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Containment of socially optimal policies in multiple-facility Markovian queueing systems

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Containment of socially optimal policies in multiple-facility Markovian queueing systems. / Shone, Robert; Knight, Vincent ; Harper, Paul; Williams, Janet; Minty, John.

In: Journal of the Operational Research Society, Vol. 67, 25.11.2015, p. 629-643.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Shone, R, Knight, V, Harper, P, Williams, J & Minty, J 2015, 'Containment of socially optimal policies in multiple-facility Markovian queueing systems', Journal of the Operational Research Society, vol. 67, pp. 629-643. https://doi.org/10.1057/jors.2015.98

APA

Shone, R., Knight, V., Harper, P., Williams, J., & Minty, J. (2015). Containment of socially optimal policies in multiple-facility Markovian queueing systems. Journal of the Operational Research Society, 67, 629-643. https://doi.org/10.1057/jors.2015.98

Vancouver

Shone R, Knight V, Harper P, Williams J, Minty J. Containment of socially optimal policies in multiple-facility Markovian queueing systems. Journal of the Operational Research Society. 2015 Nov 25;67:629-643. https://doi.org/10.1057/jors.2015.98

Author

Shone, Robert ; Knight, Vincent ; Harper, Paul ; Williams, Janet ; Minty, John. / Containment of socially optimal policies in multiple-facility Markovian queueing systems. In: Journal of the Operational Research Society. 2015 ; Vol. 67. pp. 629-643.

Bibtex

@article{9f9d1c3ce8434c9595001d54f8d4ce98,
title = "Containment of socially optimal policies in multiple-facility Markovian queueing systems",
abstract = "We consider a Markovian queueing system with N heterogeneous service facilities, each of which has multiple servers available, linear holding costs, a fixed value of service and a first-come-first-serve queue discipline. Customers arriving in the system can be either rejected or sent to one of the N facilities. Two different types of control policies are considered, which we refer to as {\textquoteleft}selfishly optimal{\textquoteright} and {\textquoteleft}socially optimal{\textquoteright}. We prove the equivalence of two different Markov Decision Process formulations, and then show that classical M/M/1 queue results from the early literature on behavioural queueing theory can be generalized to multiple dimensions in an elegant way. In particular, the state space of the continuous-time Markov process induced by a socially optimal policy is contained within that of the selfishly optimal policy. We also show that this result holds when customers are divided into an arbitrary number of heterogeneous classes, provided that the service rates remain non-discriminatory.",
keywords = "queues with balking; Markov Decision Processes; equilibrium strategies; optimal strategies; dynamic programming",
author = "Robert Shone and Vincent Knight and Paul Harper and Janet Williams and John Minty",
year = "2015",
month = nov,
day = "25",
doi = "10.1057/jors.2015.98",
language = "English",
volume = "67",
pages = "629--643",
journal = "Journal of the Operational Research Society",
issn = "0160-5682",
publisher = "Taylor and Francis Ltd.",

}

RIS

TY - JOUR

T1 - Containment of socially optimal policies in multiple-facility Markovian queueing systems

AU - Shone, Robert

AU - Knight, Vincent

AU - Harper, Paul

AU - Williams, Janet

AU - Minty, John

PY - 2015/11/25

Y1 - 2015/11/25

N2 - We consider a Markovian queueing system with N heterogeneous service facilities, each of which has multiple servers available, linear holding costs, a fixed value of service and a first-come-first-serve queue discipline. Customers arriving in the system can be either rejected or sent to one of the N facilities. Two different types of control policies are considered, which we refer to as ‘selfishly optimal’ and ‘socially optimal’. We prove the equivalence of two different Markov Decision Process formulations, and then show that classical M/M/1 queue results from the early literature on behavioural queueing theory can be generalized to multiple dimensions in an elegant way. In particular, the state space of the continuous-time Markov process induced by a socially optimal policy is contained within that of the selfishly optimal policy. We also show that this result holds when customers are divided into an arbitrary number of heterogeneous classes, provided that the service rates remain non-discriminatory.

AB - We consider a Markovian queueing system with N heterogeneous service facilities, each of which has multiple servers available, linear holding costs, a fixed value of service and a first-come-first-serve queue discipline. Customers arriving in the system can be either rejected or sent to one of the N facilities. Two different types of control policies are considered, which we refer to as ‘selfishly optimal’ and ‘socially optimal’. We prove the equivalence of two different Markov Decision Process formulations, and then show that classical M/M/1 queue results from the early literature on behavioural queueing theory can be generalized to multiple dimensions in an elegant way. In particular, the state space of the continuous-time Markov process induced by a socially optimal policy is contained within that of the selfishly optimal policy. We also show that this result holds when customers are divided into an arbitrary number of heterogeneous classes, provided that the service rates remain non-discriminatory.

KW - queues with balking; Markov Decision Processes; equilibrium strategies; optimal strategies; dynamic programming

U2 - 10.1057/jors.2015.98

DO - 10.1057/jors.2015.98

M3 - Journal article

VL - 67

SP - 629

EP - 643

JO - Journal of the Operational Research Society

JF - Journal of the Operational Research Society

SN - 0160-5682

ER -