General queueing network models for computer system performance analysis. A maximum entropy method of analysis and aggregation of general queueing network models with application to computer systems.

摘要

In this study the maximum entropy formalism [JAYN 57] is suggestedudas an alternative theory for general queueing systems of computerudperformance analysis. The motivation is to overcome some of theudproblems arising in this field and to extend the scope of the resultsudderived in the context of Markovian queueing theory.udFor the M/G/l model a unique maximum entropy solution., satisfyingudlocALl balance is derived independent of any assumptions about the serviceudtime distribution. However, it is shown that this solution is identicaludto the steady state solution of the underlying Marko-v process when theudservice time distribution is of the generalised exponential (CE) type.ud(The GE-type distribution is a mixture of an exponential term and a unitudimpulse function at the origin). For the G/M/1 the maximum entropyudsolution is identical in form to that of the underlying Markov process,udbut a GE-type distribution still produces the maximum overall similaruddistributions.udFor the GIG11 model there are three main achievements:udfirst, the spectral methods are extended to give exaft formulae forudthe average number of customers in the system for any G/G/l with rationaludLaplace transform. Previously, these results are obtainable only throughudsimulation and approximation methods.ud(ii) secondly, a maximum entropy model is developed and used to obtainudunique solutions for some types of the G/G/l. It is also discussed howudthese solutions can be related to the corresponding stochastic processes.ud(iii) the importance of the G/GE/l and the GE/GE/l for the analysis ofudgeneral networks is discussed and some flow processes for these systemsudare characterised.udFor general queueing networks it is shown that the maximum entropyudsolution is a product of the maximum entropy solutions of the individualudnodes. Accordingly, existing computational algorithms are extended toudcover general networks with FCFS disciplines. Some implementations areudsuggested and a flow algorithm is derived. Finally, these results areudiised to improve existing aggregation methods.udIn addition, the study includes a number of examples, comparisons,udsurveys, useful comments and conclusions.