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The Decay Parameter and Invariant Measures for Markovian Bulk-Arrival Queues with Control at Idle Time |
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| Authors: | Li Junping Chen Anyue |
| Institution: | 1. School of Mathematical Science and Computing Technology, Central South University, Changsha, 410075, China 2. Division of Statistics and Probability, Department of Mathematical Sciences, The University of Liverpool, Liverpool, L69 7ZL, UK 3. Department of Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, 215123, China |
| Abstract: | We consider properties regarding 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 λ Z , is firstly revealed. An elegant criterion regarding λ Z -recurrence and λ Z -positive is obtained. The corresponding subinvariant and invariant measures are considered and the structure of all the subinvariant and invariant measures are presented. |
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