Performance evaluation of a queuing system with correlated packet-trains and server interruption

Abstract

In this paper, we consider a practical queuing system with a finite number of input links and whose arrival process is correlated and consists of a train of a fixed number of fixed-length packets and a single server which is subjected to random interruptions. We model the server interruptions by a correlated Markovian on/off process with geometrically distributed on and off periods. We first derive an expression for the functional equation describing the transient evolution of this queuing system. This functional equation is then manipulated and transformed into a mathematical tractable form. This allows us to derive the probability generating function (pgf) of the system occupancy. From this pgf, closed-form expressions for various performance measures, such as mean and variance of system contents and customer delay can be derived. Finally, we illustrate our solution technique with some numerical examples, whereby we demonstrate the negative effect of correlation in the interruption process on the performance of the system. The paper presents new insights into the performance analysis of queuing systems with correlated arrivals and service interruption and it also covers some previously published results as a special case.