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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

7 Citations (Scopus)

Abstract

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.

Original language	English
Title of host publication	Proceedings of the 29th International Teletraffic Congress, ITC 2017
Publisher	IEEE
Pages	232-240
Number of pages	9
Volume	1
ISBN (Electronic)	9780988304536
DOIs	https://doi.org/10.23919/ITC.2017.8064360
Publication status	Published - 10 Oct 2017
MoE publication type	A4 Article in a conference publication
Event	International Teletraffic Congress - Genoa, Italy Duration: 4 Sep 2017 → 8 Sep 2017 Conference number: 29 http://itc29.org/

Conference

Conference	International Teletraffic Congress
Abbreviated title	ITC
Country/Territory	Italy
City	Genoa
Period	04/09/2017 → 08/09/2017
Internet address	http://itc29.org/

Keywords

Batch arrivals
Generating function
Laplace transform
LST
M/G/1
MDP
Value function

Access to Document

10.23919/ITC.2017.8064360

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Cite this

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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.",

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AU - Virtamo, Jorma

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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.

AB - 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 - Generating function

KW - Laplace transform

KW - LST

KW - M/G/1

KW - MDP

KW - Value function

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

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