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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.

##### MSC:
 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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