Moment Formulae for a Class of Mixed Multi-Job-Type Queueing Networks

Performance analysis and modeling activities are essential for answering key questions at various stages of a computer system's lifecycle, ranging from initial conception to maintaining and growing a mature system. Although both the questions asked and the analysis approaches may differ from stage to stage, in each of these stages broadly applicable performance analysis tools are needed to support 709 such activities. This paper presents new results which contribute to the foundation of one such tool: algorithmic techniques for efficiently solving a class of queueing networks. In dealing with some performance issues, it is important to be able to quantify distribution or moment information (e.g., delay variability as opposed to only the mean delay)1 because these quantities can influence system capacity and service and performance measures. It is also important that models include the effect of congestion adaptive i/o devices, in a stable and efficient manner, for this inclusion can significantly affect the outcome of studying certain performance issues (e.g., the impact of multiprogramming).2,3 In this paper, we present results for the direct recursive computation of moments of the queue size distributions at a class of service centers embedded in a mixed network of queues. The class of service centers allows us to efficiently treat, in a stable manner, a parameterized class of state-dependent processing rates useful in modeling congestion adaptive i/o devices.3,4'5 By dealing with mixed systems, we allow consideration of systems with workloads from a finite population (e.g., a collection of terminals), multiprogrammed systems, together with workloads from basically infinite customer populations.