Performance Evaluation of Distributed Systems Based on a Discrete
Real- and Stochastic-Time Process Algebra
J. Markovski and E.P. de Vink

We present a process-algebraic framework for performance evaluation of
discrete-time discrete-event systems. The modeling of the system
builds on a process algebra with conditionally-distributed
discrete-time delays and generally-distributed stochastic delays. In
the general case, the performance analysis is done with the toolset of
the modeling language Chi by means of discrete-event simulation. The
process-algebraic setting allows for expansion laws for the parallel
composition and the maximal progress operator, so one can directly
manipulate the process terms and transform the specification in a
required form. This approach is illustrated by specifying and solving
the recursive specification of the G/G/1/infinity queue, as well as by
specifying a variant of the concurrent alternating bit protocol with
generally-distributed unreliable channels. In a specific situation
when all delays are assumed deterministic, we turn to performance
analysis of probabilistic timed systems. This work employs
discrete-time probabilistic reward graphs, which comprise
deterministic delays and immediate probabilistic choices. Here, we
extend previous investigations on the topic, which only touched
long-run analysis, to tackle transient analysis as well. The
theoretical results obtained allow us to extend the Chi-toolset. For
illustrative purposes, we analyze the concurrent alternating bit
protocol in the extended environment of the Chi-toolset using
discrete-event simulation for generally-distributed channels, the
developed analytical method for deterministic channels, and Markovian
analysis for exponentially-distributed delays.