On the Transient and Steady-State Analysis of a Special Single Server Queuing System with HOL Priority Scheduling

In this paper, we consider a special discrete-time queuing system with two head-of-line (HOL) priority queues and a mix of correlated and uncorrelated arrivals. The arrival process to the high priority queue is correlated and consists of a train of a fixed number of fixed-length packets, while the low priority traffic consists of batch arrivals that are independent and identically distributed from slot-to-slot. We derive an expression for the functional equation describing the transient evolution of this priority queuing system. This functional equation is then manipulated and transformed into a mathematical tractable form. By applying the final-value theorem, the corresponding exact expressions for the steady-state marginal pgfs are derived. We also show how the transient analysis provides insights into the derivation of the system’s busy period distribution. Finally, we illustrate our solution technique with some numerical examples, whereby we demonstrate the negative effect of correlation (in the high-priority queue) on the performance of the low-priority queue.