12/01/1990 09:00 AM
Computer Science
Stochastic service systems in which no queueing is allowed have been around for quite some time as models of telephone systems. Recently, such loss systems with a finite number of request sources were shown to be of interest in the modeling of path contention occurring in many current I/O computer architectures. This paper considers two aspects of finite source loss sytems with several classes of requests (``customers\'\') arising, for instance, in the representation of more realistic I/O workloads. First, we present a simple approach to the solution of such systems in the case of classical multiple servers. This approach is based on the use of recurrence relationships which can be shown to exist among conditional averages, and leads to an efficient computation of server utilizations and loss probabilities. In the second part of this paper, we consider generalized loss systems in which the service resources are viewed as a global quantity (rather than a specific fixed number of servers), each class of customers requesting a given amount of the global resource. Such systems are useful, for example, as models of bus bandwidth shared among several types of transfers. We find that, although these systems exhibit a product-form solution, the simple recurrences derived for regular multiserver loss systems do not seem to carry over to the generalized systems. Therefore, we present an alternative approach, based on equivalence techniques, which allows to obtain the solution of such generalized systems through repeated solutions of a single-class loss model. A comparison with the existing convolution method for evaluation the product-form solution, indicates that the proposed method is significantly more efficient both in terms of computational complexity and computer memory requirements. (Supersedes 90-03.)
