Open AccessProduct forms for queueing networks with state-dependent multiple job transitions
Author(s) -
Richard J. Boucherie,
N.M. van Dijk
Publication year - 1991
Publication title -
advances in applied probability
Language(s) - English
Resource type - Journals
eISSN - 1475-6064
pISSN - 0001-8678
DOI - 10.2307/1427516
Subject(s) - queueing theory , product (mathematics) , mathematics , computation , state (computer science) , layered queueing network , routing (electronic design automation) , mathematical optimization , decomposition , constructive , stationary distribution , computer science , algorithm , computer network , markov chain , ecology , statistics , geometry , biology , process (computing) , operating system
A general framework of continuous-time queueing networks is studied with simultaneous state dependent service completions such as due to concurrent servicing or discrete-time slotting and with state dependent batch routings such as most typically modelling blocking. By using a key notion of group-local-balance, necessary and sufficient conditions are given for the stationary distribution to be of product form. These conditions and a constructive computation of the product form are based upon merely local solutions of the group-local-balance equations which can usually be solved explicitly for concrete networks. Moreover, a decomposition theorem is presented to separate service and routing conditions. General batch service and batch routing examples yielding a product form are hereby concluded. As illustrated by various examples, known results on both discrete- and continuoustime queueing networks are unified and extended. DISCRETE-TIME QUEUEING NETWORK; BATCH SERVICE; BATCH ROUTING; BLOCKING; GROUP-LOCAL-BALANCE
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