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Heavy-Traffic Extreme-Value Limits for Queues
extreme values queues maximum waiting time diffusion approximations
2015/7/8
We consider the maximum waiting time among the first n customers in the GI/G/1 queue. We use strong approximations to prove, under regularity conditions, convergence of the normalized maximum wait to ...
On the Transition from Heavy Traffic to Heavy Tails for the M/G/1 Queue: The Regularly Varying Case
M/G/1 queue heavy traffi c heavy tails uniform approximations large deviations
2015/7/6
Two of the most popular approximations for the distribution of the steady-state waiting time, W∞, of the M/G/1 queue are the socalled heavy-traffic approximation and heavy-tailed asymptotic, respectiv...
Heavy traffic limit theorems for a queue with Poisson ON/OFF long-range dependent sources and general service time distribution
reflecting fractional Brownian motion reflecting Gaussian process longrange dependence queueing process weak convergence
2011/6/21
In Internet environment, traffic flow to a link is typically modeled by superposition of
ON/OFF based sources. During each ON-period for a particular source, packets arrive
according to a Poisson pr...
Distributions of suprema of Levy processes via the Heavy Traffic Invariance Principle
Livy process supremum heavy traflic queueing systems
2009/9/21
We study the relationship between the distribution of
the supremum functional M, = sup,,,,,(X(t)-fit) for a process
X with stationary, but not necessarily independent increments, and the
I limiting...
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...