Analysis of the State-Dependent Queueing Model and Its Application to Battery Swapping and Charging Stations

Choi, Doo Il; Lim, Dae-Eun

doi:10.3390/su12062343

Cited by 10 publications

(6 citation statements)

References 26 publications

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“…Below, we evaluate the Lyapunov exponent for block triangular matrices of special form. Consider a dynamic system with state transition matrices A(k) of block triangular form defined as (6) in the framework of max-plus algebra. We suppose that the upper diagonal block reduces to an RV α k and the lower is a constant nonrandom matrix D to write…”

Section: Proof Since the Matrix Product Amentioning

confidence: 99%

“…Modern research on the implementation of battery swapping offers a range of models to study various aspects of the BSCS's operations, including the battery logistics and transportation strategy as well as energy management and operation scheduling in EVs' battery swapping and charging systems and networks. A queueing model of BSCSs with Poisson arrival and constant service times was proposed by Choi and Lim in [6] to develop and analyze queue-length-dependent overload control policies. The queue distributions under different policies are derived using an embedded Markov chain, and system performance measures such as blocking probability and mean waiting time are examined by numerical examples.…”

Section: Introductionmentioning

confidence: 99%

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Tropical Modeling of Battery Swapping and Charging Station

Krivulin,

Garg

2024

Mathematics

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We propose and investigate a queueing model of a battery swapping and charging station (BSCS) for electric vehicles (EVs). A new approach to the analysis of the queueing model is developed, which combines the representation of the model as a stochastic dynamic system with the use of the methods and results of tropical algebra, which deals with the theory and applications of algebraic systems with idempotent operations. We describe the dynamics of the queueing model by a system of recurrence equations that involve random variables (RVs) to represent the interarrival time of incoming EVs. A performance measure for the model is defined as the mean operation cycle time of the station. Furthermore, the system of equations is represented in terms of the tropical algebra in vector form as an implicit linear state dynamic equation. The performance measure takes on the meaning of the mean growth rate of the state vector (the Lyapunov exponent) of the dynamic system. By applying a solution technique of vector equations in tropical algebra, the implicit equation is transformed into an explicit one with a state transition matrix with random entries. The evaluation of the Lyapunov exponent reduces to finding the limit of the expected value of norms of tropical matrix products. This limit is then obtained using results from the tropical spectral theory of deterministic and random matrices. With this approach, we derive a new exact formula for the mean cycle time of the BSCS, which is given in terms of the expected value of the RVs involved. We present the results of the Monte Carlo simulation of the BSCS’s operation, which show a good agreement with the exact solution. The application of the obtained solution to evaluate the performance of one BSCS and to find the optimal distribution of battery packs between stations in a network of BSCSs is discussed. The solution may be of interest in the case when the details of the underlying probability distributions are difficult to determine and, thus, serves to complement and supplement other modeling techniques with the need to fix a distribution.

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Section: Proof Since the Matrix Product Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tropical Modeling of Battery Swapping and Charging Station

Krivulin,

Garg

2024

Mathematics

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“…Using embedded Markov chain and supplementary variable technology, the queue length distribution of vehicles at departure time and at any time is derived so as to ease the congestion of the battery switching station and improve the utilization rate [71]. These studies are summarized in Table 5.…”

Section: Assignment Problem Of Bssmentioning

confidence: 99%

Construction Planning and Operation of Battery Swapping Stations for Electric Vehicles: A Literature Review

Feng

2021

Energies

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The popularity of electric vehicles has been limited by factors such as range, long charging times and fast power failure in winter. In order to overcome these challenges, battery swapping stations (BSS) have been constructed and greatly promoted in recent years. In this paper, the related literature on electric vehicle service is reviewed and the co-occurrence of keywords is analyzed using CiteSpace. The literature is classified according to clustering results and recurring themes, such as the location of BSS, inventory decisions, charging strategies and BSS assignment. In each topic, typical optimization models and algorithms proposed in previous studies are summarized. Then, this paper gives a case about the business model and revenue capacity calculation of BSS. Finally, it points out the future research direction of battery swapping stations for electric vehicles.

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“…Zhang et al [9] controlled CS service quality by a two-stage priority queue to optimize the station, battery inventory level, and the number of superchargers at selected stations. Choi and Lim [10] proposed a queuing model and two congestion control policies based on EV queue length thresholds. Wang et al [11] used the M/G/k system to model the queuing of charging stations and incorporate it into an expanded network to capture the optimal recharging strategies for EV drivers.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Traffic Flow considering Electric Vehicle Market Share and Random Charging

Yan

Zha

Shi

et al. 2023

Journal of Advanced Transportation

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This paper mainly studies the multiclass stochastic user equilibrium problem considering the market share of battery electric vehicles (BEVs) and random charging behavior (RCB) in a mixed transport network containing electric vehicles and gasoline vehicles (GVs). In order to analyze the random charging and path choice behaviors of BEV users and extract the differences in travel behaviors between BEV and GV users, an improved logit-based model, multilabel algorithm, and queuing theory are applied. The influencing factors of charging possibility mainly include the initial state of charge (SOC), the SOC at the beginning of charging, and the psychologically acceptable safe SOC threshold arriving at the destination. Diversity choices of user paths and charging locations will result in changes in queuing traffic and differences in queuing time. Conversely, different stations have different queuing dwell times, which will also affect the routing and charging locations for BEVs with RCB. The path-based method of successive averages (MSA) is adopted to solve the model. Through the simulation of the test network Sioux Falls, the equilibrium traffic flow and possible charging flow under different market shares and initial SOC are predicted, and the properties of the model and the feasibility of the algorithm are verified.

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Analysis of the State-Dependent Queueing Model and Its Application to Battery Swapping and Charging Stations

Cited by 10 publications

References 26 publications

Tropical Modeling of Battery Swapping and Charging Station

Tropical Modeling of Battery Swapping and Charging Station

Construction Planning and Operation of Battery Swapping Stations for Electric Vehicles: A Literature Review

Prediction of Traffic Flow considering Electric Vehicle Market Share and Random Charging

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