TY - JOUR
T1 - Explicit solution for the stationary distribution of a discrete-time finite buffer queue
AU - Kim, Bara
AU - Kim, Jeongsim
N1 - Funding Information:
B. Kim's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005831). J. Kim's research was supported by Basic Science Re-search Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A4A01003813).
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016
Y1 - 2016
N2 - We consider a discrete-time single server queue with finite buffer. The customers arrive according to a discrete-time batch Markovian arrival process with geometrically distributed batch sizes and the service time is one time slot. For this queueing system, we obtain an exact closed-form expression for the stationary queue length distribution. The expression is in a form of mixed matrix-geometric solution.
AB - We consider a discrete-time single server queue with finite buffer. The customers arrive according to a discrete-time batch Markovian arrival process with geometrically distributed batch sizes and the service time is one time slot. For this queueing system, we obtain an exact closed-form expression for the stationary queue length distribution. The expression is in a form of mixed matrix-geometric solution.
KW - Discrete-time batch markovian arrival process
KW - Discrete-time queue
KW - Mixed matrix-geometric solution
KW - Quadratic matrix equation
KW - Stationary distribution
UR - http://www.scopus.com/inward/record.url?scp=84954443938&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84954443938&partnerID=8YFLogxK
U2 - 10.3934/jimo.2016.12.1121
DO - 10.3934/jimo.2016.12.1121
M3 - Article
AN - SCOPUS:84954443938
VL - 12
SP - 1121
EP - 1133
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
SN - 1547-5816
IS - 3
ER -