IJPAM: Volume 101, No. 2 (2015)

STEADY-STATE BEHAVIOR OF AN $M/M/1$ QUEUE
IN RANDOM ENVIRONMENT SUBJECT TO SYSTEM
FAILURES AND REPAIRS

S. Sophia$^1$, B. Praba$^2$
$^{1,2}$Department of Mathematics
SSN College of Engineering
SSN Nagar, 603 110, TamilNadu, INDIA


Abstract. In this paper, we consider an $M/M/1$ queueing model with disasters in random environment. This model contains a repair state, a checking state along with a set of operational units. When a disaster occurs the system is transferred to the failure state(state o) and then to the checking state(state 1) for the verification process. After the verification process, the system moves to any one of the operational units. The steady-state behavior of the underlying queueing model along with the average queue size is analyzed. Numerical illustrations are provided to study the effect of parameters on the average queue size.

Received: November 19, 2014

AMS Subject Classification:

Key Words and Phrases: $M/M/1$ queueing model, disasters, generating functions, steady-state equations, average queue size

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DOI: 10.12732/ijpam.v101i2.11 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 2
Pages: 267 - 279


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