Throughput analysis for finite-buffered queueing networks with emphasis on the fork/join type

Abstract

This thesis is concerned with the throughput analysis of communication, computer, and manufacturing systems where system performance is affected by their physical resource limitations (storage spaces or buffers). A finite-buffered queueing network has been a useful tool for predicting several performance measures of such real-life systems. An important feature of queueing networks with finite buffers is that a phenomenon called blocking occurs, which seriously degrades network performances, particularly throughput. These queueing networks are known to be difficult to analyze as they are analytically intractable in general. First, we deal with finite-buffered fork/join queueing networks(FJQNs), which have been extensively used to predict the performances of parallel processing, assembly/disassembly manufacturing, and distributed replicated database systems. Introducing the notion of evolutionarily equivalent relations, a key result on the throughput equivalence between dissimilar-appearing FJQNs with finite buffers and GI service time distributions is obtained. And additional throughput equivalencies are also noticed along with an observation on a multi-server case. The practical significance of these results is that throughput calculation of a general FJQN can be significantly facilitated from the multiplicity of equivalent networks which appear different in configuration. Moreover, these equivalent relations are very useful for developing some approximation and bounding methods. To understand the effect of service times and buffer capacities on throughput of finite-buffered FJQNs we introduce the sample path technique, and show that speeding up service, reducing variability of service times, and increasing buffer capacities improve the network throughput. We also explore the concavity property of throughput with respect to buffer capacities, which has important implications in optimization studies. And then the comparisons between networks with different block...