Transient Analysis for State-Dependent Queues with Catastrophes

Abstract

Queueing systems with catastrophes and state-dependent arrival and service rates are considered. For two types of queueing systems namely, queues with discouraged arrivals and infinite server queue, explicit expressions for the transient probabilities of system size are obtained by using continued fractions technique. Some system performance measures and steady-state probabilities are studied. The effect of system parameters on system size probabilities are also illustrated numerically. It is observed that the steady-state probabilities differ when catastrophes are present, while they are identical in the absence of catastrophes.

Keywords:

• Catastrophes
• Continued fractions
• Discouraged arrivals
• Infinite server

Mathematics Subject Classification:

• Primary 60K25, 90B22
• Secondary 60G10

The authors wish to thank the referee for valuable suggestions and remarks which helped in improving the presentation of this article.