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A finite-buffer queue with a single vacation policy: An analytical study with evolutionary positioning

Abstract

In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments are presented. A cost optimization problem is solved using an evolutionary strategy for a class of queueing systems described by exponential and Erlang distributions.

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Analysis of an MAP/PH/1 Queue with Flexible Group Service

Abstract

A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer’s service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace–Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.

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Ergodicity and Perturbation Bounds for Inhomogeneous Birth and Death Processes with Additional Transitions from and to the Origin

References Chen, A., Pollett, P., Li, J. and Zhang, H. (2010). Markovian bulk-arrival and bulk-service queues with state-dependent control, Queueing Systems 64 (3): 267–304. Chen, A. and Renshaw, E. (1997). The m | m |1 queue with mass exodus and mass arrives when empty, Journal of Applied Probability 34 (1): 192–207. Chen, A. and Renshaw, E. (2004). Markov bulk-arriving queues with state-dependent control at idle time, Advances in Applied Probability 36 (2): 499–524. Daleckij, J. and Krein, M. (1975). Stability of solutions of

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