Queueing Network with Moving Servers as a Model of Car Sharing Systems

Chesoong Kim, Sergei Dudin and Olga Dudina
Additional contact information
Chesoong Kim: Department of Industrial Engineering, Sangji University, Wonju, Kangwon 26339, Korea
Sergei Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Ave., Minsk 220030, Belarus
Olga Dudina: Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Ave., Minsk 220030, Belarus

Mathematics, 2019, vol. 7, issue 9, 1-17

Abstract: 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.

Keywords: queueing network; moving servers; car sharing; marked Markovian arrival process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/9/825/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/9/825/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:9:p:825-:d:264766

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().