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1 results

  • Product forms for queueing networks with state-dependent multiple job transitions

  • Richard J. Boucherie, Nico M. Van DIJK
  • Journal:
    Advances in Applied Probability / Volume 23 / Issue 1 / March 1991
    Published online by Cambridge University Press:
    01 July 2016, pp. 152-187
    Print publication:
    March 1991

  • 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 continuous-time queueing networks are unified and extended.