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- Title
Markovian bulk-arrival and bulk-service queues with state-dependent control.
- Authors
Chen, Anyue; Pollett, Phil; Junping Li; Hanjun Zhang
- Abstract
We study a modified Markovian bulk-arrival and bulk-service queue incorporating 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 hitting time and busy period distributions are answered in detail and the Laplace transforms of these distributions are presented. Further properties including expectations of hitting times and busy period are also explored.
- Subjects
BULK queues; QUEUING theory; MARKOV processes; DISTRIBUTION (Probability theory); PROBABILITY theory
- Publication
Queueing Systems, 2010, Vol 64, Issue 3, p267
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-009-9162-5