Inspired by several recent papers that focus on scheduling disciplines for network flows, we present a mean delay analysis of Multilevel Processor Sharing (MLPS) scheduling disciplines in the context of M/G/1 queues. Such disciplines have been proposed to model the effect of the differentiation between short and long TCP flows in the Internet. Under MLPS, jobs are classified into classes depending on their attained service. We consider scheduling disciplines where jobs within the same class are served either with Processor Sharing (PS) or Foreground Background (FB) policy, and the class that contains jobs with the smallest attained service is served first. It is known that the FB policy minimizes (maximizes) the mean delay when the hazard rate of the job size distribution is decreasing (increasing). Our analysis, based on pathwise and meanwise arguments of the unfinished truncated work, shows that Two-Level Processor Sharing (TLPS) disciplines, e.g., FB+PS and PS+PS, are better than PS scheduling when the hazard rate of the job size distribution is decreasing. If the hazard rate is increasing and bounded, we show that PS outperforms PS+PS and FB+PS. We further extend our analysis to study local optimality within a level of an MLPS scheduling discipline.

The Internet today carries different types of traffic that have different service requirements. A large fraction of the traffic is either Web traffic requiring low response time or peer-to-peer traffic requiring high throughput. Meeting both performance requirements in a network where routers use droptail or RED for buffer management and FIFO as service policy is an elusive goal. It is therefore worthwhile to investigate alternative scheduling and buffer management policies for bottleneck links.

scheduling disciplines permit to model a wide variety of non-anticipating scheduling disciplines. Such disciplines have recently attracted attention in the context of the Internet as an appropriate flow-level model for the bandwidth sharing obtained when priority is given to short TCP connections. In this paper, we compare the mean delay in an M/G/1 queue among MLPS disciplines under the assumption that the service time distribution belongs to class Decreasing Hazard Rate (DHR). We are able to prove that, given an MLPS discipline, the mean delay is reduced whenever a level is added by splitting an existing one in several cases. The exceptions concern splitting the upper levels with PS internal discipline. Our numerical examples, however, indicate that the level splitting be advantageous even in these cases. Furthermore, we characterize the effect on the mean delay of changing internal disciplines within levels. By numerical means we demonstrate that the mean delay of an MLPS discipline can get close to the minimum optimal delay with just a few levels. As the number of levels increases in an MLPS discipline, the MLPS queue mimics closer and closer the behavior of a Foreground-Background queue, which is known to minimize the mean delay among all disciplines. Thus, our result provides a constructive way to demonstrate the optimality of FB. I.

We analyze a Processor-Sharing queue with Batch arrivals. Our analysis is based on the integral equation derived by Kleinrock, Muntz and Rodemich. Using the contraction mapping principle, we demonstrate the existence and uniqueness of a solution to the integral equation. Then we provide asymptotical analysis as well as tight bounds for the expected response time conditioned on the service time. In particular, the asymptotics for large service times depends only on the first moment of the service time distribution and on the first two moments of the batch size distribution. That is, similarly to the Processor-Sharing with single arrivals, in the Processor-Sharing queue with batch arrivals the expected conditional response time is finite even when the service time distribution has infinite second moment. Finally, we show how the present results can be applied to the Multi-Level Processor-Sharing scheduling.

This paper elaborates on a paradigm for Quality-of-Service (QoS) that is local, i.e., it does not depend on multi-node cooperation. In order to maintain short queuing delays, we individuate flows that occupy a large fraction of a buffer and segregate those flows into a separate queue. The algorithm is provably fair and can avoid all packet re-orderings. We show through extensive simulations that state requirements are minimal, and that other flows will benefit from short queuing delays while aggressive flows can still maintain high throughput.

apport de recherche ISSN 0249-6399 ISRN INRIA/RR--????--FR+ENG

We consider the mean delay optimization in the M/G/1 queue for jobs with a service time distribution that has a tail with decreasing hazard rate (DHR). If the DHR property is valid for the whole distribution, then it is known that the Foreground-Background (FB) discipline, which gives priority to the job with least amount of attained service, is optimal among nonanticipating scheduling disciplines. However, FB may fail to be optimal if the DHR property is valid only for the tail of the distribution. An important example is the Pareto distribution bounded away from zero. In this paper we show that for a class of service time distributions with a DHR tail (including the Pareto distribution), the optimal nonanticipating discipline is a combination of FCFS and FB disciplines, which gives priority to the jobs with attained service less than some fixed threshold θ ∗. These priority jobs are served in the FCFS manner. If there are no jobs with attained service less than θ ∗ , priority is given to the job with least amount of attained service.

Multilevel Processor Sharing scheduling disciplines have recently been resurrected in papers that focus on the differentiation between short and long TCP flows in the Internet. We prove that, for M/G/1 queues, such disciplines are better than the Processor Sharing discipline with respect to the mean delay whenever the hazard rate of the service time distribution is decreasing.

We introduce MarkMax a new flow-aware Active Queue Management algorithm for Additive Increase Multiplicative Decreases protocols (like TCP). MarkMax sends a congestion signal to a selected connection whenever the total backlog reaches a given threshold. The selection mechanism is based on the state of large flows. Using a fluid model we derive some bounds that can be used to analyze the behavior of MarkMax and we compute the per-flow backlog. We conclude the paper with simulation results, using NS-2, comparing MarkMax with Drop Tail and showing how Mark-Max improves both the fairness and link utilization when connections have significantly different Round Trip Times.

Abstract. With the introduction of new generation high speed routers, and with the help of “flow-aware ” traffic management, it becomes possible to improve the Quality of Service for users as well as the network efficiency for ISPs. An example of the “flow-aware ” traffic management is the Alcatel-Lucent “Semantic Networking ” framework where short-lived flows are processed with high priority and long-lived flows are controlled on a per flow basis. In order to control efficiently the flows, it is useful to know an estimate of the Round Trip Time (RTT). In the present work, we provide an online RTT estimation algorithm which is passive and needs one-way traffic only. The one-way traffic requirement is essential for the application of the algorithm for “flow-aware ” traffic management inside the network. To the best of our knowledge, there was no online one-way traffic RTT estimators. Tests on a controlled testbed and on the Internet demonstrate high accuracy of the proposed estimator. 1