Generalized Processor Sharing System Research Articles

Performance analysis of an integrated scheduling scheme in the presence of bursty MMPP traffic

Contemporary communication networks are expected to support multimedia applications which require diversified Quality-of-Services (QoS). An integrated scheduling discipline of Priority Queueing (PQ) and Generalized Processor Sharing (GPS), referred to as P–G, has recently emerged as a promising scheme for cost-effective QoS differentiation. In this paper, we develop a new analytical model for the integrated P–G system subject to bursty traffic. The Markov-Modulated Poisson Process (MMPP) is adopted to capture traffic burstiness because it can qualitatively model time-varying arrival rate and important correlation between inter-arrival times. To derive the desired performance metrics for individual sessions, the integrated P–G system is decomposed into a set of Single-Server Single-Queue (SSSQ) systems. Specifically, the integrated system is first divided into an SSSQ system and a GPS system. Next, a bounding approach is adopted to decompose the GPS system into individual SSSQ systems. Extensive comparisons between analytical and simulation results validate the accuracy of the analytical model. To demonstrate its merits, the model is used to investigate the configuration of the GPS weights under the QoS constraints of different traffic flows.

Bandwidth allocation for fluid input generalized processor sharing servers

Generalized processor sharing (GPS) service policy is a scheduling algorithm to allocate the bandwidth of a queueing system with multi-class input traffic. Simulating the GPS system in realistic traffic environments requires a large amount of time. Thus, fluid simulation is useful because it requires much less time. We analyze the bandwidth allocation for fluid simulation in GPS servers, in which the traffic into the server is treated as fluid. Three properties which characterize GPS servers with fluid input are discussed. We show that there exists a unique bandwidth allocation with the properties. It is shown that our previously proposed algorithm gives the unique bandwidth allocation and it is equivalent to the well-known Newton-Rapson method. In numerical study, the performance of finding the unique bandwidth allocation based on other known root finding methods is compared with that of our previous algorithm. We also investigate the impact of the length of the unit time on the accuracy of the performance measures.

Analytical queue length distributions of GPS systems with long range dependent service capacity

Generalized Processor Sharing (GPS) is an idealized scheduling mechanism with given weights assigned to individual traffic flows for service differentiation. Based on the principle of GPS, a number of variants have been proposed and deployed in real-world communication systems where the service capacity of network channels is usually variable. This paper proposes an analytical performance model for GPS systems with the variable service capacity characterized by Long Range Dependent (LRD) processes. The model is able to accommodate heterogeneous fractional Brownian motion (fBm) and Poisson traffic in multi-service networks. We derive the expressions of the queue length distributions of the GPS system and individual traffic flows. The accuracy of the analytical model is validated through comparison between analytical and simulation results.

Asymptotic behavior of generalized processor sharing queues under subexponential assumptions

We analyze the behavior of Generalized Processor Sharing (GPS) queues with heavy-tailed service times. We compute the exact tail asymptotics of the stationary workload of an individual class and give new conditions for reduced-load equivalence and induced burstiness to hold. We also show that both phenomena can occur simultaneously. Our proofs rely on the single big event theorem and new fluid limits obtained for the GPS system that can be of interest by themselves.

Performance modelling of generalized processor sharing systems with multiple self-similar traffic flows

The Generalized Processor Sharing (GPS) is an important service differentiation scheme in telecommunication systems and has attracted great research interests due to the desirable properties of fairness, traffic isolation, and work conservation. The major limitation of the existing analytical performance models of GPS systems subject to self-similar traffic is that these models have been restricted to a simplified scenario with only two traffic flows. To overcome such a limitation, this study proposes a new flow-decomposition approach to modelling GPS systems subject to multiple self-similar traffic flows. We present and prove the existence of a feasible ordering of GPS systems based on the required and guaranteed service rates of traffic flows. With the aid of the feasible ordering, we decompose the GPS system into a group of single-queue systems and then derive the queue length distributions and loss probabilities of individual self-similar traffic flows in the original GPS system. Extensive simulation experiments are conducted to validate the accuracy of the developed analytical model.

A heuristic flow-decomposition approach for generalized processor sharing under self-similar traffic

The well-known Generalized Processor Sharing (GPS) scheduling principle and its variants have received tremendous research efforts due to their appealing properties of fairness, traffic isolation, and work conservation. Traffic self-similarity is highly detrimental to the performance of scheduling mechanisms and communication networks. This paper proposes a novel and heuristic flow-decomposition approach to performance modeling of the GPS system under self-similar traffic. Based on the comprehensive analysis of the excess service sharing behavior of traffic flows, we decompose the GPS system equivalently into a group of single-server single-queue systems. Extensive simulation experiments are used to validate the correctness of the proposed flow-decomposition approach as well as the analytical performance results.

On Generalized Processor Sharing With Regulated Multimedia Traffic Flows

Multimedia traffic is becoming an increasing portion of today's Internet traffic due to the flourishing of multimedia applications such as music/video streaming, video teleconferencing, IP telephony, and distance learning. In this paper, we study the problem of supporting multimedia traffic using a generalized processor sharing (GPS) server. By examining the sample path behavior and exploring the inherent feasible ordering of the classes, we derive tight performance bounds on backlog and delay for regulated multimedia traffic classes in a GPS system. Our approach is quite general since we do not assume any arriving traffic model or any specific traffic regulator, other than that each traffic flow is deterministically regulated. Such deterministic regulators, as well as approximations of the GPS server, are widely implemented in commercial routers. In addition, our analysis is very accurate and achieves a high utilization of the server capacity, since we exploit the independence among the traffic flows for higher statistical multiplexing gains. Numerical examples and simulation results are presented to demonstrate the accuracy and merits of our approach, which is practical and well suited for supporting multimedia applications in the Internet

Analysis of generalized processor-sharing systems with two classes of customers and exponential services

We derive in this paper closed formulae for the joint probability generating function of the number of customers in the two FIFO queues of a generalized processor-sharing (GPS) system with two classes of customers arriving according to Poisson processes and requiring exponential service times. In contrast to previous studies published on the GPS system, we show that it is possible to establish explicit expressions for the generating functions of the number of customers in each queue without calling for the formulation of a Riemann–Hilbert problem. We specifically prove that the problem of determining the unknown functions due to the reflecting conditions on the boundaries of the positive quarter plane can be reduced to a Poisson equation. The explicit formulae are then used to derive some characteristics of the GPS system (in particular the tails of the probability distributions of the numbers of customers in each queue).

Analysis of generalized processor-sharing systems with two classes of customers and exponential services

We derive in this paper closed formulae for the joint probability generating function of the number of customers in the two FIFO queues of a generalized processor-sharing (GPS) system with two classes of customers arriving according to Poisson processes and requiring exponential service times. In contrast to previous studies published on the GPS system, we show that it is possible to establish explicit expressions for the generating functions of the number of customers in each queue without calling for the formulation of a Riemann–Hilbert problem. We specifically prove that the problem of determining the unknown functions due to the reflecting conditions on the boundaries of the positive quarter plane can be reduced to a Poisson equation. The explicit formulae are then used to derive some characteristics of the GPS system (in particular the tails of the probability distributions of the numbers of customers in each queue).

Call admission control in generalized processor sharing schedulers with tight deterministic delay bounds

Generalized processor sharing (GPS) is reported as the most important ideal fluid scheduling discipline, which many practical packet scheduling algorithms (WFQ, WF 2Q) are built on. However, all of them bear the bandwidth–delay coupling property due to the commonly used rate-proportional weighting of sessions and offer too loose deterministic delay bounds. These deficiencies lead to poor network utilization and preclude the development of efficient call admission control (CAC) schemes. In this paper we address these problems by proposing an algorithm for tight individual session delay bound computation and several CAC algorithms for session resource assignment in a bandwidth–delay decoupled GPS system. Besides the analytical framework numerical examples as well as the complexity analysis of different CAC algorithms are also presented.

Large deviations and the generalized processor sharing scheduling for a multiple-queue system

We establish asymptotic upper and lower bounds on the asymptotic decay rate of per-session queue length tail distributions for a multiple-queue system where a single constant rate server services the queues using the generalized processor sharing (GPS) scheduling discipline. In the special case where there are only two queues, the upper and lower bounds match, yielding the optimal bound proved in l15r. The dynamics of bandwidth sharing of a multiple-queue GPS system is captured using the notion of partial feasible sets, and the bounds are obtained using the sample-path large deviation principle. The results have implications in call admission control for high-speed communication networks.