The stationary workload of the G/M/1 queue with impatient customers

Jongho Bae; Sunggon Kim

doi:10.1007/s11134-009-9159-0

The stationary workload of the G/M/1 queue with impatient customers

Jongho Bae, Sunggon Kim

Department of Statistics

Chungnam National University

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We consider a G/M/1 queue in which the patience time of the customers is constant. The stationary distribution of the workload of the server, or the virtual waiting time, is derived by the level crossing argument. To this end, we obtain the expected downcrossings of a level in the workload process during a busy cycle and then the expected length of a busy cycle. For both the expectations, we use the dual property between the M/G/1 and G/M/1 queue.

Original language	English
Pages (from-to)	253-265
Number of pages	13
Journal	Queueing Systems
Volume	64
Issue number	3
DOIs	https://doi.org/10.1007/s11134-009-9159-0
State	Published - Mar 2010

Keywords

G/M/1 queue
Impatient customers
Virtual waiting time
Workload

Access to Document

10.1007/s11134-009-9159-0

Cite this

@article{68d807780de44ef486ee3c90b1bc1b9c,

title = "The stationary workload of the G/M/1 queue with impatient customers",

abstract = "We consider a G/M/1 queue in which the patience time of the customers is constant. The stationary distribution of the workload of the server, or the virtual waiting time, is derived by the level crossing argument. To this end, we obtain the expected downcrossings of a level in the workload process during a busy cycle and then the expected length of a busy cycle. For both the expectations, we use the dual property between the M/G/1 and G/M/1 queue.",

keywords = "G/M/1 queue, Impatient customers, Virtual waiting time, Workload",

author = "Jongho Bae and Sunggon Kim",

year = "2010",

month = mar,

doi = "10.1007/s11134-009-9159-0",

language = "English",

volume = "64",

pages = "253--265",

journal = "Queueing Systems",

issn = "0257-0130",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - The stationary workload of the G/M/1 queue with impatient customers

AU - Bae, Jongho

AU - Kim, Sunggon

PY - 2010/3

Y1 - 2010/3

N2 - We consider a G/M/1 queue in which the patience time of the customers is constant. The stationary distribution of the workload of the server, or the virtual waiting time, is derived by the level crossing argument. To this end, we obtain the expected downcrossings of a level in the workload process during a busy cycle and then the expected length of a busy cycle. For both the expectations, we use the dual property between the M/G/1 and G/M/1 queue.

AB - We consider a G/M/1 queue in which the patience time of the customers is constant. The stationary distribution of the workload of the server, or the virtual waiting time, is derived by the level crossing argument. To this end, we obtain the expected downcrossings of a level in the workload process during a busy cycle and then the expected length of a busy cycle. For both the expectations, we use the dual property between the M/G/1 and G/M/1 queue.

KW - G/M/1 queue

KW - Impatient customers

KW - Virtual waiting time

KW - Workload

UR - http://www.scopus.com/inward/record.url?scp=77950458777&partnerID=8YFLogxK

U2 - 10.1007/s11134-009-9159-0

DO - 10.1007/s11134-009-9159-0

M3 - Article

AN - SCOPUS:77950458777

SN - 0257-0130

VL - 64

SP - 253

EP - 265

JO - Queueing Systems

JF - Queueing Systems

IS - 3

ER -

The stationary workload of the G/M/1 queue with impatient customers

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this