• MATRIX-GEOMETRIC METHOD FOR QUEUEING MODEL WITH MULTIPLE VACATION, N-POLICY, SERVER BREAKDOWN, REPAIR AND INTERRUPTION VACATION

Abstract

In this paper, we study an matrix-geometric method for queueing model with multiple vacation, N-policy, system breakdown and vacation interruption. Where the system is subject to breakdown while in operation. Service resumes immediately after a repair process, and a vacation starts at the end of each busy period. The server come back to the regular busy period of a service completion without completion the vacation. Such policy is called vacation interruption. Arrivals follows a Poisson process with rate depending upon the system, namely, vacation, service or breakdown state. In terms of matrix-geometric solution method, we obtain the stationary queue length distribution. Towards the end of this paper a numerical example is provided to illustrate how the system characteristic behave as the input parameter change.