A Compositional Approach to Performance Modelling by Jane Hillston

By Jane Hillston

This is often the 1st booklet featuring a stochastic extension of method algebra, PEPA; this can be proven to be compatible for specifying a Markov procedure, which may then be utilized to functionality modelling. the tactic, that's illustrated with case experiences taken from the world of verbal exchange structures, can simply be used to build various types that may be analysed utilizing commonplace numerical suggestions. one of many significant merits of PEPA over the traditional tools for specifying stochastic functionality versions is the inherent equipment for reasoning concerning the constitution and behavior of types. within the later chapters this gear is exploited to outline 4 equivalence kin over PEPA parts. each one of those notions of equivalence has intrinsic curiosity from a approach algebra standpoint. even if, also they are established to be priceless in a functionality modelling context. To finish the publication, a bit has been additional surveying contemporary leads to the realm and discussing open questions.

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Extra info for A Compositional Approach to Performance Modelling (Distinguished Dissertations in Computer Science)

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Again, concern has been expressed that it would not be possible to reduce the partition sizes and exploit this feature, because of memory requirements [16]. Our results indicate that rather small partition sizes may suffice in many cases. 2 M o d e l i n g M e m o r y Usage A separate issue is the modeling of memory usage for use in simulations and analysis. SpecificMly, we would like to be able to model how resource requirements change when applications scale to larger systems. Three models have been proposed in the literature: - - - F i x e d w o r k .

The model parameters extracted from these moments are given in table 3. rives at an analytical expression for the cdf of the models used in this paper, namely n-1 2 cdf(xj)= l- Epie i=l -~"~J ( E (~J%---i k! )]~'~ k=O (20) From this expression of the edf and a uniform random number generator, U[O,I], the random variables { z j } that are commensurate with equation 5 can be obtained by solving for x j in equation 19. 91 Table 10. First three non-central moments of the distribution of the CPU time used by the jobs in the observed workload.

Unit of time is in seconds. The symbols are defined in Sections 3 and 5. 37 Table 7. First three non-central moments of the of inter-arrival time distribution in the observed workload. Unit of time is in seconds. The symbols are defined in Sections 3 and 5. The model parameters extracted from these moments are given in table 1. The only remaining algorithm that needs to be discussed here is a method to generate random numbers from a Hyper Erlang distribution of Common Order with appropriate model parameters for a particular class.

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