On Multiserver Queues with Synchronous Fluctuation of Traffic Intensity

Walter SOTELO; Akira FUKUDA

On Multiserver Queues with Synchronous Fluctuation of Traffic Intensity

Walter SOTELO, Akira FUKUDA

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A study is presented on the generalization of the M/M/1 model with synchronous fluctuation of traffic intensity for the case of more than one server. The parameters of the queueing system fluctuates between two phases and the phase process is assumed to make changes according to an irreducible Markov chain. Phase changes may occur only when a customer arrives to the queue, further, his service time is also determined at his arrival instant. We compare our results to that of the asynchronous one and the comparison clearly shows that we can approximate the performance of the asynchronous model by that of the synchronous one and vice-versa. However, we point out that, to extend the M/M/K (M/M/) model with fluctuating parameters to the case of general interarrival, service, or sojourn time distribution, is easier in the case of the synchronous model than in the case of the asynchronous one since the latter introduces very considerable analytic complications. Two models, the M/M/K and M/M/, with synchronous fluctuation of parameters are analyzed in depth. Explicit results for the expected queue length are presented and discussed. Finally, numerical examples are used to support the theoretical analysis for a variety of traffic conditions.

Publication: IEICE TRANSACTIONS on transactions Vol.E70-E No.10 pp.951-959

Publication Date: 1987/10/25

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Type of Manuscript: PAPER

Category: Engineering Science in General

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Walter SOTELO
Akira FUKUDA

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Walter SOTELO, Akira FUKUDA, "On Multiserver Queues with Synchronous Fluctuation of Traffic Intensity" in IEICE TRANSACTIONS on transactions, vol. E70-E, no. 10, pp. 951-959, October 1987, doi: .
Abstract: A study is presented on the generalization of the M/M/1 model with synchronous fluctuation of traffic intensity for the case of more than one server. The parameters of the queueing system fluctuates between two phases and the phase process is assumed to make changes according to an irreducible Markov chain. Phase changes may occur only when a customer arrives to the queue, further, his service time is also determined at his arrival instant. We compare our results to that of the asynchronous one and the comparison clearly shows that we can approximate the performance of the asynchronous model by that of the synchronous one and vice-versa. However, we point out that, to extend the M/M/K (M/M/) model with fluctuating parameters to the case of general interarrival, service, or sojourn time distribution, is easier in the case of the synchronous model than in the case of the asynchronous one since the latter introduces very considerable analytic complications. Two models, the M/M/K and M/M/, with synchronous fluctuation of parameters are analyzed in depth. Explicit results for the expected queue length are presented and discussed. Finally, numerical examples are used to support the theoretical analysis for a variety of traffic conditions.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e70-e_10_951/_p

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@ARTICLE{e70-e_10_951,
author={Walter SOTELO, Akira FUKUDA, },
journal={IEICE TRANSACTIONS on transactions},
title={On Multiserver Queues with Synchronous Fluctuation of Traffic Intensity},
year={1987},
volume={E70-E},
number={10},
pages={951-959},
abstract={A study is presented on the generalization of the M/M/1 model with synchronous fluctuation of traffic intensity for the case of more than one server. The parameters of the queueing system fluctuates between two phases and the phase process is assumed to make changes according to an irreducible Markov chain. Phase changes may occur only when a customer arrives to the queue, further, his service time is also determined at his arrival instant. We compare our results to that of the asynchronous one and the comparison clearly shows that we can approximate the performance of the asynchronous model by that of the synchronous one and vice-versa. However, we point out that, to extend the M/M/K (M/M/) model with fluctuating parameters to the case of general interarrival, service, or sojourn time distribution, is easier in the case of the synchronous model than in the case of the asynchronous one since the latter introduces very considerable analytic complications. Two models, the M/M/K and M/M/, with synchronous fluctuation of parameters are analyzed in depth. Explicit results for the expected queue length are presented and discussed. Finally, numerical examples are used to support the theoretical analysis for a variety of traffic conditions.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - On Multiserver Queues with Synchronous Fluctuation of Traffic Intensity
T2 - IEICE TRANSACTIONS on transactions
SP - 951
EP - 959
AU - Walter SOTELO
AU - Akira FUKUDA
PY - 1987
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E70-E
IS - 10
JA - IEICE TRANSACTIONS on transactions
Y1 - October 1987
AB - A study is presented on the generalization of the M/M/1 model with synchronous fluctuation of traffic intensity for the case of more than one server. The parameters of the queueing system fluctuates between two phases and the phase process is assumed to make changes according to an irreducible Markov chain. Phase changes may occur only when a customer arrives to the queue, further, his service time is also determined at his arrival instant. We compare our results to that of the asynchronous one and the comparison clearly shows that we can approximate the performance of the asynchronous model by that of the synchronous one and vice-versa. However, we point out that, to extend the M/M/K (M/M/) model with fluctuating parameters to the case of general interarrival, service, or sojourn time distribution, is easier in the case of the synchronous model than in the case of the asynchronous one since the latter introduces very considerable analytic complications. Two models, the M/M/K and M/M/, with synchronous fluctuation of parameters are analyzed in depth. Explicit results for the expected queue length are presented and discussed. Finally, numerical examples are used to support the theoretical analysis for a variety of traffic conditions.
ER -