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

• Autorzy: Arianna Brugno , Ciro D'Apice , Alexander Dudin , Rosanna Manzo
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

queueing system; batch service; multi-rate service; stationary distribution; optimization

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: 27
• Numer: 1
• Strony: 119-131

Daty

wydano

2017

otrzymano

2016-07-19

poprawiono

2016-11-06

zaakceptowano

2016-11-09

Twórcy

autor

Arianna Brugno

• Department of Information Engineering, Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano (SA), Italy

autor

Ciro D'Apice

• Department of Information Engineering, Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano (SA), Italy

autor

Alexander Dudin

• Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Av., Minsk, 220030, Belarus

autor

Rosanna Manzo

• Department of Information Engineering, Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano (SA), Italy

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Identyfikatory

DOI

10.1515/amcs-2017-0009