In this paper we extend the class of MAP queueing\udnetworks to include blocking models, which are useful to describe the performance of service instances which have a limited concurrency level. We consider two different blocking mechanisms: Repetitive Service-Random Destination (RS-RD) and Blocking\udAfter Service (BAS). We propose a methodology to evaluate MAP queueing networks with blocking based on the recently proposed Quadratic Reduction (QR), a state space transformation that decreases the number of states in the Markov chain underlying\udthe queueing network model. From this reduced state space, we obtain boundable approximations on average performance\udindexes such as throughput, response time, utilizations. The two\udapproximations that dramatically enhance the QR bounds are based on maximum entropy and on a novel minimum mutual information principle, respectively. Stress cases of increasing complexity illustrate the excellent accuracy of the proposed approximations on several models of practical interest.
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