The multiple phase service network with generalized processor sharing

Abstract:Consider an M/G/1 queue which is idle at time 0. The number of customers sampled at an independent exponential time is shown to have the same geometric distribution under the preemptive resume last in first out (LIFO) and the processor sharing (PS) disciplines. Hence, the marginal distribution of the queue length at any time is identical for both disciplines. We then give a detailed analysis of the time until the first departure for any symmetric queueing discipline. We characterize its distribution and show that it is insensitive to the service discipline. Finally we study the tail behavior of this distribution.

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“…Classical papers include [4], [9], [1], [11], and [5]; see [12] for a textbook treatment. Recent interesting papers are [3] and [7].…”

Section: Introductionmentioning

confidence: 99%

Some Time-Dependent Properties of Symmetric M/G/1 Queues

2005

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“…This is due to insensitivity results for networks of generalized processor sharing queues, as was shown by Cohen [5].…”

Section: General Think-time and File-size Distributions For Large Bufmentioning

confidence: 83%

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

Mandjes

Mitra²,

Scheinhardt

2003

Computer Networks

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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

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“…(3) results in the expression given in Eq. (2). The corresponding expression for s j min can be obtained by substituting n j π * into Eq.…”

Section: Variance-based Metricmentioning

confidence: 99%

“…Assuming that each user has equal rights or priority to the resource, a hypothetical service discipline that is fair is a bit-by-bit round-robin (BR) discipline, since at every instant in time, each user is receiving its fair share. For users that can be characterized as jobs (e.g., in a supermarket set-up), the Processor-sharing model (introduced in [1] and generalized in [2]) is commonly used to evaluate the efficiency of the BR discipline as the bit size tends to zero. Recently, a resource-allocation queueing fairness measure (RAQFM) has been proposed in [3] that accounts for both seniority differences (times of arrival) and service-time differences (job sizes).…”

Section: Introductionmentioning

confidence: 99%

Design and analysis of a class-aware recursive loop scheduler for class-based scheduling

Rom

Sidi

Tan

2006

Performance Evaluation

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In this paper, we consider the problem of devising a loop scheduler that allocates slots to users according to their relative weights as smoothly as possible. Instead of the existing notion of smoothness based on balancedness, we propose a variance-based metric which is more intuitive and easier to compute.We propose a recursive loop scheduler for a class-based scheduling scenario based on an optimal Weighted Round Robin scheduler. We show that it achieves very good allocation smoothness with almost no degradation in intra-class fairness. In addition, we also demonstrate the equivalence between our proposed metric and the balancedness-based metric.

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The multiple phase service network with generalized processor sharing

Cited by 185 publications

References 17 publications

Some Time-Dependent Properties of Symmetric M/G/1 Queues

Some Time-Dependent Properties of Symmetric M/G/1 Queues

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

Design and analysis of a class-aware recursive loop scheduler for class-based scheduling

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