Sample-path large deviations for tandem and priority queues with Gaussian inputs

This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large-deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently used Gaussian inputs. The last part of the paper concentrates on a model for a single node, equipped with a priority scheduling policy. We show that the analysis of the tandem queue directly carries over to this priority queueing system.Comment: Published at http://dx.doi.org/10.1214/105051605000000133 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Investigation of delay jitter of heterogeneous traffic in broadband networks

Scope and Methodology of Study: A critical challenge for both wired and wireless networking vendors and carrier companies is to be able to accurately estimate the quality of service (QoS) that will be provided based on the network architecture, router/switch topology, and protocol applied. As a result, this thesis focuses on the theoretical analysis of QoS parameters in term of inter-arrival jitter in differentiated services networks by deploying analytic/mathematical modeling technique and queueing theory, where the analytic model is expressed in terms of a set of equations that can be solved to yield the desired delay jitter parameter. In wireless networks with homogeneous traffic, the effects on the delay jitter in reference to the priority control scheme of the ARQ traffic for the two cases of: 1) the ARQ traffic has a priority over the original transmission traffic; and 2) the ARQ traffic has no priority over the original transmission traffic are evaluated. In wired broadband networks with heterogeneous traffic, the jitter analysis is conducted and the algorithm to control its effect is also developed.Findings and Conclusions: First, the results show that high priority packets always maintain the minimum inter-arrival jitter, which will not be affected even in heavy load situation. Second, the Gaussian traffic modeling is applied using the MVA approach to conduct the queue length analysis, and then the jitter analysis in heterogeneous broadband networks is investigated. While for wireless networks with homogeneous traffic, binomial distribution is used to conduct the queue length analysis, which is sufficient and relatively easy compared to heterogeneous traffic. Third, develop a service discipline called the tagged stream adaptive distortion-reducing peak output-rate enforcing to control and avoid the delay jitter increases without bound in heterogeneous broadband networks. Finally, through the analysis provided, the differential services, was proved not only viable, but also effective to control delay jitter. The analytic models that serve as guidelines to assist network system designers in controlling the QoS requested by customer in term of delay jitter

Large deviations for complex buffer architectures: the short-range dependent case

This paper considers Gaussian flows multiplexed in a queueing network, where the underlying correlation structure is assumed to be short-range dependent. Whereas previous work mainly focused on the FIFO setting, this paper addresses overflow characteristics of more complex buffer architectures. We subsequently analyze the tandem queue, a priority system, and generalized processor sharing. In a many-sources setting, we explicitly compute the exponential decay rate of the overflow probability. Our study relies on large-deviations arguments, e.g., Schilder's theore

Sample-path large deviations for tandem and priority queues with Gaussian inputs

This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently-used Gaussian inputs. The last part of the paper concentrates on a model for a single node, equipped with a priority scheduling policy. We show that the analysis of the tandem queue directly carries over to this priority queueing system. iffalse {it Perhaps:} We conclude by presenting a number of motivated conjectures for the analysis of a queue operating under the generalized processor sharing discipline

Sample-path large deviations for generalized processor sharing queues with Gaussian inputs

In this paper we consider the Generalized Processor Sharing (GPS) mechanism serving two traffic classes. These classes consist of a large number of independent identically distributed Gaussian flows with stationary increments. We are interested in the logarithmic asymptotics or exponential decay rates of the overflow probabilities. We first derive both an upper and a lower bound on the overflow probability. Scaling both the buffer sizes of the queues and the service rate with the number of sources, we apply Schilder's sample-path large deviations theorem to calculate the logarithmic asymptotics of the upper and lower bound. We discuss in detail the conditions under which the upper and lower bound match. Finally we show that our results can be used to choose the values of the GPS weights. The results are illustrated by numerical examples

Statistical Service Guarantees for Traffic Scheduling in High-Speed Data Networks

School of Electrical and Computer Engineerin

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

GPS Schedulers and Gaussian Traffic

This article considers Gaussian flows which are fed into a GPS (Generalized Processor Sharing) scheduler. The system is analyzed using a most probable path approach. This method gives quite good approximations for performance measures, like queue length distributions in the full range of queue levels. The approximations are based on the distinction whether it is more probable that an aggregated queue consists of traffic from one class only or whether it is a combination of several classes. The approximate queue length distribution for a specific flow is then calculated either using the Empty Buffer Approximation or the authors' Rough Full Link Approximation, respectively