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QueueingSystems22 (1996) 203-247 203 Stationary tail probabilities in exponential server tandems
 

Summary: QueueingSystems22 (1996) 203-247 203
Stationary tail probabilities in exponential server tandems
with renewal arrivals
A. Ganesha and V. Anantharamb'*
aDepartmentof ComputerScience, Universityof Edinburgh,
EdinburghEH9 3JZ, UK
E-mail: ajg@dcs.ed.ac.uk
bEECS Department, Universityof California,Berkeley, CA 94720, USA
E-mail: ananth@eecs.berkeley.edu
Received6 April 1995;revised9 August 1995
The problemconsideredis that ofestimatingthe tail stationaryprobabilityfor two
exponentialserverqueuesin seriesfed by renewalarrivals.We compute the tail of the
marginalqueuelengthdistributionat the secondqueue.Themarginalat thefirstqueue
isknown by the classicalresultfor the GI/M/1queue.The approach involvesderiving
necessary and sufficientconditions on the paths of the arrival and virtual service
processes in order to get a large queue size at the second queue. We then use large
deviationsestimatesofthe probabilitiesofthesepaths, and solvea constrainedconvex
optimizationproblemto findthe most likelypath leadingto a largequeuesize.Wefind
that the stationary queuelengthdistribution at the secondqueuehas an exponentially
decayingtail, and obtain the exact rate of decay.

  

Source: Anantharam, Venkat - Department of Electrical Engineering and Computer Sciences, University of California at Berkeley

 

Collections: Engineering