Coupled processors with regularly varying service times

S.C. Borst, O.J. Boxma, P.R. Jelenkovic

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

16 Citations (Scopus)

Abstract

Consider two M/G/1 queues that are coupled in the following way. Whenever both queues are non-empty, each server serves its own queue at unit speed. However, if server 2 has no work in its own queue, then it assists server 1, resulting in an increased service speed r/sub 1//sup *//spl ges/1 in the first queue. This kind of coupling is related to generalized processor sharing. We assume that the service request distributions at both queues are regularly varying at infinity of index -v/sub 1/ and -v/sub 2/, namely, they are heavy-tailed. Under this assumption, we present a detailed analysis of the tail behaviour of the workload distribution at each queue. If the guaranteed unit speed of server 1 is already sufficient to handle its offered traffic, then the workload distribution at the first queue is shown to be regularly varying at infinity of index 1-v/sub 1/. But if it is not sufficient, then the workload distribution at the first queue is shown to be regularly varying at infinity of index 1-min(v/sub 1/,v/sub 2/). In particular, traffic at server 1 is then no longer protected from worse-behaved (heavier-tailed) traffic at server 2.
Original languageEnglish
Title of host publicationProceedings INFOCOM 2000 (Tel Aviv, Israel, March 26-30, 2000)
EditorsR. Rom, H. Schulzrinne, M. Sidi
PublisherInstitute of Electrical and Electronics Engineers
Pages157-164
Number of pages8
ISBN (Print)0-7803-5880-5
DOIs
Publication statusPublished - 2000

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