677 research outputs found
Documentation administrative des universités le cas d\u27une université parisienne, un exemple pour la constitution d\u27un fonds spécifique à la bibliothèque de l\u27Institut National de la Recherche Pédagogique (La)
single server queue;service in random order;heavy-tailed distribution;waiting time asymptotics;heavy-traffic limit theoremInternational audienceWe consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals and regularly varying service time distribution with index −ν, it is shown that the waiting time distribution is also regularly varying, with index 1 − ν, and the pre-factor is determined explicitly. Another contribution of the paper is the heavy-traffic analysis of the waiting time distribution in the M/G/1 case. We consider not only the case of finite service time variance, but also the case of regularly varying service time distribution with infinite variance
Queue Length Asymptotics for Generalized Max-Weight Scheduling in the presence of Heavy-Tailed Traffic
We investigate the asymptotic behavior of the steady-state queue length
distribution under generalized max-weight scheduling in the presence of
heavy-tailed traffic. We consider a system consisting of two parallel queues,
served by a single server. One of the queues receives heavy-tailed traffic, and
the other receives light-tailed traffic. We study the class of throughput
optimal max-weight-alpha scheduling policies, and derive an exact asymptotic
characterization of the steady-state queue length distributions. In particular,
we show that the tail of the light queue distribution is heavier than a
power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic
characterization also contains an intuitively surprising result - the
celebrated max-weight scheduling policy leads to the worst possible tail of the
light queue distribution, among all non-idling policies. Motivated by the above
negative result regarding the max-weight-alpha policy, we analyze a
log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees
an exponentially decaying light queue tail, while still being throughput
optimal
Customer sojourn time in GI/G/1 feedback queue in the presence of heavy tails
We consider a single-server GI/GI/1 queueing system with feedback. We assume
the service times distribution to be (intermediate) regularly varying. We find
the tail asymptotics for a customer's sojourn time in two regimes: the customer
arrives in an empty system, and the customer arrives in the system in the
stationary regime. In particular, in the case of Poisson input we use the
branching processes structure and provide more precise formulae. As auxiliary
results, we find the tail asymptotics for the busy period distribution in a
single-server queue with an intermediate varying service times distribution and
establish the principle-of-a-single-big-jump equivalences that characterise the
asymptotics.Comment: 34 pages, 4 figures, to appear in Journal of Statistical Physic
Heavy traffic analysis of a polling model with retrials and glue periods
We present a heavy traffic analysis of a single-server polling model, with
the special features of retrials and glue periods. The combination of these
features in a polling model typically occurs in certain optical networking
models, and in models where customers have a reservation period just before
their service period. Just before the server arrives at a station there is some
deterministic glue period. Customers (both new arrivals and retrials) arriving
at the station during this glue period will be served during the visit of the
server. Customers arriving in any other period leave immediately and will retry
after an exponentially distributed time. As this model defies a closed-form
expression for the queue length distributions, our main focus is on their
heavy-traffic asymptotics, both at embedded time points (beginnings of glue
periods, visit periods and switch periods) and at arbitrary time points. We
obtain closed-form expressions for the limiting scaled joint queue length
distribution in heavy traffic and use these to accurately approximate the mean
number of customers in the system under different loads.Comment: 23 pages, 2 figure
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