Queueing network with moving servers as a model of car sharing systems

We consider a queueing network with a finite number of nodes and servers moving between the nodes as a model of car sharing. The arrival process of customers to various nodes is defined by a marked Markovian arrival process. The customer that arrives at a certain node when there is no idle server (car) is lost. Otherwise, he/she is able to start the service. With known probability, which depends on the node and the number of available cars, this customer can balk the service and leave the system. The service time of a customer has an exponential distribution. Location of the server in the network after service completion is random with the known probability distribution. The behaviour of the network is described by a multi-dimensional continuous-time Markov chain. The generator of this chain is derived which allows us to compute the stationary distribution of the network states. The formulas for computing the key performance indicators of the system are given. Numerical results are presented. They characterize the dependence of some performance measures of the network and the nodes on the total number of cars (fleet size of the car sharing system) and correlation in the arrival process. © 2019 by the authors.

Авторы
Kim C.1 , Dudin S. 2, 3 , Dudina O. 2, 3
Журнал
Издательство
MDPI AG
Номер выпуска
9
Язык
Английский
Статус
Опубликовано
Номер
825
Том
7
Год
2019
Организации
  • 1 Department of Industrial Engineering, Sangji University, Wonju, Kangwon, 26339, South Korea
  • 2 Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Ave., Minsk, 220030, Belarus
  • 3 Applied Mathematics and Communications Technology Institute, Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Ключевые слова
Car sharing; Marked Markovian arrival process; Moving servers; Queueing network
Дата создания
24.12.2019
Дата изменения
24.12.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/55058/
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