Large Deviations and the Generalized Processor Sharing Scheduling: Upper and Lower Bounds Part I: Two-Queue Systems

We prove asymptotic upper and lower bounds on the asymptotic decay rate of per-session queue length tail distributions for a single constant service rate server queue shared by multiple sessions with the generalized processor sharing (GPS) scheduling discipline. The simpler case of a GPS system with only two queues needs special attention, as under this case, it is shown that the upper bounds and lower boundsmatch, thus yielding exact bounds. This result is established in this part (Part I) of the paper. The general case is much more complicated, and is treated separately in Part II of the paper [42], where tight upper and lower bound results are proved by examining the dynamics of bandwidth sharing nature of GPS scheduling. The proofs use sample-path large deviation principle and are based on some recent large deviation results for a single queue with a constant service rate server. These results have implications in call admission control for high-speed communication networks

Fast symbolic computation of the worst-case delay in tandem networks and applications

International audienceComputing deterministic performance guarantees is a defining issue for systems with hard real-time constraints , like reactive embedded systems. In this paper, we use burst-rate constrained arrivals and rate-latency servers to deduce tight worst-case delay bounds in tandem networks under arbitrary multiplexing. We present a constructive method for computing the exact worst-case delay, which we prove to be a linear function of the burstiness and latencies; our bounds are hence symbolic in these parameters. Our algorithm runs in quadratic time in the number of servers. We also present an application of our algorithm to the case of stochastic arrivals and server capacities. For a generalization of the exponentially bounded burstiness (EBB) model, we deduce a polynomial-time algorithm for stochastic delay bounds that strictly improve the state-of-the-art separated flow analysis (SFA) type bounds

On the large deviations behaviour of acyclic networks of G/G/1 queues

Includes bibliographical references (p. 39-41).Supported by a Presidential Young Investigator award. DDM-9158118 Supported by the ARO. DAAL03-92-G-0115 Supported by funds from the Draper Laboratory.Dimitris Bertsimas, Ioannis Ch. Paschalidis, John N. Tsitsiklis

On Using Storage and Genset for Mitigating Power Grid Failures

Although modern society is critically reliant on power grids, even modern power grids are subject to unavoidable outages due to storms, lightning strikes, and equipment failures. The situation in developing countries is even worse, with frequent load shedding lasting several hours a day due to unreliable generation. We study the use of battery storage to allow a set of homes in a single residential neighbour- hood to avoid power outages. Due to the high cost of storage, our goal is to choose the smallest battery size such that, with high target probability, there is no loss of power despite a grid out- age. Recognizing that the most common approach today for mitigating outages is to use a diesel generator (genset), we study the related problem of minimizing the carbon footprint of genset operation. Drawing on recent results, we model both problems as buffer sizing problems that can be ad- dressed using stochastic network calculus. We show that this approach greatly improves battery sizing in contrast to prior approaches. Specifically, a numerical study shows that, for a neigh- bourhood of 100 homes, our approach computes a battery size, which is less than 10% more than the minimum possible size necessary to satisfy a one day in ten years loss probability (2.7 ∗ 10^4 ). Moreover, we are able to estimate the carbon footprint reduction, compared to an exact numerical analysis, within a factor of 1.7. We also study the genset scheduling problem when the rate of genset fuel consumption is given by an affine function instead of a linear function of the current power. We give alternate scheduling, an online scheduling strategy that has a competitive ratio of (k1 G/C +k2)/(k1+k2) , where G is the genset capacity, C is the battery charging rate, and k1, k2 are the affine function constants. Numerically, we show that for a real industrial load alternate scheduling is very close to the offline optimal strategy

Analise de desempenho da disciplina de serviço "generalized processor sharing" sob trafego auto-similar

Orientador : Dalton Soares Arantes, Nelson Luis Saldanha da FonsecaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoMestrad