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doi:10.1016/j.peva.2005.05.005 
Copyright © 2005 Elsevier B.V. All rights reserved.
M/G/1 queue with multiple working vacations
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Received 8 September 2002;
Abstract
We study an M/G/1 queue with multiple vacations and exhaustive service discipline such that the server works with different service times rather than completely stopping service during a vacation. Both service times in a vacation and in a service period are generally distributed random variables. It is assumed that the Laplace–Stieltjes transform (LST) for the distribution of the vacation length is a rational function. We derive the distributions for the queue size and the system time for an arbitrary customer in the steady state. Several special cases, namely, exponentially distributed vacation lengths and/or exponentially distributed service times in a vacation, are considered. Finally some numerical examples are presented.
Keywords: M/G/1 queue; Multiple vacations; Working vacation
Article Outline
- 1. Introduction
- 2. System description and notation
- 3. Transient behavior of an M/G/1 queue
- 4. Queue size in an embedded Markov chain
- 5. Queue size at an arbitrary time
- 6. System time of an arbitrary customer
- 7. When the length of a vacation follows an exponential distribution
- 8. When the service time in a vacation follows an exponential distribution
- 8.1. Queue size and system time
- 8.2. Numerical example for erlang distributed vacation length
- 8.3. Numerical example for constant vacation length
- 9. Summary
- Appendix A. Means and variances for the queue size and the system time in special cases
- A.1. Case of exponentially distributed vacation length
- A.2. Case of exponentially distributed service time in a vacation
- References
- Vitae
