Value (Generating) Functions for the MX/G/1 Queue

Esa Hyytia; Rhonda Righter; Jorma Virtamo; Lauri Viitasaari

doi:10.23919/ITC.2017.8064360

Value (Generating) Functions for the M^X/G/1 Queue

Esa Hyytia, Rhonda Righter, Jorma Virtamo, Lauri Viitasaari

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference contribution › Scientific › vertaisarvioitu

4 Sitaatiot (Scopus)

Abstrakti

We analyze the M^X/G/1 queue in the framework of Markov decision processes (MDPs). The service times become known upon arrival, and each job incurs a cost according to a given cost function. The value function is a central concept in MDP theory as it characterizes the value of the system's state with respect to future developments. We derive compact expressions for the generating functions for general families of value functions corresponding to often used cost structures defined in terms of waiting and sojourn times. Moreover, we consider systems with and without setup delays.

Alkuperäiskieli	Englanti
Otsikko	Proceedings of the 29th International Teletraffic Congress, ITC 2017
Kustantaja	IEEE
Sivut	232-240
Sivumäärä	9
Vuosikerta	1
ISBN (elektroninen)	9780988304536
DOI - pysyväislinkit	https://doi.org/10.23919/ITC.2017.8064360
Tila	Julkaistu - 10 lokakuuta 2017
OKM-julkaisutyyppi	A4 Artikkeli konferenssijulkaisuussa
Tapahtuma	International Teletraffic Congress - Genoa, Italia Kesto: 4 syyskuuta 2017 → 8 syyskuuta 2017 Konferenssinumero: 29 http://itc29.org/

Conference

Conference	International Teletraffic Congress
Lyhennettä	ITC
Maa	Italia
Kaupunki	Genoa
Ajanjakso	04/09/2017 → 08/09/2017
www-osoite	http://itc29.org/

Pääsy asiakirjaan

10.23919/ITC.2017.8064360

Link to publication in Scopus

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Siteeraa tätä

Hyytia, E., Righter, R., Virtamo, J., & Viitasaari, L. (2017). Value (Generating) Functions for the M^X/G/1 Queue. teoksessa Proceedings of the 29th International Teletraffic Congress, ITC 2017 (Vuosikerta 1, Sivut 232-240). [8064360] IEEE. https://doi.org/10.23919/ITC.2017.8064360

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title = "Value (Generating) Functions for the MX/G/1 Queue",

abstract = "We analyze the MX/G/1 queue in the framework of Markov decision processes (MDPs). The service times become known upon arrival, and each job incurs a cost according to a given cost function. The value function is a central concept in MDP theory as it characterizes the value of the system's state with respect to future developments. We derive compact expressions for the generating functions for general families of value functions corresponding to often used cost structures defined in terms of waiting and sojourn times. Moreover, we consider systems with and without setup delays.",

keywords = "Batch arrivals, Generating function, Laplace transform, LST, M/G/1, MDP, Value function",

author = "Esa Hyytia and Rhonda Righter and Jorma Virtamo and Lauri Viitasaari",

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AU - Hyytia, Esa

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Y1 - 2017/10/10

N2 - We analyze the MX/G/1 queue in the framework of Markov decision processes (MDPs). The service times become known upon arrival, and each job incurs a cost according to a given cost function. The value function is a central concept in MDP theory as it characterizes the value of the system's state with respect to future developments. We derive compact expressions for the generating functions for general families of value functions corresponding to often used cost structures defined in terms of waiting and sojourn times. Moreover, we consider systems with and without setup delays.

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KW - Batch arrivals

KW - Generating function

KW - Laplace transform

KW - LST

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KW - MDP

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BT - Proceedings of the 29th International Teletraffic Congress, ITC 2017

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