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The decay parameter and invariant measures for Markovian bulk-arrival queues with control at idle time. (English) Zbl 1270.60102
Summary: We consider properties regarding the decay parameter and invariant measures for unstable Markovian bulk-arrival queues with control at idle time. The exact value of the decay parameter, denoted by \(\lambda _{Z }\), is firstly presented. An elegant criterion regarding \(\lambda _{Z }\)-recurrence and \(\lambda _{Z }\)-positivity is obtained. The corresponding subinvariant and invariant measures are considered, and the structures of all the subinvariant and invariant measures are presented.

60K25 Queueing theory (aspects of probability theory)
60J27 Continuous-time Markov processes on discrete state spaces
90B22 Queues and service in operations research
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