This chapter shows that, under various assumptions, the kernel iterates are equal to the lifted QPLEX iterates, i.e., QPLEX iterates after applying a multinomial lift map. We call such a result an exactness result, and we establish such results in three specific settings. In the first two settings, we consider QPLEX chains that encompass as special cases the multiserver queueing model from Chap. 2 in which (1) the service duration distribution is geometric and does not vary over time and (2) the number of servers is infinite. The third setting considers an arbitrary single activity QPLEX chain in which the size functions only take on values 0 or 1.

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Exactness Results

  • Antonius B. Dieker,
  • Steven T. Hackman

摘要

This chapter shows that, under various assumptions, the kernel iterates are equal to the lifted QPLEX iterates, i.e., QPLEX iterates after applying a multinomial lift map. We call such a result an exactness result, and we establish such results in three specific settings. In the first two settings, we consider QPLEX chains that encompass as special cases the multiserver queueing model from Chap. 2 in which (1) the service duration distribution is geometric and does not vary over time and (2) the number of servers is infinite. The third setting considers an arbitrary single activity QPLEX chain in which the size functions only take on values 0 or 1.