برنامه ریزی و تجزیه و تحلیل عملکرد تحت یک مدل تصادفی برای ایستگاه های شارژ خودرو الکتریکی  Scheduling and Performance Analysis under a Stochastic Model for Electric Vehicle Charging Stations

1 Introduction Electric vehicles (EVs) are considered to be the most significant green transportation alternative for the foreseeable future. Recent studies concerning EVs address many aspects, including EV development, the social impact of substituting fossil-fuel vehicles, and public policy that enables the spread of EVs. Although government-provided motivation and environmental benefits exist, EV implementation has not been significantly fast. One of the primary restrictions of the public spread of EVs is the lack of EV battery charging infrastructures [8, 9, 17]. In conventional battery charging technology, slow (regular) chargers require an average of three to six hours in order to fully charge an empty battery for common-size EVs, whereas fast chargers can substantially reduce the charging time to less than half an hour. However, high-speed charging facilities incur significantly higher costs and still require substantially more service time than conventional fuel-based automobile stations. When compared with existing gas stations, the battery charging time required for even fast charging equipment can be considered too long by many drivers. Therefore, the efficient operation of battery charging stations is an important factor in the acceleration of the public spread of EVs. Some recent publications examine the strategic levels of EV battery charging stations, such as stochastic demands, optimal locations, and spread [6, 12, 13, 14]. However, analytic or computational approaches to operational levels, such as system efficiency and charge scheduling performance, remain relatively unexplored [2, 15, 18]. This paper proposes a more realistic stochastic model for EV battery charging stations. Two typical charge scheduling methods, the first-in-first-served (FIFO) and processor sharing (PS),are considered. The framework for the incoming stream of EVs under the proposed stochastic model addresses the time-varying behavior of EV arrivals by exploiting a flexible Poisson process of the Markov-modulated Poisson process (MMPP). Performance measures for the charging scheduling are analytically derived by obtaining stationary distributions for the states that account for the status of inbound EVs, waiting time distributions, and joint distributions of parking time and charged electricity amount during random parking times.