Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-13T00:30:00.509Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the virtual waiting time in the stationary PH/M/c+D queue

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  30 March 2016

Ken'ichi Kawanishi  and
Tetsuya Takine
Ken'ichi Kawanishi*
Affiliation:
Gunma University
Tetsuya Takine*
Affiliation:
Osaka University
*
∗ Postal address: Division of Electronics and Informatics, Gunma University, Kiryu, 376-8515, Japan. Email address: kawanisi@cs.gunma-u.ac.jp
∗∗ Postal address: Department of Information and Communications Technology, Graduate School of Engineering, Osaka University, Suita, 565-0871, Japan. Email address: takine@comm.eng.osaka-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we consider the stationary PH/M/c queue with deterministic impatience times (PH/M/c+D). We show that the probability density function of the virtual waiting time takes the form of a matrix exponential whose exponent is given explicitly by system parameters.

Keywords

PH/M/c queuedeterministic impatience timevirtual waiting timematrix exponential form

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Short Communications
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 899 - 903
Copyright
Copyright © 2015 by the Applied Probability Trust 

References

Choi, B. D., Kim, B. and Zhu, D. (2004). MAP/M/c queue with constant impatient time. Math. Operat. Res. 29, 309–325.Google Scholar
Sakuma, Y. and Takine, T. (2015). Multi-class M/PH/1 queues with deterministic impatience times. Submitted.Google Scholar
Swensen, A. R. (1986). On a GI/M/c queue with bounded waiting times. Operat. Res. 34, 895–908.Google Scholar
Tijms, H. C. (1994). Stochastic Models: An Algorithmic Approach, John Wiley, Chichester.Google Scholar
Van Loan, C. F. (1978). Computing integrals involving the matrix exponential. IEEE Trans. Automatic Control 23, 395-404.CrossRefGoogle Scholar