Abstract
We consider a discrete time single server queueing system where the arrival process is governed by a discrete autoregressive process of order p (DAR(p)), and the service time of a customer is one slot. For this queueing system, we give an expression for the mean queue size, which yields upper and lower bounds for the mean queue size. Further we propose two approximation methods for the mean queue size. One is based on the matrix analytic method and the other is based on simulation. We show, by illustrations, that the proposed approximations are very accurate and computationally efficient.
| Original language | English |
|---|---|
| Pages (from-to) | 69-83 |
| Number of pages | 15 |
| Journal | Annals of Operations Research |
| Volume | 162 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2008 Sep 1 |
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Keywords
- Discrete autoregressive process
- Discrete time queueing system
- Mean queue size
ASJC Scopus subject areas
- Management Science and Operations Research
- Decision Sciences(all)
Cite this
Mean queue size in a queue with discrete autoregressive arrivals of order p. / Kim, Jeongsim; Kim, Bara; Sohraby, Khosrow.
In: Annals of Operations Research, Vol. 162, No. 1, 01.09.2008, p. 69-83.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Mean queue size in a queue with discrete autoregressive arrivals of order p
AU - Kim, Jeongsim
AU - Kim, Bara
AU - Sohraby, Khosrow
PY - 2008/9/1
Y1 - 2008/9/1
N2 - We consider a discrete time single server queueing system where the arrival process is governed by a discrete autoregressive process of order p (DAR(p)), and the service time of a customer is one slot. For this queueing system, we give an expression for the mean queue size, which yields upper and lower bounds for the mean queue size. Further we propose two approximation methods for the mean queue size. One is based on the matrix analytic method and the other is based on simulation. We show, by illustrations, that the proposed approximations are very accurate and computationally efficient.
AB - We consider a discrete time single server queueing system where the arrival process is governed by a discrete autoregressive process of order p (DAR(p)), and the service time of a customer is one slot. For this queueing system, we give an expression for the mean queue size, which yields upper and lower bounds for the mean queue size. Further we propose two approximation methods for the mean queue size. One is based on the matrix analytic method and the other is based on simulation. We show, by illustrations, that the proposed approximations are very accurate and computationally efficient.
KW - Discrete autoregressive process
KW - Discrete time queueing system
KW - Mean queue size
UR - http://www.scopus.com/inward/record.url?scp=43049167564&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=43049167564&partnerID=8YFLogxK
U2 - 10.1007/s10479-008-0318-1
DO - 10.1007/s10479-008-0318-1
M3 - Article
AN - SCOPUS:43049167564
VL - 162
SP - 69
EP - 83
JO - Annals of Operations Research
JF - Annals of Operations Research
SN - 0254-5330
IS - 1
ER -