A Fluid Limit for the Engset Model: An Application to Retrial Queues

Stylianos Georgiadis; Pascal  Moyal; Tamás Bérczes; János  Sztrik

A Fluid Limit for the Engset Model: An Application to Retrial Queues

Stylianos Georgiadis, Pascal Moyal, Tamás Bérczes, János Sztrik

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

We represent the classical Engset-loss model by the stochastic process counting the number of customers in the system. A fluid limit for this process is established for a ll the possible values of the various parameters of the system, as the number of servers tends to infinity along with the number of sources. Our results are derived through a semi-martingale decomposition method. A numerical application is provided to illustrate these results. Then, we represent a finite-source retrial queue considering in addition the number of sources in orbit. Finally, we extend the fluid limit results to a retrial queueing system, discussing different cases.

Original language	English
Title of host publication	Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013)
Publication date	2013
Pages	315-320
Publication status	Published - 2013
Externally published	Yes
Event	2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013) - Barcelona, Spain Duration: 16 Feb 2013 → 18 Feb 2013 Conference number: 2 http://www.icores.org/?y=2013

Conference

Conference	2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013)
Number	2
Country	Spain
City	Barcelona
Period	16/02/2013 → 18/02/2013
Internet address	http://www.icores.org/?y=2013

Keywords

Engset Model
Fluid Limit
Semi-martingale Decomposition
Retrial Queues

Cite this

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title = "A Fluid Limit for the Engset Model: An Application to Retrial Queues",

abstract = "We represent the classical Engset-loss model by the stochastic process counting the number of customers in the system. A fluid limit for this process is established for a ll the possible values of the various parameters of the system, as the number of servers tends to infinity along with the number of sources. Our results are derived through a semi-martingale decomposition method. A numerical application is provided to illustrate these results. Then, we represent a finite-source retrial queue considering in addition the number of sources in orbit. Finally, we extend the fluid limit results to a retrial queueing system, discussing different cases.",

keywords = "Engset Model, Fluid Limit, Semi-martingale Decomposition, Retrial Queues",

author = "Stylianos Georgiadis and Pascal Moyal and Tam{\'a}s B{\'e}rczes and J{\'a}nos Sztrik",

year = "2013",

language = "English",

pages = "315--320",

booktitle = "Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013)",

note = "2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013), ICORES ; Conference date: 16-02-2013 Through 18-02-2013",

url = "http://www.icores.org/?y=2013",

}

A Fluid Limit for the Engset Model : An Application to Retrial Queues. / Georgiadis, Stylianos; Moyal, Pascal ; Bérczes, Tamás; Sztrik, János .

Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013). 2013. p. 315-320.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - A Fluid Limit for the Engset Model

T2 - 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013)

AU - Georgiadis, Stylianos

AU - Moyal, Pascal

AU - Bérczes, Tamás

AU - Sztrik, János

N1 - Conference code: 2

PY - 2013

Y1 - 2013

N2 - We represent the classical Engset-loss model by the stochastic process counting the number of customers in the system. A fluid limit for this process is established for a ll the possible values of the various parameters of the system, as the number of servers tends to infinity along with the number of sources. Our results are derived through a semi-martingale decomposition method. A numerical application is provided to illustrate these results. Then, we represent a finite-source retrial queue considering in addition the number of sources in orbit. Finally, we extend the fluid limit results to a retrial queueing system, discussing different cases.

AB - We represent the classical Engset-loss model by the stochastic process counting the number of customers in the system. A fluid limit for this process is established for a ll the possible values of the various parameters of the system, as the number of servers tends to infinity along with the number of sources. Our results are derived through a semi-martingale decomposition method. A numerical application is provided to illustrate these results. Then, we represent a finite-source retrial queue considering in addition the number of sources in orbit. Finally, we extend the fluid limit results to a retrial queueing system, discussing different cases.

KW - Engset Model

KW - Fluid Limit

KW - Semi-martingale Decomposition

KW - Retrial Queues

M3 - Article in proceedings

SP - 315

EP - 320

BT - Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013)

Y2 - 16 February 2013 through 18 February 2013

ER -

A Fluid Limit for the Engset Model: An Application to Retrial Queues

Abstract

Conference

Keywords

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