Application of Resolvent Decomposition Theorem in Markovian Bulk Queues

Xiaohan Wu

2023, v.29, Issue 1, 99-143


We use the so-called resolvent decomposition theorem to study a modified Markovian bulk-arrival and bulk-service queue
incorporating the state-dependent control. The stopped bulk-arrival
and bulk-service queue is first investigated and the relationship
with our queueing model is examined and exploited. Equilibrium
behaviour is studied and the probability generating function of the
equilibrium distribution is obtained. Queue length behaviour is
also examined and the Laplace transform of the queue length
distribution is presented. The important questions regarding busy period distributions are answered in detail and the
Laplace transforms of these distributions are presented. Furthermore, two interesting examples are provided in the last section of this paper.

Keywords: Bulk-arrival and bulk-service queues, state-dependent control, equilibrium distribution, queue length distributions, busy period distributions


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