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Waitingtime tail probabilities in queues with longtail servicetime distributions
 QUEUEING SYSTEMS
, 1994
"... We consider the standard GI/G/1 queue with unlimited waiting room and the firstin firstout service discipline. We investigate the steadystate waitingtime tail probabilities P(W> x) when the servicetime distribution has a longtail distribution, i.e., when the servicetime distribution fails ..."
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Cited by 73 (23 self)
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We consider the standard GI/G/1 queue with unlimited waiting room and the firstin firstout service discipline. We investigate the steadystate waitingtime tail probabilities P(W> x) when the servicetime distribution has a longtail distribution, i.e., when the servicetime distribution fails
Explicit M/G/1 waitingtime distributions for a class of longtail servicetime distributions
 OPERATIONS RESEARCH LETTERS
, 1999
"... ..."
The Impact of a HeavyTailed ServiceTime Distribution upon the M/GI/s WaitingTime Distribution
"... By exploiting an infiniteservermodel lower bound, we show that the tails of the steadystate and transient waitingtime distributions in the M/GI/s queue with unlimited waiting room and the firstcome firstserved discipline are bounded below by tails of Poisson distributions. As a consequence, th ..."
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, the tail of the steadystate waitingtime distribution is bounded below by a constant times the sth power of the tail of the servicetime stationaryexcess distribution. We apply that bound to show that the steadystate waitingtime distribution has a heavy tail (with appropriate definition) whenever
Fitting Mixtures Of Exponentials To LongTail Distributions To Analyze Network Performance Models
, 1997
"... Traffic measurements from communication networks have shown that many quantities characterizing network performance have longtail probability distributions, i.e., with tails that decay more slowly than exponentially. File lengths, call holding times, scene lengths in MPEG video streams, and interva ..."
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Cited by 206 (14 self)
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distributions cause longtail waitingtime distributions in queues, but it is often difficult to describe this effect in detail, because performance models with component longtail distributions tend to be difficult to analyze. We address this problem by developing an algorithm for approximating a longtail
Asymptotics for M/G/1 lowpriority waitingtime tail probabilities
, 1997
"... We consider the classical M/G/1 queue with two priority classes and the nonpreemptive and preemptiveresume disciplines. We show that the lowpriority steadystate waitingtime can be expressed as a geometric random sum of i.i.d. random variables, just like the M/G/1 FIFO waitingtime distribution. ..."
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Cited by 52 (6 self)
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for the lowpriority waitingtime transform. We also establish asymptotic results for cases with longtail servicetime distributions. As with FIFO, the exponential asymptotics tend to provide excellent approximations, while the nonexponential asymptotics do not, but the asymptotic relations indicate
Fluid Queues with Longtailed Activity Period Distributions
, 1997
"... This is a survey paper on fluid queues, with a strong emphasis on recent attempts to represent phenomena like longrange dependence. The central model of the paper is a fluid queueing system fed by N independent sources that alternate between silence and activity periods. The distribution of the a ..."
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Cited by 42 (2 self)
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of the activity periods of at least one source is assumed to be longtailed, which may give rise to longrange dependence. We consider the effect of this tail behaviour on the steadystate distributions of the buffer content at embedded points in time and at arbitrary time, and on the busy period distribution
Overflow Behavior in Queues with Many LongTailed Inputs
 ADVANCES IN APPLIED PROBABILITY
, 1999
"... We consider a fluid queue fed by a superposition of n homogeneous onoff sources with generally distributed on and offperiods. We scale buffer space B and link rate C by n, such that we get nb and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponenti ..."
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Cited by 16 (7 self)
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We consider a fluid queue fed by a superposition of n homogeneous onoff sources with generally distributed on and offperiods. We scale buffer space B and link rate C by n, such that we get nb and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays
Modeling servicetime distributions with nonexponential tails: beta mixtures of exponentials
 STOCHASTIC MODELS
, 1999
"... Motivated by interest in probability density functions (pdf’s) with nonexponential tails in queueing and related areas, we introduce and investigate two classes of beta mixtures of exponential pdf’s. These classes include distributions introduced by Boxma and Cohen (1997) and Gaver and Jacobs (1998) ..."
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Cited by 8 (3 self)
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) to study queues with longtail servicetime distributions. When the standard beta pdf is used as the mixing pdf, we obtain pdf’s with an exponentially damped power tail, i.e., f(t) ∼ αt −q e −ηt as t → ∞. This pdf decays exponentially, but analysis is complicated by the power term. When the beta pdf
Over behavior in queues with many longtailed inputs
 Advances in Applied Probability
, 2001
"... and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of ..."
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Cited by 2 (1 self)
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and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of
Results 1  10
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