The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Elena Kokoliou - One of the best experts on this subject based on the ideXlab platform.
-
KM System theory_2018.pptx
internal, 2018Co-Authors: Elena KokoliouAbstract:and Answers KM System Intuitive, simple and focused presentation of Knowledge Search, Locate and Relate provider Enabler for all processes Sharing Processes Reference
Bert Zwart - One of the best experts on this subject based on the ideXlab platform.
-
Diffusion limits of limited processor sharing queues
The Annals of Applied Probability, 2011Co-Authors: Jiheng Zhang, Jim Dai, Bert ZwartAbstract:We consider a processor sharing queue where the number of jobs served at any time is limited to K, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this measure-valued process is obtained under diffusion scaling and heavy traffic conditions. As a consequence, the limit of the system size process is proved to be a piece-wise reflected Brownian motion. © Institute of Mathematical Statistics, 2011.
-
tail robust scheduling via limited processor sharing
Performance Evaluation, 2010Co-Authors: Jayakrishnan Nair, Adam Wierman, Bert ZwartAbstract:From a rare events perspective, scheduling disciplines that work well under light (exponential) tailed workload distributions do not perform well under heavy (power) tailed workload distributions, and vice versa, leading to fundamental problems in designing schedulers that are robust to distributional assumptions on the job sizes. This paper shows how to exploit partial workload information (system load) to design a scheduler that provides robust performance across heavy-tailed and light-tailed workloads. Specifically, we derive new asymptotics for the tail of the stationary sojourn time under Limited processor sharing (LPS) scheduling for both heavy-tailed and light-tailed job size distributions, and show that LPS can be robust to the tail of the job size distribution if the multiprogramming level is chosen carefully as a function of the load.
-
Limits of Limited processor sharing Queues
2009Co-Authors: Jiheng Zhang, Jim Dai, Bert ZwartAbstract:We consider a processor sharing queue where the number of jobs served at any time is limited to K, with the excess jobs waiting in a buer.
-
Law of Large Number Limits of Limited processor-sharing Queues
Mathematics of Operations Research, 2009Co-Authors: Jiheng Zhang, J G Dai, Bert ZwartAbstract:Motivated by applications in computer and communication systems, we consider a processor-sharing queue where the number of jobs served is not larger than K. We propose a measure-valued fluid model for this limited processor-sharing queue and show that there exists a unique associated fluid model solution. In addition, we show that this fluid model arises as the limit of a sequence of appropriately scaled processor-sharing queues.
-
Fluid Limits for processor-sharing Queues with Impatience
Mathematics of Operations Research, 2008Co-Authors: H. Christian Gromoll, Philippe Robert, Bert ZwartAbstract:We investigate a processor-sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue or renege before completing service. The random time representing a job's patience has a general distribution and may be dependent on its initial service time requirement. A scaling procedure that gives rise to a fluid model with nontrivial yet tractable steady state behavior is presented. This fluid model captures many essential features of the underlying stochastic model, and it is used to analyze the impact of impatience in processor-sharing queues.
Pascal Moyal - One of the best experts on this subject based on the ideXlab platform.
-
Stability of a processor-sharing Queue with Varying Throughput
Journal of Applied Probability, 2008Co-Authors: Pascal MoyalAbstract:In this paper we present a stability criterion for processor-sharing queues, in which the throughput may depend on the number of customers in the system (such as in the case of interferences between users). Such a system is represented by a point measure-valued stochastic recursion keeping track of the remaining processing times of the customers.
Scott Jordan - One of the best experts on this subject based on the ideXlab platform.
-
Violation Probability in processor-sharing Queues
IEEE Transactions on Automatic Control, 2008Co-Authors: Na Chen, Scott JordanAbstract:processor-sharing queues are often used to model file transmission in networks. While sojourn time is a common performance metric in the queueing literature, average transmission rate is the more commonly discussed metric in the networking literature. Whereas much is known about sojourn times, there is little known about the average service rate experienced by jobs in processor-sharing queues. We focus here upon performance requirements in the form of an upper bound on the probability of failing to achieve a specified minimum transmission rate or a specified minimum average rate. For an M/G/l processor-sharing queue, we give a closed-form expression for this violation probability. We derive closed-form expressions for the marginal service rate with respect to the violation probability and to the minimum transmission rate, and characterize when each is binding. We then consider the effect of using connection access control by modeling an M/G/l/K processor-sharing queue, and discuss the relationship between queue service rate, queue limit, violation probability, and blocking probability. Finally, we consider a two-class discriminatory processor-sharing queue, and discuss what combinations of class weighting and service rate can be used to achieve specified minimum rate violation probabilities for both classes.
-
Throughput in processor-sharing queues - eScholarship
2007Co-Authors: Na Chen, Scott JordanAbstract:processor-sharing queues are often used to model file transmission in networks. While sojourn time is a common performance metric in the queueing literature, average transmission rate is the more commonly discussed metric in the networking literature. Whereas much is known about sojourn times, there is little known about the average service rate experienced by jobs in processor-sharing queues. We first define the average rate as observed by users and by the queue. In an M/M/1 processor-sharing queue, we give closed-form expressions for these average rates, and prove a strict ordering amongst them. We prove that the queue service rate (in bps) is an increasing function of the minimum required average transmission rate, and give a closed-form expression for the marginal cost associated with such a performance requirement. We then consider the effect of using connection access control by modeling an M/M/1/K processor-sharing queue. We give closed-form expressions for average transmission rates, and discuss the relationship between the queue service rate (in bps), the queue limit, the average rate, and the blocking probability.
-
Throughput in processor-sharing Queues
IEEE Transactions on Automatic Control, 2007Co-Authors: Na Chen, Scott JordanAbstract:processor-sharing queues are often used to model file transmission in networks. While sojourn time is a common performance metric in the queueing literature, average transmission rate is the more commonly discussed metric in the networking literature. Whereas much is known about sojourn times, there is little known about the average service rate experienced by jobs in processor-sharing queues. We first define the average rate as observed by users and by the queue. In an M/M/1 processor-sharing queue, we give closed-form expressions for these average rates, and prove a strict ordering amongst them. We prove that the queue service rate (in bps) is an increasing function of the minimum required average transmission rate, and give a closed-form expression for the marginal cost associated with such a performance requirement. We then consider the effect of using connection access control by modeling an M/M/1/K processor-sharing queue. We give closed-form expressions for average transmission rates, and discuss the relationship between the queue service rate (in bps), the queue limit, the average rate, and the blocking probability
Rudesindo Nunez-queija - One of the best experts on this subject based on the ideXlab platform.
-
Beyond processor sharing
ACM SIGMETRICS Performance Evaluation Review, 2007Co-Authors: Samuli Aalto, Urtzi Ayesta, Sem Borst, Vishal Misra, Rudesindo Nunez-queijaAbstract:While the (Egalitarian) processor-sharing (PS) discipline offers crucial insights in the performance of fair resource allocation mechanisms, it is inherently limited in analyzing and designing differentiated scheduling algorithms such as Weighted Fair Queueing and Weighted Round-Robin. The Discriminatory processor-sharing (DPS) and Generalized processor-sharing (GPS) disciplines have emerged as natural generalizations for modeling the performance of such service differentiation mechanisms. A further extension of the ordinary PS policy is the Multilevel processor-sharing (MLPS) discipline, which has captured a pivotal role in the analysis, design and implementation of size-based scheduling strategies. We review various key results for DPS, GPS and MLPS models, highlighting to what extent these disciplines inherit desirable properties from ordinary PS or are capable of delivering service differentiation.
-
Asymptotic regimes and approximations for discriminatory processor sharing
ACM SIGMETRICS Performance Evaluation Review, 2004Co-Authors: Gijs Van Kessel, Rudesindo Nunez-queija, Sem BorstAbstract:We study the joint queue length distribution of the Discriminatory processor sharing model, assuming all classes have phase-type service requirement distributions. We show that the moments of the joint queue length distribution can be obtained by solving linear equations. We use this to study the system in two asymptotic regimes. In the first regime, the different user classes operate on strictly separated time scales. Then we study the system in heavy traffic.
-
SOJOURN TIMES IN NON-HOMOGENEOUS QBD PROCESSES WITH processor sharing
Stochastic Models, 2001Co-Authors: Rudesindo Nunez-queijaAbstract:We study sojourn times of customers in a processor sharing queue with a service rate that varies over time, depending on the number of customers and on the state of a random environment. An explicit expression is derived for the Laplace–Stieltjes transform of the sojourn time conditional on the state upon arrival and the amount of work brought into the system. Particular attention is paid to the conditional mean sojourn time of a customer as a function of his required amount of work, and we establish the existence of an asymptote as the amount of work tends to infinity. The method of random time change is then extended to include the possibility of a varying service rate. By means of this method, we explain the well-established proportionality between the conditional mean sojourn time and required amount of work in processor sharing queues without random environment. Based on numerical experiments, we propose an approximation for the conditional mean sojourn time. Although first presented for exponentiall...
-
INFOCOM - Discriminatory processor sharing revisited
Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies., 1Co-Authors: Konstantin Avrachenkov, Urtzi Ayesta, Patrick Brown, Rudesindo Nunez-queijaAbstract:As a natural multi-class generalization of the well-known (egalitarian) processor sharing (PS) service discipline, discriminatory processor sharing (DPS) is of great interest in many application areas, including telecommunications. Under DPS, the mean response time conditional on the service requirement is only known in closed form when all classes have exponential service requirement distributions. For generally distributed service requirements, Fayolle et al. (1980) showed that the expected conditional response times satisfy a system of integro-differential equations. In this paper, we exploit that result to prove that, provided the system is stable, for each class the expected unconditional response time is finite and that the expected conditional response time has an asymptote. The asymptotic bias of each class is found in closed form, involving the mean service requirements of all classes and the second moments of all classes but the one under consideration. In the course of the development we prove two other results that are of independent interest: we establish a conservation law for the time average unfinished work of all classes and, using a stochastic coupling argument, we show that the response times of different classes are stochastically ordered according to the DPS weights. Finally, we study DPS as a tool to achieve size based scheduling and we provide guidelines as to how the weights of DPS must be chosen such that DPS outperforms PS.
