651 research outputs found
Externalities in the M/G/1 queue:LCFS-PR versus FCFS
Consider a stable M/G/1 system in which, at time t= 0 , there are exactly n customers with residual service times equal to v1, v2, … , vn . In addition, assume that there is an extra customer c who arrives at time t= 0 and has a service requirement of x. The externalities which are created by c are equal to the total waiting time that others will save if her service requirement is reduced to zero. In this work, we study the joint distribution (parameterized by n, v1, v2, … , vn, x) of the externalities created by c when the underlying service distribution is either last-come, first-served with preemption or first-come, first-served. We start by proving a decomposition of the externalities under the above-mentioned service disciplines. Then, this decomposition is used to derive several other results regarding the externalities: moments, asymptotic approximations as x→ ∞ , asymptotics of the tail distribution, and a functional central limit theorem.</p
Moderate deviations of many-server queues in the Halfin-Whitt regime and weak convergence methods
This paper obtains logarithmic asymptotics of moderate deviations of the
stochastic process of the number of customers in a many--server queue with
generally distributed interarrival and service times in the Halfin--Whitt heavy
traffic regime. The deviation function is expressed in terms of the solution to
a Fredholm equation of the second kind. The proof uses characterisation of
large deviation relatively compact sequences of probability measures as
exponentially tight ones
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Heavy Loads and Heavy Tails
The present paper is concerned with the stationary workload of queues with
heavy-tailed (regularly varying) characteristics. We adopt a transform
perspective to illuminate a close connection between the tail asymptotics and
heavy-traffic limit in infinite-variance scenarios. This serves as a tribute to
some of the pioneering results of J.W. Cohen in this domain. We specifically
demonstrate that reduced-load equivalence properties established for the tail
asymptotics of the workload naturally extend to the heavy-traffic limit
- …