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On stochastic processes in a multilevel control bulk queueing system |
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| Authors: | Lev Abolnikov Jewgeni Dshalalow Alexander Dukhovny |
| Institution: | 1. Department of Mathematics , Loyola Marymount University , Los Angeles, CA, 90045, USA;2. Department of Applied Mathematics , Florida Institute of Technology , Melbourne, FL, 32901, USA;3. Department of Mathematics , Sun-Francisco State University , Sun-Francisco, CA, 94132, USA |
| Abstract: | This article analyzes some stochastic processes that arise in a bulk single server queue with continuously operating server, state dependent compound Poisson input flow and general state dependent service process. The authors treat the queueing process as a semi–regenerative process and obtain the invariant probability measure and the transient distribution for the embedded Markov chain. The stationary probability measure for the queueing process with continuous time parameter is found by using semi-regenerative techniques. The authors also study the input and output processes and establish ergodic theorems for some functionals of these processes. The results are obtained in terms of the invariant probability measure for the embedded process and the stationary measure for the queueing process with continuous time parameter |
| Keywords: | Controlled Input Controlled Service Controlled Batch Size Single-Server Queue Queueing Process Markov Chain Semi-Regenerative Process Semi-Markov Process Ergodic Theorems Output Process Optimization |