On the GIM1 Queue with Vacations and Multiple Service Phases
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-08-08
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
This paper considers a GI/M/1 queue with vacations and multiple service phases.
Whenever the system becomes empty, the server takes a vacation, causing the system to move to vacation phase 0.
If the server returns from a vacation to find no customer waiting, another vacation begins.
Otherwise, the system jumps from phase 0 to some service phase i with probability qi, i=1,2,…,N.
Using the matrix geometric solution method and semi-Markov process, we obtain the distributions of the stationary system size at both arrival and arbitrary epochs.
The distribution of the stationary waiting time of an arbitrary customer is also derived.
In addition, we present some performance measures such as mean waiting time of an arbitrary customer, mean length of the type-i cycle, and mean number of customers in the system at the end of phase 0.
Finally, some numerical examples are presented.
American Psychological Association (APA)
Li, Jianjun& Liu, Liwei. 2017. On the GIM1 Queue with Vacations and Multiple Service Phases. Mathematical Problems in Engineering،Vol. 2017, no. 2017, pp.1-14.
https://search.emarefa.net/detail/BIM-1190111
Modern Language Association (MLA)
Li, Jianjun& Liu, Liwei. On the GIM1 Queue with Vacations and Multiple Service Phases. Mathematical Problems in Engineering No. 2017 (2017), pp.1-14.
https://search.emarefa.net/detail/BIM-1190111
American Medical Association (AMA)
Li, Jianjun& Liu, Liwei. On the GIM1 Queue with Vacations and Multiple Service Phases. Mathematical Problems in Engineering. 2017. Vol. 2017, no. 2017, pp.1-14.
https://search.emarefa.net/detail/BIM-1190111
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1190111