About the cumulative idle time in multiphase queues

The paper is designated to the analysis of queueing systems, arising in the network theory and communications theory (called multiphase queueing systems, tandem queues or series of queueing systems). Also we note that multiphase queueing systems can be useful for modelling practical multi-stage service systems in a variety of disciplines, especially on manufacturing (assembly lines), computer networking (packet switch structures), and in telecommunications (e.g. cellular mobile networks), etc. This research presents heavy traffic limit theorems for the cumulative idle time in multiphase queues. In this work, functional limit theorems are proved for the values of important probability characteristics of the queueing system (a cumulative idle time of a customer)

Heavy traffic limit for the workload plateau process in a tandem queue with identical service times

We consider a two-node tandem queueing network in which the upstream queue is GI/GI/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. To investigate the evolution of workload in the second queue, we introduce and study a process M, called the plateau process, which encodes most of the information in the workload process. We focus on the case of infinite-variance service times and show that under appropriate scaling, workload in the first queue converges, and although the workload in the second queue does not converge, the plateau process does converges to a limit that is a certain function of two independent Levy processes. Using excursion theory, we compare a time changed version of the limit to a limit process derived in previous work

Mathematical Analysis of Queue with Phase Service: An Overview

We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent

Integrating Algorithmic and Systemic Load Balancing Strategies in Parallel Scientific Applications

Load imbalance is a major source of performance degradation in parallel scientific applications. Load balancing increases the efficient use of existing resources and improves performance of parallel applications running in distributed environments. At a coarse level of granularity, advances in runtime systems for parallel programs have been proposed in order to control available resources as efficiently as possible by utilizing idle resources and using task migration. At a finer granularity level, advances in algorithmic strategies for dynamically balancing computational loads by data redistribution have been proposed in order to respond to variations in processor performance during the execution of a given parallel application. Algorithmic and systemic load balancing strategies have complementary set of advantages. An integration of these two techniques is possible and it should result in a system, which delivers advantages over each technique used in isolation. This thesis presents a design and implementation of a system that combines an algorithmic fine-grained data parallel load balancing strategy called Fractiling with a systemic coarse-grained task-parallel load balancing system called Hector. It also reports on experimental results of running N-body simulations under this integrated system. The experimental results indicate that a distributed runtime environment, which combines both algorithmic and systemic load balancing strategies, can provide performance advantages with little overhead, underscoring the importance of this approach in large complex scientific applications

Predictive and distributed routing balancing (PR-DRB) : high speed interconnection networks

Current parallel applications running on clusters require the use of an interconnection network to perform communications among all computing nodes available. Imbalance of communications can produce network congestion, reducing throughput and increasing latency, degrading the overall system performance. On the other hand, parallel applications running on these networks posses representative stages which allow their characterization, as well as repetitive behavior that can be identified on the basis of this characterization. This work presents the Predictive and Distributed Routing Balancing (PR-DRB), a new method developed to gradually control network congestion, based on paths expansion, traffic distribution and effective traffic load, in order to maintain low latency values. PR-DRB monitors messages latencies on intermediate routers, makes decisions about alternative paths and record communication pattern information encountered during congestion situation. Based on the concept of applications repetitiveness, best solution recorded are reapplied when saved communication pattern re-appears. Traffic congestion experiments were conducted in order to evaluate the performance of the method, and improvements were observed.Les aplicacions paral·leles actuals en els Clústers requereixen l'ús d'una xarxa d'interconnexió per comunicar a tots els nodes de còmput disponibles. El desequilibri en la càrrega de comunicacions pot congestionar la xarxa, incrementant la latència i disminuint el throughput, degradant el rendiment total del sistema. D'altra banda, les aplicacions paral·leles que s'executen sobre aquestes xarxes contenen etapes representatives durant la seva execució les quals permeten caracteritzar-les, a més d'extraure un comportament repetitiu que pot ser identificat en base a aquesta caracterització. Aquest treball presenta el Balanceig Predictiu de Encaminament Distribuït (PR-DRB), un nou mètode desenvolupat per controlar la congestió a la xarxa en forma gradual, basat en l'expansió de camins, la distribució de trànsit i càrrega efectiva actual per tal de mantenir una latència baixa. PR-DRB monitoritza la latència dels missatges en els encaminadors, pren decisions sobre els camins alternatius a utilitzar i registra la informació de la congestió sobre la base del patró de comunicacions detectat, utilitzant com a concepte base la repetitivitat de les aplicacions per després tornar a aplicar la millor solució quan aquest patró es repeteixi. Experiments de trànsit amb congestió van ser portats a terme per avaluar el rendiment del mètode, els quals van mostrar la bondat del mateix.Las aplicaciones paralelas actuales en los Clústeres requieren el uso de una red de interconexión para comunicar a todos los nodos de cómputo disponibles. El desbalance en la carga de comunicaciones puede congestionar la red, incrementando la latencia y disminuyendo el throughput, degradando el rendimiento total del sistema. Por otro lado, las aplicaciones paralelas que corren sobre estas redes contienen etapas representativas durante su ejecución las cuales permiten caracterizarlas, además de un comportamiento repetitivo que puede ser identificado en base a dicha caracterización. Este trabajo presenta el Balanceo Predictivo de Encaminamiento Distribuido (PR-DRB), un nuevo método desarrollado para controlar la congestión en la red en forma gradual; basado en la expansión de caminos, la distribución de tráfico y carga efectiva actual, a fin de mantener una latencia baja. PR-DRB monitorea la latencia de los mensajes en los encaminadores, toma decisiones sobre los caminos alternativos a utilizar y registra la información de la congestión en base al patrón de comunicaciones detectado, usando como concepto base la repetitividad de las aplicaciones para luego volver a aplicar la mejor solución cuando dicho patrón se repita. Experimentos de tráfico con congestión fueron llevados a cabo para evaluar el rendimiento del método, los cuales mostraron la bondad del mismo

A Robust Queueing Network Analyzer Based on Indices of Dispersion

In post-industrial economies, modern service systems are dramatically changing the daily lives of many people. Such systems are often complicated by uncertainty: service providers usually cannot predict when a customer will arrive and how long the service will be. Fortunately, useful guidance can often be provided by exploiting stochastic models such as queueing networks. In iterating the design of service systems, decision makers usually favor analytical analysis of the models over simulation methods, due to the prohibitive computation time required to obtain optimal solutions for service operation problems involving multidimensional stochastic networks. However, queueing networks that can be solved analytically require strong assumptions that are rarely satisfied, whereas realistic models that exhibit complicated dependence structure are prohibitively hard to analyze exactly. In this thesis, we continue the effort to develop useful analytical performance approximations for the single-class open queueing network with Markovian routing, unlimited waiting space and the first-come first-served service discipline. We focus on open queueing networks where the external arrival processes are not Poisson and the service times are not exponential. We develop a new non-parametric robust queueing algorithm for the performance approximation in single-server queues. With robust optimization techniques, the underlying stochastic processes are replaced by samples from suitably defined uncertainty sets and the worst-case scenario is analyzed. We show that this worst-case characterization of the performance measure is asymptotically exact for approximating the mean steady-state workload in G/G/1 models in both the light-traffic and heavy-traffic limits, under mild regularity conditions. In our non-parametric Robust Queueing formulation, we focus on the customer flows, defined as the continuous-time processes counting customers in or out of the network, or flowing from one queue to another. Each flow is partially characterized by a continuous function that measures the change of stochastic variability over time. This function is called the index of dispersion for counts. The Robust Queueing algorithm converts the index of dispersion for counts into approximations of the performance measures. We show the advantage of using index of dispersion for counts in queueing approximation by a renewal process characterization theorem and the ordering of the mean steady-state workload in GI/M/1 models. To develop generalized algorithm for open queueing networks, we first establish the heavy-traffic limit theorem for the stationary departure flows from a GI/GI/1 model. We show that the index of dispersion for counts function of the stationary departure flow can be approximately characterized as the convex combination of the arrival index of dispersion for counts and service index of dispersion for counts with a time-dependent weight function, revealing the non-trivial impact of the traffic intensity on the departure processes. This heavy-traffic limit theorem is further generalized into a joint heavy-traffic limit for the stationary customer flows in generalized Jackson networks, where the external arrival are characterized by independent renewal processes and the service times are independent and identically distributed random variables, independent of the external arrival processes. We show how these limiting theorems can be exploited to establish a set of linear equations, whose solution serves as approximations of the index of dispersion for counts of the flows in an open queueing network. We prove that this set of equations is asymptotically exact in approximating the index of dispersion for counts of the stationary flows. With the index of dispersion for counts available, the network is decomposed into single-server queues and the Robust Queueing algorithm can be applied to obtain performance approximation. This algorithm is referred to as the Robust Queueing Network Analyzer. We perform extensive simulation study to validate the effectiveness of our algorithm. We show that our algorithm can be applied not only to models with non-exponential distirbutions but also to models with more complex arrival processes than renewal processes, including those with Markovian arrival processes

Queues: Flows, Systems, Networks

В сборнике излагаются новые результаты научных исследований в области разработки и оптимизации моделей процессов передачи информации в телекоммуникационных сетях с использованием аппарата теории систем и сетей массового обслуживания. Предназначен специалистам в области вероятностного анализа, случайных процессов, математического моделирования, и математической статистики, а также специалистам в области проектирования и эксплуатации сетей связи и компьютерных сетей

Treatment-Based Classi?cation in Residential Wireless Access Points

IEEE 802.11 wireless access points (APs) act as the central communication hub inside homes, connecting all networked devices to the Internet. Home users run a variety of network applications with diverse Quality-of-Service requirements (QoS) through their APs. However, wireless APs are often the bottleneck in residential networks as broadband connection speeds keep increasing. Because of the lack of QoS support and complicated configuration procedures in most off-the-shelf APs, users can experience QoS degradation with their wireless networks, especially when multiple applications are running concurrently. This dissertation presents CATNAP, Classification And Treatment iN an AP , to provide better QoS support for various applications over residential wireless networks, especially timely delivery for real-time applications and high throughput for download-based applications. CATNAP consists of three major components: supporting functions, classifiers, and treatment modules. The supporting functions collect necessary flow level statistics and feed it into the CATNAP classifiers. Then, the CATNAP classifiers categorize flows along three-dimensions: response-based/non-response-based, interactive/non-interactive, and greedy/non-greedy. Each CATNAP traffic category can be directly mapped to one of the following treatments: push/delay, limited advertised window size/drop, and reserve bandwidth. Based on the classification results, the CATNAP treatment module automatically applies the treatment policy to provide better QoS support. CATNAP is implemented with the NS network simulator, and evaluated against DropTail and Strict Priority Queue (SPQ) under various network and traffic conditions. In most simulation cases, CATNAP provides better QoS supports than DropTail: it lowers queuing delay for multimedia applications such as VoIP, games and video, fairly treats FTP flows with various round trip times, and is even functional when misbehaving UDP traffic is present. Unlike current QoS methods, CATNAP is a plug-and-play solution, automatically classifying and treating flows without any user configuration, or any modification to end hosts or applications

A Method for Evaluating and Prioritizing Candidate Intersections for Transit Signal Priority Implementation

Transit agencies seeking to improve transit service delivery are increasingly considering the deployment of transit signal priority (TSP). However, the impact of TSP on transit service and on the general traffic stream is a function of many factors, including intersection geometry, signal timings, traffic demands, TSP strategies and parameters, transit vehicle headways, timing when transit vehicles arrive at the intersection, etc. Previous studies have shown that depending on these factors, the net impact of TSP in terms of vehicle or person delay can be positive or negative. Furthermore, due to financial constraints, transit agencies are often able to deploy TSP at only a portion of all of the candidate intersections. Consequently, there is a need to estimate the impact of TSP prior to implementation in order to assist in determining at which intersections TSP should be deployed. Currently, the impacts of TSP are often estimated using microscopic simulation models. However, the application of these models is resource intensive and requires specialized expertise that is often not available in-house to transit agencies. In this thesis, an analytical model was proposed for estimating the delay impacts of green extension and early green (red truncation) TSP strategies. The proposed model is validated with analytical model reported in the literature and microscopic simulation model. This is followed by model sensitivity analysis. A software module is developed using the proposed model. The usefulness of the model is illustrated through its application to estimate the TSP performance. Finally, a prioritization is conducted on sixteen intersections with different geometric and operational traffic strategies. The overall results indicate that the proposed model is suitable for both estimating the pre-deployment and post-deployment TSP performance. The proposed model is suitable for implementation within a spreadsheet and requires considerably less effort, and less technical expertise, to apply than a typical micro-simulation model and therefore is a more suitable tool for transit agencies to use for prioritising TSP deployment

Stochastic Modeling of Intrusion-Tolerant Server Architectures for Dependability and Performance Evaluation

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryDARPA / F30602-00-C-017