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Analysis of an MAP/PH/1 queue with flexible group service

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Brugno A., D'Apice C., Dudin A., Manzo R.
International Journal of Applied Mathematics and Computer Science
|
2017
|
tom 27
|
nr 1
119-131
EN
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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Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

100%
Gaidamaka Y., Pechinkin A., Razumchik R., Samouylov K., Sopin E.
International Journal of Applied Mathematics and Computer Science
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2014
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tom 24
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nr 3
519-534
EN
Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system $M^{[X]}|G|1⟨L,H⟩|⟨H,R⟩$ with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number of customers in the system. Two control policies defined by instants when it is decided to change the system's mode are considered. The expression for an important performance characteristic of each policy (the mean time between changes in the system mode) is presented. Numerical examples that allow comparison of the efficiency of both policies are given.
3
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A finite-buffer queue with a single vacation policy: an analytical study with evolutionary positioning

86%
Woźniak M., Kempa W., Gabryel M., Nowicki R.
International Journal of Applied Mathematics and Computer Science
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2014
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tom 24
|
nr 4
887-900
EN
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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