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Estimating Tail Probabilities in Queues via Extremal Statistics
Extreme values queues regenerative processes rare events estimation asymptotics
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
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...
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
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
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
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
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...