PERFORMANCE ANALYSIS OF A TWO-QUEUE MODEL WITH AN (M, N)-THRESHOLD SERVICE SCHEDULE

Abstract In this paper, we consider a polling system consisting of two-parallel queues and a single server under an (M, N)-threshold nonpreemptive priority service schedule. Two thresholds M and N (0 <: M < N) are set up in one of two queues, say, the second queue. At each epoch of service completion, the server decides which queue is to be served next according to the control level reached by the number of customers in the second queue. For the queueing model, we carry out the performance analysis by using the transform method and propose an algorithm to compute the generating functions of the stationary joint queue length distributions a t service completion instants. We also determine the Laplace-Stieltjes transforms of the waiting time distributions for both queues, and obtain their mean waiting times. 1. In t roduct ion Polling systems used for modeling distributed multiqueue systems sharing a single server such as a communication channel or a processor, have received a considerable amount of attention in the recent literature. Examples of such systems are local area networks (LAN), high-speed Asynchronous Transfer Mode (ATM) networks, multiprocessor systems, distributed computation, and so forth. An excellent survey may be found in Levy and Sidi[23]. See also the detailed discussion and references in Takagif31, 321 on this sub