Transient Solution of M/M/2/N System Subjected to Catastrophe cum Restoration

Dhanesh Garg

Department of Mathematics, Maharishi Markandeshwar University, Mullana, India.

DOI: 10.4236/oalib.1101404                

Abstract

In this paper, we study the distribution of the number of times that a finite capacity with equal servers Markovian queuing model catastrophic-cum-restorations reaches its capacity in time t. The occurrence of a catastrophe makes the system empty instantly but the system takes its own time to be ready to accept new customers. This time is referred to as “restoration time”. The aforesaid distribution is obtained as a marginal distribution of the joint distribution of the number of customers in the system at time t and the number of times system reaches its capacity in time t under the conditions of catastrophes and restorations.

Keywords

Catastrophes, Markovian Queue, Restoration, Transient State, Laplace Transform

Conflicts of Interest

The authors declare no conflicts of interest.

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