Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity

Bong Dae Choi; Bara Kim; Jeongsim Kim; In Suk Wee

doi:10.1023/A:1024468421028

Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity

Bong Dae Choi, Bara Kim, Jeongsim Kim, In Suk Wee

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

4 Citations (Scopus)

Abstract

We obtain the exact convergence rate of the stationary distribution π^(K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution π of the embedded Markov chain in GI/M/c queue as K → ∞. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c = 1 by nontrivial ways. Our results also strengthen the Simonot's results [5].

Original language	English
Pages (from-to)	125-136
Number of pages	12
Journal	Queueing Systems
Volume	44
Issue number	2
DOIs	https://doi.org/10.1023/A:1024468421028
Publication status	Published - 2003 Jun

Keywords

GI/M/c queue
GI/M/c/K queue
Stationary distribution

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

Access to Document

10.1023/A:1024468421028

Cite this

@article{dab76c4683e74e0eb6ef5bc8a2375172,

title = "Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity",

abstract = "We obtain the exact convergence rate of the stationary distribution π(K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution π of the embedded Markov chain in GI/M/c queue as K → ∞. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c = 1 by nontrivial ways. Our results also strengthen the Simonot's results [5].",

keywords = "GI/M/c queue, GI/M/c/K queue, Stationary distribution",

author = "Choi, {Bong Dae} and Bara Kim and Jeongsim Kim and Wee, {In Suk}",

note = "Funding Information: ∗This work was supported by Korea Research Foundation Grant (KRF-2001-042-D00009).",

year = "2003",

month = jun,

doi = "10.1023/A:1024468421028",

language = "English",

volume = "44",

pages = "125--136",

journal = "Queueing Systems",

issn = "0257-0130",

publisher = "Springer Netherlands",

number = "2",

}

TY - JOUR

T1 - Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity

AU - Choi, Bong Dae

AU - Kim, Bara

AU - Kim, Jeongsim

AU - Wee, In Suk

N1 - Funding Information: ∗This work was supported by Korea Research Foundation Grant (KRF-2001-042-D00009).

PY - 2003/6

Y1 - 2003/6

N2 - We obtain the exact convergence rate of the stationary distribution π(K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution π of the embedded Markov chain in GI/M/c queue as K → ∞. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c = 1 by nontrivial ways. Our results also strengthen the Simonot's results [5].

AB - We obtain the exact convergence rate of the stationary distribution π(K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution π of the embedded Markov chain in GI/M/c queue as K → ∞. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c = 1 by nontrivial ways. Our results also strengthen the Simonot's results [5].

KW - GI/M/c queue

KW - GI/M/c/K queue

KW - Stationary distribution

UR - http://www.scopus.com/inward/record.url?scp=0038083005&partnerID=8YFLogxK

U2 - 10.1023/A:1024468421028

DO - 10.1023/A:1024468421028

M3 - Article

AN - SCOPUS:0038083005

SN - 0257-0130

VL - 44

SP - 125

EP - 136

JO - Queueing Systems

JF - Queueing Systems

IS - 2

ER -

Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this