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.
Bibliographical noteFunding 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).
- 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