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

Abstract

Abstact. In this paper, we develop a finite queueing model having single and batch service modes for telecommunication system, where two types of traffic, i.e. voice and data arrive in Poisson fashion. The server starts service only when N packets are accumulated in the system. The server performs service singly until there are C packets in the system. After then type 2 packets are discarded and all type 1 packets are served in a batch. The arrival rates of packets depend upon the server's status. The transient state probabilities of system states are obtained by solving a set of linear equations with the help of Laplace Transform technique. Performance indices such as average queue length, expected idle time, and expected busy period are determined. We also investigate the optimal value of threshold parameter N and C after which the server changes the mode of service in order to minimize the expected cost. The numerical illustrations are provided to visualize the effect of various parameters on system performance.

Transient analysis of M/M/C queuing model with reneging, finite capacity and population

“…There are many real life congestion situations where the transient model may represent the more accurate behaviour of the concerned system. Jain et al (2009) investigated bi-level control policy for telecommunication system using transient model for the concerned system. Jain (2013) developed Markovian queuing model with priority queue by using the concept of death-birth process to study the transient behaviour of the machining systems supported by standby and unreliable server.…”