On the Gittins index in the M/G/1 queue

For an M/G/1 queue with the objective of minimizing the mean number of jobs in the system, the Gittins index rule is known to be optimal among the set of non-anticipating policies. We develop properties of the Gittins index. For a single-class queue it is known that when the service time distribution is of type Decreasing Hazard Rate (New Better than Used in Expectation), the Foreground-Background (First-Come-First-Served) discipline is optimal. By utilizing the Gittins index approach, we show that in fact, Foreground-Background and First-Come-First-Served are optimal if and only if the service time distribution is of type Decreasing Hazard Rate and New Better than Used in Expectation, respectively. For the multi-class case, where jobs of different classes have different service distributions, we obtain new results that characterize the optimal policy under various assumptions on the service time distributions. We also investigate distributions whose hazard rate and mean residual lifetime are not monotonic. © Springer Science+Business Media, LLC 2009

SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers

The shortest-remaining-processing-time (SRPT) scheduling policy has been extensively studied, for more than 50 years, in single-server queues with infinitely patient jobs. Yet, much less is known about its performance in multiserver queues. In this paper, we present the first theoretical analysis of SRPT in multiserver queues with abandonment. In particular, we consider the M/GI/s+GI queue and demonstrate that, in the many-sever overloaded regime, performance in the SRPT queue is equivalent, asymptotically in steady state, to a preemptive two-class priority queue where customers with short service times (below a threshold) are served without wait, and customers with long service times (above a threshold) eventually abandon without service. We prove that the SRPT discipline maximizes, asymptotically, the system throughput, among all scheduling disciplines. We also compare the performance of the SRPT policy to blind policies and study the effects of the patience-time and service-time distributions

Improved Load Balancing in Large Scale Systems using Attained Service Time Reporting

Our interest lies in load balancing jobs in large scale systems consisting of multiple dispatchers and FCFS servers. In the absence of any information on job sizes, dispatchers typically use queue length information reported by the servers to assign incoming jobs. When job sizes are highly variable, using only queue length information is clearly suboptimal and performance can be improved if some indication can be provided to the dispatcher about the size of an ongoing job. In a FCFS server measuring the attained service time of the ongoing job is easy and servers can therefore report this attained service time together with the queue length when queried by a dispatcher. In this paper we propose and analyse a variety of load balancing policies that exploit both the queue length and attained service time to assign jobs, as well as policies for which only the attained service time of the job in service is used. We present a unified analysis for all these policies in a large scale system under the usual asymptotic independence assumptions. The accuracy of the proposed analysis is illustrated using simulation. We present extensive numerical experiments which clearly indicate that a significant improvement in waiting (and thus also in response) time may be achieved by using the attained service time information on top of the queue length of a server. Moreover, the policies which do not make use of the queue length still provide an improved waiting time for moderately loaded systems

Differentiation between Short and Long TCP Flows: Predictability of the Response Time

Internet measurements show that a small number of large TCP flows are responsible for the largest amount of data transferred, whereas most of the TCP sessions are made up of few packets. Several authors have invoked this property to suggest the use of scheduling algorithms which favor short jobs, such as LAS (Least Attained Service), to differentiate between short and long TCP flows

Performance evaluation of multicast networks and service differentiation mechanisms in IP networks

The performance of a communication network depends on how well the network is designed in terms of delivering the level of service required by a given type of traffic. The field of teletraffic theory is concerned with quantifying the three-way relationship between the network, its level of service and the traffic arriving at the network. In this thesis, we study three different problems concerning this three-way relationship and present models to assist in designing and dimensioning networks to satisfy the different quality of service demands. In the first part of the thesis, we consider service differentiation mechanisms in packet-switched IP networks implementing a Differentiated Services (DiffServ) architecture. We study how bandwidth can be divided in a weighted fair manner between persistent elastic TCP flows, and between these TCP flows and streaming real-time UDP flows. To this end, we model the traffic conditioning and scheduling mechanisms on the packet and the flow level. We also model the interaction of these DiffServ mechanisms with the TCP congestion control mechanism and present closed-loop models for the sending rate of a TCP flow that reacts to congestion signals from the network. In the second part, we concentrate on non-persistent elastic TCP traffic in IP networks and study how flows can be differentiated in terms of mean delay by giving priority to flows based on their age. We study Multi Level Processor Sharing (MLPS) disciplines, where jobs are classified into levels based on their age or attained service. Between levels, a strict priority discipline is applied; the level containing the youngest jobs has the highest priority. Inside a particular level, any scheduling discipline could be used. We present an implementation proposal of a two-level discipline, PS+PS, with the Processor Sharing discipline used inside both levels. We prove that, as long as the hazard rate of the job-size distribution is decreasing, which is the case for Internet traffic, PS+PS, and any MLPS discipline that favors young jobs, is better than PS with respect to overall mean delay. In the final part, we study distribution-type streaming traffic in a multicast network, where there is, at most, one copy of each channel transmission in each network link, and quantify the blocking probability. We derive an exact blocking probability algorithm for multicast traffic in a tree network based on the convolution and truncation algorithm for unicast traffic. We present a new convolution operation, the OR-convolution, to suit the transmission principle of multicast traffic, and a new truncation operator to take into account the case of having both unicast and multicast traffic in the network. We also consider different user models derived from the single-user model.reviewe

Delay analysis for wireless applications using a multiservice multiqueue processor sharing model

The ongoing development of wireless networks supporting multimedia applications requires service providers to efficiently deliver complex Quality of Service (QoS) requirements. The wide range of new applications in these networks significantly increases the difficulty of network design and dimensioning to meet QoS requirements. Medium Access Control (MAC) protocols affect QoS achieved by wireless networks. Research on analysis and performance evaluation is important for the efficient protocol design. As wireless networks feature scarce resources that are simultaneously shared by all users, processor sharing (PS) models were proposed for modelling resource sharing mechanisms in such systems. In this thesis, multi-priority MAC protocols are proposed for handling the various service traffic types. Then, an investigation of multiservice multiqueue PS models is undertaken to analyse the delay for some recently proposed wireless applications. We start with an introduction to MAC protocols for wireless networks which are specified in IEEE standards and then review scheduling algorithms which were proposed to work with the underlying MAC protocols to cooperatively achieve QoS goals. An overview of the relevant literature is given on PS models for performance analysis and evaluation of scheduling algorithms. We propose a multiservice multiqueue PS model using a scheduling scheme in multimedia wireless networks with a comprehensive description of the analytical solution. Firstly, we describe the existing multiqueue processor sharing (MPS) model, which uses a fixed service quantum at each queue, and correct a subtle incongruity in previous solutions presented in the literature. Secondly, a new scheduling framework is proposed to extend the previous MPS model to a general case. This newly proposed analytical approach is based on the idea that the service quantum arranged by a MAC scheduling controller to service data units can be priority-based. We obtain a closed-form expression for the mean delay of each service class in this model. In summary, our new approach simplifies MAC protocols for multimedia applications into an analytical model that includes more complex and realistic traffic models without compromising details of the protocol and significantly reduces the number of MAC headers, thus the overall average delay will be decreased. In response to using the studied multiservice multiqueue PS models, we apply the MPS model to two wireless applications: Push to Talk (PTT) service over GPRS/GSM networks and the Worldwide Interoperability for Microwave Access (WiMAX) networks. We investigate the uplink delay of PTT over traditional GPRS/GSM networks and the uplink delay for WiMAX Subscriber Station scheduler under a priority-based fair scheduling. MAC structures capable of supporting dynamically varying traffic are studied for the networks, especially, with the consideration of implementation issues. The model provides useful insights into the dynamic performance behaviours of GPRS/GSM and WiMAX networks with respect to various system parameters and comprehensive traffic conditions. We then evaluate the model under some different practical traffic scenarios. Through modelling of the operation of wireless access systems, under a variety of multimedia traffic, our analytical approaches provide practical analysis guidelines for wireless network dimensioning