3,576 research outputs found
Closed queueing networks under congestion: non-bottleneck independence and bottleneck convergence
We analyze the behavior of closed product-form queueing networks when the
number of customers grows to infinity and remains proportionate on each route
(or class). First, we focus on the stationary behavior and prove the conjecture
that the stationary distribution at non-bottleneck queues converges weakly to
the stationary distribution of an ergodic, open product-form queueing network.
This open network is obtained by replacing bottleneck queues with per-route
Poissonian sources whose rates are determined by the solution of a strictly
concave optimization problem. Then, we focus on the transient behavior of the
network and use fluid limits to prove that the amount of fluid, or customers,
on each route eventually concentrates on the bottleneck queues only, and that
the long-term proportions of fluid in each route and in each queue solve the
dual of the concave optimization problem that determines the throughputs of the
previous open network.Comment: 22 page
A stochastic analysis of resource sharing with logarithmic weights
The paper investigates the properties of a class of resource allocation
algorithms for communication networks: if a node of this network has
requests to transmit, then it receives a fraction of the capacity proportional
to , the logarithm of its current load. A detailed fluid scaling
analysis of such a network with two nodes is presented. It is shown that the
interaction of several time scales plays an important role in the evolution of
such a system, in particular its coordinates may live on very different time
and space scales. As a consequence, the associated stochastic processes turn
out to have unusual scaling behaviors. A heavy traffic limit theorem for the
invariant distribution is also proved. Finally, we present a generalization to
the resource sharing algorithm for which the function is replaced by an
increasing function. Possible generalizations of these results with nodes
or with the function replaced by another slowly increasing function are
discussed.Comment: Published at http://dx.doi.org/10.1214/14-AAP1057 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Simple models of network access, with applications to the design of joint rate and admission control
At the access to networks, in contrast to the core, distances and feedback delays, as well as link capacities are small, which has network engineering implications that are investigated in this paper. We consider a single point in the access network which multiplexes several bursty users. The users adapt their sending rates based on feedback from the access multiplexer. Important parameters are the user's peak transmission rate p, which is the access line speed, the user's guaranteed minimum rate r, and the bound ε on the fraction of lost data. Two feedback schemes are proposed. In both schemes the users are allowed to send at rate p if the system is relatively lightly loaded, at rate r during periods of congestion, and at a rate between r and p, in an intermediate region. For both feedback schemes we present an exact analysis, under the assumption that the users' job sizes and think times have exponential distributions. We use our techniques to design the schemes jointly with admission control, i.e., the selection of the number of admissible users, to maximize throughput for given p, r, and ε. Next we consider the case in which the number of users is large. Under a specific scaling, we derive explicit large deviations asymptotics for both models. We discuss the extension to general distributions of user data and think times
An integrated packet/flow model for TCP performance analysis
Processor sharing (PS) models for TCP behavior nicely capture the bandwidth sharing and statistical multiplexing effect of TCP flows on the flow level. However, these ‘rough’ models do not provide insight into the impact of packet-level parameters (such as round trip time and buffer size) on, e.g., throughput and flow transfer times. This paper proposes an integrated packet/flow-level model: it exploits the advantages of PS approach on the flow level and, at the same time, it incorporates the most significant packet-level effects
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