Performance Evaluation 36–37 (1999) 19–33 www.elsevier.com/locate/peva Mean value analysis of product form solution queueing networks with repetitive service blocking Matteo Sereno Dipartimento di Informatica, Universita ` di Torino, Corso Svizzera 185, 10149 Turin, Italy Abstract 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.  1999 Elsevier Science B.V. All rights reserved. Keywords: Queueing networks with blocking; Repetitive service blocking; Product form solution; Computational algorithms; Mean value analysis algorithm 1. Introduction Queueing networks are used to model complex service systems such as production, communication and computer systems. Networks of queues with blocking are used to represent resource constraints such as memory constraints or software constraints in computer systems, as well as window flow control in communication networks. Various types of blocking have been reported in the literature (e.g., [4,5, 13,15]) in order to model different system behaviours. Each blocking mechanism describes how a node becomes blocked, what happens in blocking situation and how the blocked node becomes unblocked. The most commonly used blocking mechanisms are the blocking after service, the blocking before service, and the repetitive service also called rejection blocking [4,5,13,15]. Queueing networks with blocking are in general difficult to treat. Product form solutions have been derived only under particular constraints and depending on the considered blocking type. A discussion of product form queueing networks with blocking can found in [5]. In this paper we concern with product form queueing networks with repetitive service blocking. 0166-5316/99/$ – see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S0166-5316(99)00038-3