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A RECENT PROGRESS IN ALGORITHMIC ANALYSIS OF FIFO QUEUES WITH MARKOVIAN ARRIVAL STEAMS
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  • A RECENT PROGRESS IN ALGORITHMIC ANALYSIS OF FIFO QUEUES WITH MARKOVIAN ARRIVAL STEAMS
  • A RECENT PROGRESS IN ALGORITHMIC ANALYSIS OF FIFO QUEUES WITH MARKOVIAN ARRIVAL STEAMS
저자명
Takine. Tetsuya
간행물명
Journal of the Korean Mathematical Society
권/호정보
2001년|38권 4호|pp.807-842 (36 pages)
발행정보
대한수학회
파일정보
정기간행물|ENG|
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이 논문은 한국과학기술정보연구원과 논문 연계를 통해 무료로 제공되는 원문입니다.
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기타언어초록

This paper summarizes recent development of analytical and algorithmical results for stationary FIFO queues with multiple Markovian arrival streams, where service time distributions are general and they may differ for different arrival streams. While this kind of queues naturally arises in considering queues with a superposition of independent phase-type arrivals, the conventional approach based on the queue length dynamics (i.e., M/G/1 pradigm) is not applicable to this kind of queues. On the contrary, the workload process has a Markovian property, so that it is analytically tractable. This paper first reviews the results for the stationary distributions of the amount of work-in-system, actual waiting time and sojourn time, all of which were obtained in the last six years by the author. Further this paper shows an alternative approach, recently developed by the author, to analyze the joint queue length distribution based on the waiting time distribution. An emphasis is placed on how to construct a numerically feasible recursion to compute the stationary queue length mass function.