Models of network access using feedback fluid queues

At the access to networks, in contrast to the core, distances and feedback delay s, 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 $epsilon$ 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 $epsilon$. 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 model s. We discuss the extension to general distributions of user data and think times

Models of network access using feedback fluid queues

At the access to networks, in contrast to the core, distances and feedback delay s, 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' 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 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 model s. We discuss the extension to general distributions of user data and think times

Rare-event simulation for tandem queues: a simple and efficient importance sampling scheme

This paper focuses on estimating the rare event of overflow in the downstream queue of a Jacksonian two-node tandem queue, relying on importance sampling. It is known that in this setting ‘traditional’ state-independent schemes perform poorly. More sophisticated state-dependent schemes yield asymptotic efficiency. Their drawback, however, is that they require a per-state computation of the new measure, so that it still consumes considerable machine time. The contribution of this paper is a scheme that combines asymptotic efficiency with low complexity. It retains the quality of the original state-dependent scheme, but its implementation is almost as simple as for state-independent analogues

On a generic class of two-node queueing systems

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on-off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in which it explicitly does. This dichotomy can be understood by using large-deviations heuristics

Design issues of a back-pressure-based congestion control mechanism

Congestion control in packet-based networks is often realized by feedback protocols -- in this paper we assess the performance under a back-pressure mechanism that has been proposed and standardized for Ethernet metropolitan networks. Relying on our earlier results for feedback fluid queues, we derive explicit expressions for the key perfomance metrics, in terms of the model parameters, as well as the parameters agreed upon in the service level agreement. Numerical experiments are performed to evaluate the main trade-offs of this model (for instance the trade-off between the signaling frequency and the throughput). These can be used to generate design guidelines. The paper is concluded by an elementary, yet powerful, Markovian model that can be used as an approximative model in situations of large traffic aggregates feeding into the system; the trade-offs and guidelines identified for the feedback fluid model turn out to carry over to this more stylized model

A feedback fluid queue with two congestion control thresholds

Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold $B_{1}$ is used to signal the beginning of congestion while the lower threshold $B_{2}$ signals the end of congestion. These two parameters together allow to make the trade--off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold $B_{1}$ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until $B_{2}$ (smaller than $B_1$) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput

Modernizing medical education in Milwaukee in 1914. Contributions of a sensational scandal, the Flexner Report, and student uprising.

This paper considers importance sampling as a tool for rareevent simulation. The focus is on estimating the probability of overflow in the downstream queue of a Jackson twonode tandem queue. It is known that in this setting ‘traditional’ state-independent importance-sampling distributions perform poorly. We therefore concentrate on developing a state-dependent change of measure that is provably asymptotically efficient.\ud More specific contributions are the following. (i) We concentrate on the probability of the second queue exceeding a certain predefined threshold before the system empties. Importantly, we identify an asymptotically efficient importancesampling distribution for any initial state of the system. (ii) The choice of the importance-sampling distribution is backed up by appealing heuristics that are rooted in largedeviations theory. (iii) Our method for proving asymptotic efficiency is substantially more straightforward than some that have been used earlier