Queueing systems fed by many exponential on-off sources: An infinite-intersection approach

Michael Mandjes, Petteri Mannersalo (Corresponding Author)

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

In queueing theory, an important class of events can be written as ‘infinite intersections’. For instance, in a queue with constant service rate c, busy periods starting at 0 and exceeding L > 0 are determined by the intersection of the events ⋂t∈[0,L]{Q0=0,At>ct} , i.e., queue Q t is empty at 0 and for all t∊ [0, L] the amount of traffic A t arriving in [0,t) exceeds the server capacity. Also the event of exceeding some predefined threshold in a tandem queue, or a priority queue, can be written in terms of this kind of infinite intersections. This paper studies the probability of such infinite intersections in queueing systems fed by a large number n of i.i.d. traffic sources (the so-called ‘many-sources regime’). If the sources are of the exponential on-off type, and the queueing resources are scaled proportional to n, the probabilities under consideration decay exponentially; we explicitly characterize the corresponding decay rate. The techniques used stem from large deviations theory (particularly sample-path large deviations).
Original languageEnglish
Pages (from-to)5-20
JournalQueueing Systems
Volume54
Issue number1
DOIs
Publication statusPublished - 2006
MoE publication typeA1 Journal article-refereed

Keywords

  • sample-path large deviations
  • on-off processes
  • busy period
  • tandem queue
  • priority queue
  • queueing theory

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