Explicit solution for the stationary distribution of a discrete-time finite buffer queue

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)1121-1133
Number of pages13
JournalJournal of Industrial and Management Optimization
Volume12
Issue number3
DOIs
Publication statusPublished - 2016

Fingerprint

Finite Buffer
Stationary Distribution
Explicit Solution
Queue
Discrete-time
Matrix-geometric Solution
Servers
Batch Markovian Arrival Process
Discrete-time Queue
Queue Length Distribution
Single Server Queue
Queueing System
Batch
Closed-form
Customers
Stationary distribution
Finite buffer
Form
Batch size
Queueing system

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 journalArticle

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