Transient Analysis of a Telecommunication System Using State Dependent Markovian Queue under Bi-Level Control Policy

Abstact. In this paper, we develop a finite queueing model havingsingle and batch service modes for telecommunication system, wheretwo types of traffic, i.e. voice and data arrive in Poisson fashion. Theserver starts service only when N packets are accumulated in thesystem. The server performs service singly until there are C packets inthe system. After then type 2 packets are discarded and all type 1packets are served in a batch. The arrival rates of packets depend uponthe server’s status. The transient state probabilities of system states areobtained by solving a set of linear equations with the help of LaplaceTransform technique. Performance indices such as average queuelength, expected idle time, and expected busy period are determined.We also investigate the optimal value of threshold parameter N and Cafter which the server changes the mode of service in order tominimize the expected cost. The numerical illustrations are providedto visualize the effect of various parameters on system performance.