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ABSTRACT: This article deals with a general single-server bulk queueing system with a server waiting until the queue will reach level r before it starts processing customers. If at least r customers are available the server takes a batch of the fixed size r of units for service. The input stream is assumed to be a compound Poisson process modulated by a semi-Markov process and with a multilevel control of service time.
International Journal of Mathematics and Mathematical Sciences. 01/1994;
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ABSTRACT: Stochastic processes in a bulk single-server queue with continuously operating server, semi-Markov modulated compound Poisson input process and general state dependent service process are studied. The authors treat the queueing process with continuous time parameter as a semi-regenerative process and obtain its stationary probability distribution. The authors also study the input and output processes and establish ergodic theorems for some functionals of these processes. The results obtained in the article are illustrated by various examples.
Statistics [?] Probability Letters 01/1993; 16(2):121-128. · 0.50 Impact Factor
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ABSTRACT: The authors study the input, output and queueing processes in a general controlled single-server bulk queueing system. It is supposed that inter-arrival time, service time, batch size of arriving units and the capacity of the server depend on the queue length.
Journal of Applied Mathematics and Stochastic Analysis. 01/1990;
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ABSTRACT: This article studies a Markov chain describing the evolution of the queue in a general single-server bulk queueing system with continuously operating (or, equivalently vacationing) server, semi-Markov modulated compound Poisson input, queue length dependent service time, and multilevel control server capacity. We establish a necessary and sufficient criterion for ergodicity of this Markov chain and find its stationary distribution. As an example a single-server queueing system is considered, and some explicit results are obtained in this case.
Operations Research Letters.
