Multiqueue Systems with Nonexhaustive Cyclic Service

Cyclic service is a frequently used mechanism for the information transfer between peripheral units and their centralized control opposed to asynchronous or synchronous interrupt mechanisms. In a cyclic service operation, the centralized control scans the peripheral units in a cyclic sequence. At each peripheral unit, the queue of waiting items (user or control data) is served either completely ("exhaustive service") or up to a specified maximum number of transferred items per scan ("nonexhaustive service") until the centralized device switches over to the succeeding unit within the cycle sequence. Examples of this type 671 of operation are found in data communications systems (polling, asynchronous multiplexing), telephone switching systems (device scanning), and certain I/O mechanisms of real-time computers. The performance of these cyclic service mechanisms is of considerable interest for traffic engineering, namely with respect to throughput and resource utilizations, delays, unbalanced load, overload behavior, and the influence of various statistical properties of the traffic. In the sequel, we refer to the general cyclic queuing model shown in Fig. 1. There are g arrival groups of "customers" and their corresponding waiting lines (queues). Customers of group j arrive according to a general independent (GI) arrival process with probability distribution function (pdf) AJ(t) = P{TAJ ^ t), where TAJ denotes the random variable of the interarrival time in queue j, j = 1,2, and Ay = 1/ ETAJ defines the arrival rate of customers in queue j.