Queueing systems fed by many exponential on-off sources: an infinite-intersection approach |
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Authors: | Michel Mandjes Petteri Mannersalo |
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Institution: | (1) VTT Technical Research Center of Finland, P.O. Box 1000, FI-02044 VTT, Finland;(2) CWI, P.O. Box 94079, NL-1090 GB Amsterdam, The Netherlands |
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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
, 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).
M. Mandjes is also with Korteweg-de Vries Institute, University of Amsterdam, Amsterdam, the Netherlands, and EURANDOM, Eindhoven,
the Netherlands.
Work done while P. Mannersalo was on leave at CWI.
MSC 2000: 60F10 (Large deviations), 60K25 (Queueing theory) |
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Keywords: | Sample-path large deviations On-off processes Busy period Tandem queue Priority queue |
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