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Models of network access using feedback fluid queues. (English) Zbl 1030.60089
Authors’ abstract: 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 $$\varepsilon$$ 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’ file 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 $$\varepsilon$$. 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.

##### MSC:
 60K25 Queueing theory (aspects of probability theory) 68M20 Performance evaluation, queueing, and scheduling in the context of computer systems 60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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