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Estimating Tail Probabilities in Queues via Extremal Statistics
Extreme values queues regenerative processes rare events estimation asymptotics
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2015/7/8
We study the estimation of tail probabilities in a queue via a semi-parametric estimator based on the maximum value of the workload, observed over the sampled time interval. Logarithmic consistency an...
Queues with breakdowns and customer discouragement
Queues with breakdowns customer discouragement
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2009/9/23
This paper considers an M/M/I queue with service
breakdowns and customer discouragement. Each of the customers
present in the system at the time of a breakdown may become
discouraged and leave with...
Asymptotic stationarity of tandem of queues
Asymptotic stationarity tandem queues
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2009/9/22
In [12] it was proved that the process of waiting times
for single server queues is asymptotically stationary if
(1) a generic process X = (Xkk, 2 1) is asymptotically stationary,
(2) X satisfies c...
Heavy-tailed dependent queues in heavy traffic
Levy process stable distribution stationary process heavy trafic queueing systems
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2009/9/21
The paper studies G/G/l queues with heavy-tailed probability
distributions of the service times and/or the interarrival times.
It relies on the fact that the heavy traffic limiting distribution of t...
TIGHTNESS OF STATIONARY WAITING TIMES IN HEAVY TRAFFIC FOR GI/GI/1 QUEUES WITH THICK TAILS
LBvy process queueing systems heavy traffic stationary waiting time tightness
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2009/9/18
Recently, a Heavy Traffic Invariance Principle was
proposed by Szczotka and Woyczyliski to characterize the heavy traffic
limiting distribution of normalized stationary waiting times of
G/G/l queue...
Martingale proofs of many-server heavy-traffic limits for Markovian queues
multiple-server queues many-server heavy-traffic limits for queues diffusion approximations martingales functional central limit theorems
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2009/5/18
This is an expository review paper illustrating the “martin- gale method” for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximatio...
On the Behavior of LIFO Preemptive Resume Queues in Heavy Traffic
LIFO queue heavy traffic measure-valued process branching feedback Wiener-Hopf factorization
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2009/5/4
This paper studies heavy traffic behavior of a G/G/1 last-in-first-out (LIFO) preemptive resume queue, by extending the techniques developed in Limic (1999). The queue length process exhibits a perhap...