Block-structured stochastic process algebra and its applications to queueing systems

A new and general stochastic process algebra with block structure, called PEPABS, is introduced, which is a generalisation of PEPAph∞. For PEPABS, the activity durations may be allowed to be generally distributed, and the corresponding transition probability matrix has a block-partitioned structure. Specifically, PEPABS is suitable for describing and analysing performance of general systems with block-structured transition probability matrices, such as Markov chains of GI/G/1 type. The steady-state probabilities of the PEPABS model can be calculated by means of censoring technique and the RG-factorisation, which have been successfully applied to study infinite-state Markov chain or Markov renewal process. Some practical examples show that the formal method is convenient to model and analyse non-Markovian systems, and can efficiently tackle an infinite-state problem under an algorithmic framework.