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
N1 - Funding Information:
Acknowledgements The authors would like to thank Prof. Jesus Artalejo and anonymous referees for their valuable comments and suggestions to improve the paper. This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).
PY - 2008/9
Y1 - 2008/9
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
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 -