Simple models of network access, with applications to the design of joint rate and admission control

Abstract

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 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 . 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. I. IntroductionIn today's communication networks, design and control of the network core and access are different, primarily because of the differences in scale in bandwidth and distance. Quite often the bottleneck is the access, rather than the core. This may happen because the access network is characterized by relatively low line speeds and the limited ability of users to buffer and shape traffic (think of the extreme case of a user with a wireless handset). Access control, supported by the use of feedback, is an important mechanism to address this problem. Since distances between users/clients and network access points are relatively short, feedback delay due to propagation is negligible, which contributes to the efficacy of feedback control. In this paper we investigate the problems of access control by introducing simple models and techniques for their evaluation, design and performance optimization. We make three main contributions. First, we present two simple models of network access. The models provide a framework for the joint design of feedback-based schemes for the adaptation of source rates and admission control. Second, we show how to compute the stationary behavior of the aforementioned feedback queues. We illustrate the use of these

Shot-noise queueing models

“…(Proof The result follows directly from Eqns (9). and(78).This result allows the evaluation of moments of M(t).In particular, it is easily verified that the mean satisfies the intuitively appealing expressionE M(t) = t (u) P(S > t − u)du. (80)Higher moments can be found as well.…”

“…In feedback fluid queues, not only is the buffer content determined by the state of a background process, but also the background process is influenced by the content process. Feedback fluid queues are also studied in [78,79,92]. In [92] the object of study was a fluid queue with a finite buffer and a background process governed by a continuous-time Markov chain whose generator, and the traffic rates, depend continuously on the buffer level.…”

Solving Multi-Regime Feedback Fluid Queues

“…The differential equation (7) and the boundary conditions (8) through (13) and the two conditions (16) and (17) can be proven by using the results of Mandjes et al [14] ; the remaining two conditions (14) and (15) are related to boundary points with repulsive states and regimes with zero drift states. Mandjes et al [14] find the following ordinary differential equations of the joint distribution functions for multi-regime feedback fluid queues:…”

“…A similar system with drifts being piecewise continuous functions of the buffer content is analyzed by Kella and Stadje [12] . The more general feedback fluid queues in which the background process is also allowed to vary with respect to buffer content are studied by Scheinhardt et al [13] and Mandjes et al [14] (see also Mandjes et al [15] ); the former study allows continuous feedback whereas the latter assumes piecewise constant feedback to model a network access system. Boxma et al [16] studies a model which can be viewed as a continuous feedback fluid queue with two background states and unlimited buffer content.…”

Busy periods in fluid queues with multiple emptying input states

“…The states, also termed phases, of the modulating process have an associated fluid arrival rate and state holding time probability distribution that can be used, for example, to distinguish different classes of traffic, including 'off', or 'silent', periods where the traffic arrival rate is 0. Fluid queueing models have seen widespread application, particularly in the analysis of packet flows in communication networks and in the analysis of congestion control regimes; see, for example, [9] and [13].…”