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

Arianna Brugno; Ciro D'Apice; Alexander Dudin; Rosanna Manzo

International Journal of Applied Mathematics and Computer Science (2017)

  • Volume: 27, Issue: 1, page 119-131
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Arianna Brugno, et al. "Analysis of an MAP/PH/1 queue with flexible group service." International Journal of Applied Mathematics and Computer Science 27.1 (2017): 119-131. <http://eudml.org/doc/288094>.

@article{AriannaBrugno2017,
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.},
author = {Arianna Brugno, Ciro D'Apice, Alexander Dudin, Rosanna Manzo},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {queueing system; batch service; multi-rate service; stationary distribution; optimization},
language = {eng},
number = {1},
pages = {119-131},
title = {Analysis of an MAP/PH/1 queue with flexible group service},
url = {http://eudml.org/doc/288094},
volume = {27},
year = {2017},
}

TY - JOUR
AU - Arianna Brugno
AU - Ciro D'Apice
AU - Alexander Dudin
AU - Rosanna Manzo
TI - Analysis of an MAP/PH/1 queue with flexible group service
JO - International Journal of Applied Mathematics and Computer Science
PY - 2017
VL - 27
IS - 1
SP - 119
EP - 131
AB - 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.
LA - eng
KW - queueing system; batch service; multi-rate service; stationary distribution; optimization
UR - http://eudml.org/doc/288094
ER -

References

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