Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T20:44:59.174Z Has data issue: false hasContentIssue false
  • English
  • Français

The infinite server queue with semi-Markovian arrivals and negative exponential services

Published online by Cambridge University Press:  14 July 2016

Marcel F. Neuts  and
Shun-Zer Chen
Marcel F. Neuts
Affiliation:
Purdue University, Lafayette, Indiana
Shun-Zer Chen
Affiliation:
Purdue University, Lafayette, Indiana
Get access Rights & Permissions [Opens in a new window]

Abstract

The queue with an infinite number of servers with a semi-Markovian arrival process and with negative exponential service times is studied. The queue length process and the type of the last customer to join the queue before time t are studied jointly, both in continuous and in discrete time. Limiting stationary probabilities are also obtained.

Keywords

INFINITE SERVER QUEUESEMI-MARKOV ARRIVALSNEGATIVE EXPONENTIAL SERVICE TIMESTRANSIENT BEHAVIORLIMITING BEHAVIORMARKOV RENEWAL THEORY
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 178 - 184
Copyright
Copyright © Applied Probability Trust 1972 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Pyke, R. (1961) Markov renewal processes: Definitions and preliminary properties. Ann. Math. Statist. 32, 1231–1242.Google Scholar
[2] Pyke, R. (1961) Markov renewal processes with finitely many states. Ann. Math. Statist. 32, 1243–1259.Google Scholar
[3] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press New York.Google Scholar