EXPECTED WAITING TIMES IN CYCLIC SERVICE SYSTEMS UNDER PRIORITY

~bstract In this paper, we analyse a service system which consists ofseveral queues (stations) polled by a single server in a cyclic order with arbitrary switchover times. Customers from several priority classes arrive into each of the queues according to independent Poisson processes and require arbitrary distributed service times. We consider the system under various priority service disciplines: head-of-the-line priority limited to one and semi-exhaustive, head-of-the-line priority limited to one with background customers, and global priority limited to one. For the first two disciplines we derive a pseudo conservation law. For the third discipline, we obtain the expected waiting time of a customer from any given priority class and for the last discipline we find the expected waiting time of a customer from the highest priority class. The principal tool for our analysis is the stochastic' decomposItion law for a single server system with vacations. A new architecture for Local Area Networks (LAN's), Token-Ring networks, became available few years ago. In such a network, several work stations (terminals, PC's and sma.ll computers) are connected by T-tap connections to a high bandwidth channel arranged as a ring. The work stations may exchange messages by accessing the ring which in turn transmits their messages. The protocol that controls the channel access is implemented by a token which is passed through the stations according to certain rules. This application has recently revived the interest in polling queueing systems which are used to model such an environment. Until recently, most of the implementations of a Token-Ring access protocol have regarded all messages as being of the same type and therefore, being transmitted with the same priority. As new applications had risen (voice and video transmissions), priority scheduling became important and two standards were proposed, IEEE 802.5 [9] and FDDI [1]. Although these two protocols have been compared via sjmul<J.tion, [8], their behavior as well as the performance of other possible .priority disciplines, are not well understood. In this study we examine a model for a Token Ring network under various priority regimes and develop analytical tools for their analysis. We consider a service system which consists of several queues (stations) polled by a single server in a cyclic order with arbitrary switchover times. Customers ftom several priority classes arrive into each of the queues according to independent Poisson processes and require arbitrary distributed service times. Four priority s~rvice disciplines (to be defined below) are …