Mean Value Analysis of Product Form Solution Queueing Networks with Repetitive Service Blocking

Queueing network models with finite capacity queues and blocking are used to represent systems with resource constraints, such as production, communication and computer systems. Various blocking mechanisms have been defined in the literature to represent the different behaviours of real systems with limited resources. Queueing networks with blocking have a product form solution under special constraints, for different blocking mechanisms. In this paper we present a Mean Value Analysis for the computation of performance measures in product form solution queueing networks with repetitive service blocking. Basic to the derivation of this algorithm are recursive expressions for the performance indices that are a non trivial generalisation of those derived for the Mean Value Analysis of product form queueing networks without blocking. In this paper we give a formal derivation of several recursive relations as well as details on their implementation. A few basic examples are evaluated with the techniques discussed in this paper to show the advantages of this approach.