Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1121-1133 |
| Number of pages | 13 |
| Journal | Journal of Industrial and Management Optimization |
| Volume | 12 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2016 |
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Keywords
- Discrete-time batch markovian arrival process
- Discrete-time queue
- Mixed matrix-geometric solution
- Quadratic matrix equation
- Stationary distribution
ASJC Scopus subject areas
- Business and International Management
- Strategy and Management
- Control and Optimization
- Applied Mathematics
Cite this
Explicit solution for the stationary distribution of a discrete-time finite buffer queue. / Kim, Bara; Kim, Jeongsim.
In: Journal of Industrial and Management Optimization, Vol. 12, No. 3, 2016, p. 1121-1133.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Explicit solution for the stationary distribution of a discrete-time finite buffer queue
AU - Kim, Bara
AU - Kim, Jeongsim
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
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 -