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

Performance analysis

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference article in proceedings › Scientific › vertaisarvioitu

7 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 lokak. 2017
OKM-julkaisutyyppi	A4 Artikkeli konferenssijulkaisussa
Tapahtuma	International Teletraffic Congress - Genoa, Italia Kesto: 4 syysk. 2017 → 8 syysk. 2017 Konferenssinumero: 29 http://itc29.org/

Conference

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

Pääsy asiakirjaan

10.23919/ITC.2017.8064360

Muut tiedostot ja linkit

Link to publication in Scopus

Siteeraa tätä

@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 article in proceedings

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 -