schematic diagram of a rebalancing and charging schedule model of a passenger station PS according to an embodiment of the present invention;
Step5, designing a service mechanism of the vehicle to passengers, constructing a service queue model, and deducing a system stability condition;
The service mechanism of the vehicle to passengers is as follows:
1) FCFS rules-passenger queues are modeled as M/M/1/K-FCFS queues, the first of the customer queues preferentially allocating vehicles;
2) Peer service and subset service-vehicles with complete charging or k-class vehicles without charging The probability of (2) is that the passenger of level I is served, wherein k is larger than or equal to l;
the service queue model is as follows:
The k-class available vehicle achievement rate lambda i k for the passenger station PS i station includes the vehicle of the passenger station PS i station itself Vehicle with passenger station PS j station rebalancing to passenger station PS i stationVehicle with charging station CS m station distributed to i station
Service rate provided by i station for k-level customers
Where lambda i d represents the class d vehicle available at the i station,Representing the probability that a class d vehicle serves a class k passenger.
The system stability comprises service queue stability and traffic flow stability of each station;
the stability of the service queue is that the service rate provided for passengers is larger than the arrival rate of the passengers:
λi sk>λi ck,k=1,...,K (7)
Wherein the method comprises the steps of K-stage passenger arrival rate for passenger station PS i station.
The maximum response time T of the system is expressed as
Then
The stability of the traffic flow of each station is that the inflow amount of the vehicles of each station is equal to the outflow amount according to the conservation law:
k-stage passenger vehicle arrival rate at passenger station PS i station The following are provided:
the vehicles rebalancing from passenger station PS i station to j station are as follows:
Wherein the method comprises the steps of Probability of rebalancing a vehicle from station i to station j
The traffic flow λ mj scheduled from the charging station CS m station to the passenger station PS j station is as follows:
Passenger station PS i traffic flow stability:
charging station CS m traffic flow stability:
In order to ensure stability and response time limit, the arrival rate lower limit of various vehicles including passenger vehicles and rebalancing vehicles at station i is as follows:
indicating that the i station does not participate in rebalancing, the k-class vehicle arrival rate for directly providing service to the i station passengers, Indicating the k-level vehicle arrival rate rebalancing from station j to station i,Representing a class k vehicle at station m,The arrival rate of the k-stage passenger at the station i is represented.
According to the above formula (6) and formula (8):
Wherein lambda j vcw represents the arrival rate of the w-class passenger vehicles at the j station, Representing the probability of a w-level vehicle selecting portion to charge,Representing the probability that a class w vehicle will choose not to charge,Representing the probability that a class w vehicle serves a class k passenger, p w-1 represents the probability that a class w-1 vehicle is reached,Representing the probability of a selected portion of the w-1 class vehicle being charged, o j representing the probability that the j-station vehicle will not participate in rebalancing to directly service the j-station passenger,Indicating the probability that the j-station vehicle chooses to rebalance to the i-station,Representing the probability that a K-class vehicle serves a K-class passenger,Represents the arrival rate of the j-station K-1 class passenger vehicles,Representing the probability of the K-1 class vehicle selecting a partial charge,Indicating the probability that the j-station vehicle selects to charge to the m-station, h mi indicates the allocation rate of the m-station vehicle to the i-station.
Summing all inequalities in (15) gives:
Equivalent to:
according to The method can obtain:
Step 6, analyzing the equilibrium state of the system, designing a joint scheduling strategy based on site rebalancing, and establishing an optimization model of the multi-objective joint scheduling problem so as to minimize the maximum response time T and the operation cost C of the system;
objective functions in the optimization model of the multi-objective joint scheduling problem comprise a system maximum response time T and a system operation cost C
Maximum response time of system:
the system operation cost comprises vehicle on-road running cost, vehicle charging cost and charging pile maintenance and use cost;
cost of vehicle driving in transit:
Vehicle charging cost:
Charging pile maintenance and use cost:
System operation cost c=c tr+Cch+Cpile (23)
Wherein, C p represents the depreciation cost and the loss cost of the vehicle in unit time, C si represents the charging cost of the vehicle at the PS i charging level 1 point, C sm represents the charging cost of the vehicle at the CS m charging level 1 point, C ri represents the maintenance cost and the use cost of the PS i charging pile, and C rm represents the maintenance cost and the use cost of the CS m charging pile.
The optimization model of the multi-objective joint scheduling problem is:
and 7, deducing an analytic solution lower bound of an optimization model of the multi-objective joint scheduling problem by utilizing Lagrange analysis and KKT conditions.
The optimization model is a non-male model, and it is quite difficult to derive a complete general solution to the non-male optimization problem. But it is feasible to obtain an analytical lower bound solution for the optimal solution using Lagrange dual optimization and KKT conditions. Before giving the result, for the sake of a concise formula, the simplified symbols A-N are defined, as shown in the following formula:
When solving using the KKT condition, we can find the exact expression or exact value of the system variable under certain conditions, but not for all possibilities, as shown in equations (25) - (30). Thus, we use the additive variables And ζ mi represents an optimal value in the case where there is a solution to the complete expression. Wherein the method comprises the steps ofAndThe decision vectors for the charging and rebalancing of the vehicles at station i,Is a vehicle service decision vector, h= [ h mi ] is an m-station vehicle allocation decision vector.A lagrangian multiplier representing the inequality associated with the client queue of class i station k,Lagrangian multipliers representing inequalities associated with the i-station and m-station k-level vehicle charge queues respectively,Represents the lagrangian equation multiplier associated with the i station k-level passenger service queue scheduling decision, γ= [ γ K ] represents the lagrangian multiplier associated with the upper bound inequality of the expected response time,And x= [ χ im ] represents the lagrangian multiplier of the equation relating to the i-station and m-station vehicle flows, respectively.
In this embodiment, the customer arrival rate follows the poisson distribution process to reach each site randomly. We classify vehicles and passengers into 8 classes according to the remaining power of the vehicles and the travel distance of the passengers. Assume that the entire system has 8 Passenger Stations (PS) and 4 Charging Stations (CS). Each PS has r i charging piles, the maintenance cost of each charging pile is 0.2, the charging rate is 0.6 level/unit time, and the charging cost is 1.2 level/unit time. Each CS has r m charging piles, the maintenance cost of each charging pile is 0.2, the charging rate is 0.8 level/unit time, and the charging cost is 0.8 level/unit time. The travel time between each station is given by the euclidean distance, with each vehicle moving 0.25 per unit step. In the simulation, we consider the charging process as an intermediate link to rebalancing. The vehicle running cost per unit time is defined as 0.75.
Example 1 assuming that the arrival rate of passengers at each station is constant, no waiting passengers are present at the initial time in the station, the vehicles are uniformly distributed at each station, and the rebalancing period t=20 mins.
Example 2 assuming that the fleet size in the system is constant, the passenger arrival rates at different time periods are randomly selected between 0, 15. Furthermore, a rebalancing period t=20 mins is set.
Example 3 actual scene analysis. In this case study, the validity of the proposed method is checked based on the actual operational data of a certain travel company. The data set mainly comprises taxi driving track data of a city in 8 th 2014 and 8 th, 65536 pieces of data are randomly extracted from the taxi driving track data for scene analysis, and 52833 pieces of partial map data imitating a center of the city are obtained through data processing. Sites were generated by using the k-means clustering algorithm, so we set up 25 customer sites and 9 charging sites in the system. The total number of vehicles in the system was 1718 and the rebalancing optimization was performed on the system every 20 minutes.
Based on the parameters, simulation verification is carried out on the multi-level charging and rebalancing combined dispatching provided by the invention. Fig. 5 shows the variation of the maximum response time of the system with the arrival rate of the passengers. Wherein Strategy denotes an automobile sharing system that does not consider the rebalancing process and the independent CSs, strategy2 denotes an automobile sharing system that does not consider the rebalancing process but does not consider the independent CSs, and Strategy3 denotes an automobile sharing system that does consider the rebalancing process and the independent CSs. From the above, it can be seen that, for the peak period of waiting vehicles, the rebalancing method can greatly reduce the response time of the system, and whether the independent CS has little influence on the system performance. Fig. 6 shows the variation of the maximum response time of the system with fleet size. From the pictures, the response time of the system can be greatly reduced by introducing a rebalancing method for the medium-small fleet-scale system. The models with and without independent CS have a larger gap in fleet size, and the gap gradually decreases as fleet size increases. This is mainly because, when the fleet size is small, the available vehicles are limited, the number of charging piles and the charging rate of PS are limited, and it is difficult to achieve the supply-demand balance, and as the fleet size increases, the available vehicles increase, and the vehicles that need to be charged decrease, so that the influence of the independent charging stations on the system becomes smaller. Fig. 7 and 8 show the operating costs, including rebalancing costs, charging pile maintenance costs, and charging costs as a function of fleet size. It can be seen that introducing a separate CS and employing low cost charging incentives for passengers not only reduces the pressure of PSi station charging and stopping, see fig. 9, but also reduces the operating and charging costs of the system. Fig. 9 and 10 show the number of charging piles of PS and CS, respectively, as a function of fleet size. Fig. 10 is a trend of rising and falling, because the charging piles of the system with multiple charging stations are required to meet the demands of passengers of different grades while minimizing the operation cost when the number of vehicles is small. When the number of vehicles increases to a certain number, there are enough types of vehicles to serve different types of passengers, so that the required charging vehicles are reduced, and the need for charging piles of the charging station is also reduced.
The proposed solution is validated using certain market instance data. Fig. 11 shows a change in the number of customers waiting from 6:00 to 24:00. The maximum waiting time of passengers at each station is shown from fig. 12. The time that passengers with only a few stops wait in the system is long, and the peak wait time distribution in fig. 12 may be due to poor stop positions in combination with the station distribution. For most stops, the waiting time can meet the QoS requirement (i.e., 0-5 minutes), but 19, 22, 23, 24 stations are far from the geographic location, and the response speed of the system is sometimes difficult to meet the passenger demand.
The foregoing description is only of the preferred embodiments of the present disclosure and description of the principles of the technology being employed. It will be appreciated by those skilled in the art that the scope of the invention in the embodiments of the present disclosure is not limited to the specific combination of the above technical features, but encompasses other technical features formed by any combination of the above technical features or their equivalents without departing from the spirit of the invention. Such as the above-described features, are mutually substituted with (but not limited to) the features having similar functions disclosed in the embodiments of the present disclosure.
Claims (6)
1. A multi-level charging and rebalancing combined scheduling method based on queuing theory is characterized by comprising the following steps:
step 1, classifying a vehicle and a passenger into K grades according to the charge state of the vehicle and the travel distance of the passenger;
classifying the vehicles from low to high according to the residual electric quantity of the vehicles, and classifying the passengers from short to long according to the travel distance of the passengers;
step 2, designing an excessively low-power vehicle, namely a 0-level vehicle charging mechanism, and other vehicles, namely a K-level vehicle charging mechanism, wherein K is {0 };
step 3, designing a dispatching mechanism of the vehicle which does not need to be charged and a dispatching mechanism of the vehicle which completes the charging task;
Step 4, a charging queue model is built according to a queuing theory, and a queue stability condition is deduced;
in the step 4, the charging queue model is built specifically, the whole vehicle charging of the passenger station PS is modeled as an M/M/1/1 queue, the partial charging of the passenger station PS is modeled as an M/M/r i/K queue, and the partial charging of the charging station CS is modeled as an M/M/r m x K queue;
1) Charging passenger station PS. The process of arrival of a passenger vehicle at a PSi station is modeled as a Poisson process, the expected rate is The arrival rate of the k-class passenger vehicles at the PSi stationRepresented asWhere p k represents the probability that the state of charge of the vehicle arriving at the system belongs to the k-class, vehicle that does not require chargingK-class vehicle that requires charging at the passenger stationSince the class 0 vehicle does not have redundant power to serve passengers and to travel to the nearby charging station CS, the class 0 vehicle can only be charged at the arrival station, and the class 0 vehicle that needs to be charged at the station isWherein the method comprises the steps ofRepresenting the arrival rate of the class-0 passenger vehicles at the station i;
2) Charging station CS charging:
The vehicle arrival rate lambda im for the i station arrival vehicle selection to charge CSm is as follows:
where N is the set of passenger stations, i.e { 1..N } and M is the set of charging stations, m.e { 1..M.,M },
The queue stability condition is that the vehicle arrival rate of each charging point must be smaller than the total service rate thereof to avoid charging delay;
1) Stability condition of passenger station PSi station partial charge queue:
Where p 0 represents the probability of reaching the vehicle as a class 0 vehicle;
2) Stability condition of passenger station PSi station fully charged queue:
Mu i g is the charging rate provided by the charging piles of the PSi station of the passenger station, and r i is the number of the charging piles of the PSi station of the passenger station;
3) Charging station CSm station charging queue stability conditions:
where r m is the number of charging piles of charging station m, A charging rate provided for the m-station charging pile;
Step5, designing a service mechanism of the vehicle to passengers, constructing a service queue model, and deducing a system stability condition;
Step 6, analyzing the equilibrium state of the system, designing a joint scheduling strategy based on site rebalancing, and establishing an optimization model of the multi-objective joint scheduling problem so as to minimize the maximum response time T and the operation cost C of the system;
and 7, deducing an analytic solution lower bound of an optimization model of the multi-objective joint scheduling problem by utilizing Lagrange analysis and KKT conditions.
2. The queuing theory-based multi-level charging and rebalancing combined scheduling method according to claim 1, wherein the k-level vehicle charging mechanism in step 2 is as follows:
after the vehicle arrives at the passenger station after finishing the last task, 1) the passenger is directly served without charging 2) Partial charging at a local station and serving passengers3) Partial charging to a charging station for passenger serviceWherein the method comprises the steps ofRepresenting the probability that a class k vehicle is not charged,Representing the probability of the vehicle part of class k charging, o i representing the probability of the vehicle charging at the own station,Representing a probability that a k-level vehicle is charged to a charging station m, wherein part of the charging is that the vehicle is charged from k-level to k+1-level;
The 0-level vehicle charging mechanism is as follows:
if the arriving vehicle is an excessively low-power vehicle, 1) the passenger is served after full vehicle charging is carried out at the site 2) Partial charging at a local station to serve passengers
3. The queuing theory-based multi-level charging and rebalancing combined dispatching method as claimed in claim 1, wherein the dispatching mechanism without charging vehicles in step 3 is that 1) the vehicles are left at the passenger station PSi to provide services o i for passengers of the passenger station, 2) the vehicles go to the PS j station to provide services for passengers of the j station
The dispatching mechanism of the vehicle completing the charging task is 1) the same as the dispatching mechanism of the vehicle not needing to be charged at the site i, and 2) the vehicle completing the charging at the CSm needs to go to the PS j station with the requirement to provide service h mj for passengers.
4. The queuing theory-based multi-level charging and rebalancing combined scheduling method according to claim 1, wherein the service mechanism of the vehicle to the passengers in step 5 is as follows:
1) FCFS rules-passenger queues are modeled as M/M/1/K-FCFS queues, the first of the customer queues preferentially allocating vehicles;
2) Peer service and subset service-vehicles with complete charging or k-class vehicles without charging The probability of (2) is that the passenger of level I is served, wherein k is larger than or equal to l;
the service queue model is as follows:
The k-level available vehicle achievement rate lambda i k for the passenger station PSi station includes the vehicle of the passenger station PSi station itself Vehicle rebalancing station PSj to station PSiVehicle with charging station CSm station assigned to i station
Service rate provided by i station for k-level customers
Where lambda i d represents the class d vehicle available at the i station,Representing the probability that a class d vehicle serves a class k passenger;
The system stability comprises service queue stability and traffic flow stability of each station;
the stability of the service queue is that the service rate provided for passengers is larger than the arrival rate of the passengers:
λi sk＞λi ck,k=1,...,K (7)
Wherein lambda i ck is the k-stage passenger arrival rate of the passenger station PSi station;
The maximum response time T of the system is expressed as
Then
The stability of the traffic flow of each station is that the inflow amount of the vehicles of each station is equal to the outflow amount according to the conservation law:
K-stage passenger vehicle arrival rate of passenger station PSi station The following are provided:
the vehicles rebalancing from passenger station PSi station to station j are as follows:
Wherein the method comprises the steps of Probability of rebalancing a vehicle from station i to station j
The traffic flow λ mj from the charging station CSm station to the passenger station PS j station is as follows:
Passenger station PSi traffic stability:
charging station CSm traffic flow stability:
In order to ensure stability and response time limit, the arrival rate lower limit of various vehicles including passenger vehicles and rebalancing vehicles at station i is as follows:
indicating that the i station does not participate in rebalancing, the k-class vehicle arrival rate for directly providing service to the i station passengers, Indicating the k-level vehicle arrival rate rebalancing from station j to station i,Representing a class k vehicle at station m,Representing the arrival rate of k-level passengers of the i station;
According to the above formula (6) and formula (8):
Wherein lambda j vcw represents the arrival rate of the w-class passenger vehicles at the j station, Representing the probability of a w-level vehicle selecting portion to charge,Representing the probability that a class w vehicle will choose not to charge,Representing the probability that a class w vehicle serves a class k passenger, p w-1 represents the probability that a class w-1 vehicle is reached,Representing the probability of a selected portion of the w-1 class vehicle being charged, o j representing the probability that the j-station vehicle will not participate in rebalancing to directly service the j-station passenger,Indicating the probability that the j-station vehicle chooses to rebalance to the i-station,Representing the probability that a K-class vehicle serves a K-class passenger,Represents the arrival rate of the j-station K-1 class passenger vehicles,Representing the probability of the K-1 class vehicle selecting a partial charge,Indicating the probability that the vehicle at station j selects to charge at station m, and h mi indicates the distribution rate of the vehicle at station m to station i;
Summing all inequalities in (15) gives:
Equivalent to:
according to Obtaining:
5. The queuing theory-based multi-level charging and rebalancing joint scheduling method according to claim 1, wherein in step 6:
objective functions in the optimization model of the multi-objective joint scheduling problem comprise a system maximum response time T and a system operation cost C
Maximum response time of system:
the system operation cost comprises vehicle on-road running cost, vehicle charging cost and charging pile maintenance and use cost;
cost of vehicle driving in transit:
Vehicle charging cost:
Charging pile maintenance and use cost:
System operation cost c=c tr+Cch+Cpile (23)
Wherein, C p represents the depreciation cost and the loss cost of the vehicle in unit time, C si represents the charging cost of the vehicle at the PSi charging level 1 point, C sm represents the charging cost of the vehicle at the CSm charging level 1 point, C ri represents the maintenance cost and the use cost of the PSi charging pile, and C rm represents the maintenance cost and the use cost of the CSm charging pile;
The optimization model of the multi-objective joint scheduling problem is:
s.t
6. The queuing theory-based multi-level charging and rebalancing joint scheduling method according to claim 1, wherein the simplified symbols a-N are defined in step 7, as shown in the following formula:
Using additive variables And ζ mi represents the optimal value in the case of solving the complete expression, whereAndThe decision vectors for the charging and rebalancing of the vehicles at station i,Is a vehicle service decision vector, h= [ h mi ] is an m-station vehicle allocation decision vector; a lagrangian multiplier representing the inequality associated with the client queue of class i station k, Lagrangian multipliers representing inequalities associated with the i-station and m-station k-level vehicle charge queues respectively,Represents the lagrangian equation multiplier associated with the i station k-level passenger service queue scheduling decision, γ= [ γ K ] represents the lagrangian multiplier associated with the upper bound inequality of the expected response time,And x= [ χ im ] represents the lagrangian multiplier of the equation relating to the i-station and m-station vehicle flows, respectively.
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