Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows

We consider a fluid queue fed by multiple On-Off flows with heavy-tailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a ``dominant'' subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation. The dominant set consists of a ``minimally critical'' set of On-Off flows with regularly varying On periods. In case the dominant set contains just a single On-Off flow, the exact asymptotics for the reduced system follow from known results. For the case of several On-Off flows, we exploit a powerful intuitive argument to obtain the exact asymptotics. Combined with the reduced-load equivalence, the results for the reduced system provide a characterization of the tail of the workload distribution for a wide range of traffic scenarios

Statistical multiplexing and connection admission control in ATM networks

Asynchronous Transfer Mode (ATM) technology is widely employed for the transport of network traffic, and has the potential to be the base technology for the next generation of global communications. Connection Admission Control (CAC) is the effective traffic control mechanism which is necessary in ATM networks in order to avoid possible congestion at each network node and to achieve the Quality-of-Service (QoS) requested by each connection. CAC determines whether or not the network should accept a new connection. A new connection will only be accepted if the network has sufficient resources to meet its QoS requirements without affecting the QoS commitments already made by the network for existing connections. The design of a high-performance CAC is based on an in-depth understanding of the statistical characteristics of the traffic sources

Some aspects of traffic control and performance evaluation of ATM networks

The emerging high-speed Asynchronous Transfer Mode (ATM) networks are expected to integrate through statistical multiplexing large numbers of traffic sources having a broad range of statistical characteristics and different Quality of Service (QOS) requirements. To achieve high utilisation of network resources while maintaining the QOS, efficient traffic management strategies have to be developed. This thesis considers the problem of traffic control for ATM networks. The thesis studies the application of neural networks to various ATM traffic control issues such as feedback congestion control, traffic characterization, bandwidth estimation, and Call Admission Control (CAC). A novel adaptive congestion control approach based on a neural network that uses reinforcement learning is developed. It is shown that the neural controller is very effective in providing general QOS control. A Finite Impulse Response (FIR) neural network is proposed to adaptively predict the traffic arrival process by learning the relationship between the past and future traffic variations. On the basis of this prediction, a feedback flow control scheme at input access nodes of the network is presented. Simulation results demonstrate significant performance improvement over conventional control mechanisms. In addition, an accurate yet computationally efficient approach to effective bandwidth estimation for multiplexed connections is investigated. In this method, a feed forward neural network is employed to model the nonlinear relationship between the effective bandwidth and the traffic situations and a QOS measure. Applications of this approach to admission control, bandwidth allocation and dynamic routing are also discussed. A detailed investigation has indicated that CAC schemes based on effective bandwidth approximation can be very conservative and prevent optimal use of network resources. A modified effective bandwidth CAC approach is therefore proposed to overcome the drawback of conventional methods. Considering statistical multiplexing between traffic sources, we directly calculate the effective bandwidth of the aggregate traffic which is modelled by a two-state Markov modulated Poisson process via matching four important statistics. We use the theory of large deviations to provide a unified description of effective bandwidths for various traffic sources and the associated ATM multiplexer queueing performance approximations, illustrating their strengths and limitations. In addition, a more accurate estimation method for ATM QOS parameters based on the Bahadur-Rao theorem is proposed, which is a refinement of the original effective bandwidth approximation and can lead to higher link utilisation

Queueing Systems with Heavy Tails

VI+227hlm.;24c

Analysis of generic discrete-time buffer models with irregular packet arrival patterns

De kwaliteit van de multimediadiensten die worden aangeboden over de huidige breedband-communicatienetwerken, wordt in hoge mate bepaald door de performantie van de buffers die zich in de diverse netwerkele-menten (zoals schakelknooppunten, routers, modems, toegangsmultiplexers, netwerkinter- faces, ...) bevinden. In dit proefschrift bestuderen we de performantie van een dergelijke buffer met behulp van een geschikt stochastisch discrete-tijd wachtlijnmodel, waarbij we het geval van meerdere uitgangskanalen en (niet noodzakelijk identieke) pakketbronnen beschouwen, en de pakkettransmissietijden in eerste instantie één slot bedragen. De grillige, of gecorreleerde, aard van een pakketstroom die door een bron wordt gegenereerd, wordt gekarakteriseerd aan de hand van een algemeen D-BMAP (discrete-batch Markovian arrival process), wat een generiek kader creëert voor het beschrijven van een superpositie van dergelijke informatiestromen. In een later stadium breiden we onze studie uit tot het geval van transmissietijden met een algemene verdeling, waarbij we ons beperken tot een buffer met één enkel uitgangskanaal. De analyse van deze wachtlijnmodellen gebeurt hoofdzakelijk aan de hand van een particuliere wiskundig-analytische aanpak waarbij uitvoerig gebruik gemaakt wordt van probabiliteitsgenererende functies, die er toe leidt dat de diverse performantiematen (min of meer expliciet) kunnen worden uitgedrukt als functie van de systeemparameters. Dit resul-teert op zijn beurt in efficiënte en accurate berekeningsalgoritmen voor deze grootheden, die op relatief eenvoudige wijze geïmplementeerd kunnen worden

Large deviations analysis of scheduling policies for a web server

With increasing demand and availability of bandwidth resources, there has been tremendous growth in the scale and speed of web servers. In web servers, scheduling plays an important role in resource allocation (for instance, bandwidth allocation, processor allocation, etc). However, as the scale of a system increases so does the number of activities/events in the system (e.g., job arrivals), as a consequence of which the analysis of scheduling becomes increasingly harder. In particular, the possible ways in which scheduling failure (e.g., queue overflow, excessively large delay, instability of a system) can occur becomes increasingly greater, thus making it more difficult to understand the behavior and develop design rules for scheduling algorithms. However, a well-known observation from large devi viations theory that large scale systems fails in a “most likely way” can potentially be used to simplify the design and analysis of scheduling. In this thesis, we study the implications and applications of this effect on scheduling in a web server accessed by a large number of sources. We analyze the delay distribution of scheduling policies for web servers under a many sources large deviation regime which models web servers in a large scale system well. Due to the difficulties brought on considering a large number of sources, only a small number of scheduling policies, such as First-Come-First-Serve (FCFS), General-ProcessorSharing (GPS), and Priority Queueing policies have been analyzed under the many sources regime. In particular, in a single queue single server setup the delay characteristics of only FCFS, Shortest-Job-First (SJF), and Longest-Job-First (LJF) has been analyzed. In this thesis, we study the Two-Dimensional-Queueing (2DQ) framework, a unifying queueing framework that allows the identification of the “most likely way” in which delay occurs, to analyze the delay of various unexplored scheduling policies. In conjunction with the 2DQ framework, we develop a new “cycle based” technique for understanding the large deviations tail probability of more complex policies. Using the combination of the 2DQ framework and the cycle based analysis, we first analyze two interesting scheduling policies, i.e., Shortest-Remaining-Processing-Time (SRPT) policy (which is mean delay optimal) and Processer-Sharing (PS) policy (which is a “fair” policy). We derive the asymptotic delay distributions (rate functions) of both policies and study their behavior across job sizes. Next, we address three problems in implementing the aforementioned scheduling policies: (i) end receivers may have bandwidth constraints that are not taken account in SRPT, (ii) the remaining processing time information might not be available to the web-server, and (iii) most actual implementations are variants of SRPT to reflect other implementation constraints and/or to jointly optimize other metrics in addition to delay, i.e., jitter, fairness, etc. To address these, we first develop finite-SRPT that takes into account the bandwidth constraint at the end receiver, and show that the policy shifts between SRPT and a PS-like policy depending on the bandwidth constraint. Second, we study the Least-Attained-Service (LAS) policy which is viewed as a good substitute for SRPT when the remaining job size is not available and we analyze the penalty associated with not using the remaining size information directly. Lastly, we analyze a class of scheduling policies known as SMART that contains many variants of SRPT with different fairness properties and show that all policies in the class have the same tail probability of delay across job sizes for a many sources regime. The results of this thesis facilitate the understanding of various scheduling policies under the many sources regime and provides an analytical queueing framework that can be used to understand other scheduling policies.Electrical and Computer Engineerin