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

5 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	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

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Value (Generating) Functions for the M<sup>X</sup>/G/1 Queue'. Together they form a unique fingerprint.

Cite this

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

@inproceedings{86f4130298de4391a0333161c853758d,

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",

year = "2017",

month = oct,

day = "10",

doi = "10.23919/ITC.2017.8064360",

language = "English",

volume = "1",

pages = "232--240",

booktitle = "Proceedings of the 29th International Teletraffic Congress, ITC 2017",

publisher = "IEEE",

address = "United States",

note = "International Teletraffic Congress, ITC ; Conference date: 04-09-2017 Through 08-09-2017",

url = "http://itc29.org/",

}

TY - GEN

T1 - Value (Generating) Functions for the MX/G/1 Queue

AU - Hyytia, Esa

AU - Righter, Rhonda

AU - Virtamo, Jorma

AU - Viitasaari, Lauri

N1 - Conference code: 29

PY - 2017/10/10

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.

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.

KW - Batch arrivals

KW - Generating function

KW - Laplace transform

KW - LST

KW - M/G/1

KW - MDP

KW - Value function

UR - http://www.scopus.com/inward/record.url?scp=85040191554&partnerID=8YFLogxK

U2 - 10.23919/ITC.2017.8064360

DO - 10.23919/ITC.2017.8064360

M3 - Conference contribution

AN - SCOPUS:85040191554

VL - 1

SP - 232

EP - 240

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

PB - IEEE

T2 - International Teletraffic Congress

Y2 - 4 September 2017 through 8 September 2017

ER -