Abstract
The aim of this paper is to derive the probability density function (pdf) of the total idle time of busy period of M/C2/1 queues operating under control policies through lattice path combinatorics (LPC) approach. The service distribution is approximated by Coxian two-phase distribution. We focus on deriving the pdf of total idle time of M/C2/1 queues under (0,k) control policy, wherein the server goes on the vacation when the system becomes empty and re-opens for service immediately at the arrival of the kthcostumer. We present an important result which is the theorem of the pdf of total idle time when system is in busy period that ends with a departure.
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