Analysis of M/M/1 Vacation Queue with Negative Arrival, Server Breakdown and First Exceptional Service

Abstract

      In this paper we have analyzed multiple vacation queueing system characterized with the negative arrival, first exceptional service, service breakdowns and repair mechanism. The negative customer enters the system only when server is active and removes one customer from the system. The positive customer enters the system during vacation, active service and repair process according to Poisson process with different rates.These types of queues are widely applicable in neural networks, controlling the traffic or congestion in computer communication networks, manufacturing processes and service sectors. Using generating function technique we obtained queue length distribution and mean queue length.