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

Renegotiation based dynamic bandwidth allocation for selfsimilar VBR traffic

The provision of QoS to applications traffic depends heavily on how different traffic types are categorized and classified, and how the prioritization of these applications are managed. Bandwidth is the most scarce network resource. Therefore, there is a need for a method or system that distributes an available bandwidth in a network among different applications in such a way that each class or type of traffic receives their constraint QoS requirements. In this dissertation, a new renegotiation based dynamic resource allocation method for variable bit rate (VBR) traffic is presented. First, pros and cons of available off-line methods that are used to estimate selfsimilarity level (represented by Hurst parameter) of a VBR traffic trace are empirically investigated, and criteria to select measurement parameters for online resource management are developed. It is shown that wavelet analysis based methods are the strongest tools in estimation of Hurst parameter with their low computational complexities, compared to the variance-time method and R/S pox plot. Therefore, a temporal energy distribution of a traffic data arrival counting process among different frequency sub-bands is considered as a traffic descriptor, and then a robust traffic rate predictor is developed by using the Haar wavelet analysis. The empirical results show that the new on-line dynamic bandwidth allocation scheme for VBR traffic is superior to traditional dynamic bandwidth allocation methods that are based on adaptive algorithms such as Least Mean Square, Recursive Least Square, and Mean Square Error etc. in terms of high utilization and low queuing delay. Also a method is developed to minimize the number of bandwidth renegotiations to decrease signaling costs on traffic schedulers (e.g. WFQ) and networks (e.g. ATM). It is also quantified that the introduced renegotiation based bandwidth management scheme decreases heavytailedness of queue size distributions, which is an inherent impact of traffic self similarity. The new design increases the achieved utilization levels in the literature, provisions given queue size constraints and minimizes the number of renegotiations simultaneously. This renegotiation -based design is online and practically embeddable into QoS management blocks, edge routers and Digital Subscriber Lines Access Multiplexers (DSLAM) and rate adaptive DSL modems

Sample path large deviations for single and multi class queues in the many sources asymptotic

In this thesis we consider prove large deviations results for two kinds of queuing systems. In the first case, we consider a queuing system fed by traffic from N independent and identically distributed marked point processes. We establish novel one-dimensional large deviations results for such a system in the previously unexplored lightly loaded case (the load vanishes as N → ∞). This case requires the introduction of novel speed scalings for such queueing systems. We also prove some important properties about the sample paths of such systems in the scaled uniform topology. However, we are unable to prove sample path large deviations principles in this case because the log moment-generating function in this case is not steep, and we are unable to find tools in the literature that enable us to deal with such scenarios. This part of the work is done using the framework introduced by Cruise [1] and Cruise et al. [2] to explore this scaling. In the second case, we consider a two-class queuing network, with each class fed by traffic from N independent and identically distributed marked point processes. We introduce a new, probabilistic interpretation of state-space collapse, and show that under a given scaling of the system, the probability of the vector of stationary queue lengths being a given distance from the identity line in R2 decreases exponentially as the distance increases, and therefore the most likely sample paths are those which stay close to the identity line in R2.James Watt scholarshi

Queueing Systems with Heavy Tails

VI+227hlm.;24c