A critical look at power law modelling of the Internet

This paper takes a critical look at the usefulness of power law models of the Internet. The twin focuses of the paper are Internet traffic and topology generation. The aim of the paper is twofold. Firstly it summarises the state of the art in power law modelling particularly giving attention to existing open research questions. Secondly it provides insight into the failings of such models and where progress needs to be made for power law research to feed through to actual improvements in network performance.Comment: To appear Computer Communication

Temporal Correlations of Local Network Losses

We introduce a continuum model describing data losses in a single node of a packet-switched network (like the Internet) which preserves the discrete nature of the data loss process. {\em By construction}, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that such a model exhibits strong fluctuations in the loss rate at the critical point and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process. The continuum model allows for rather general incoming data packet distributions and can be naturally generalized to consider the buffer server idleness statistics

Fast simulation of overflow probabilities in a queue with Gaussian input

In this paper, we study a queue fed by a large number $n$ of independent discrete-time Gaussian processes with stationary increments. We consider the {it many sources} asymptotic regime, i.e., the buffer exceedance threshold $B$ and the service capacity $C$ are scaled by the number of sources ($Bequiv nb$ and $Cequiv nc$). We discuss three methods for simulating the steady-state probability that the buffer threshold is exceeded: the single twist method (suggested by large deviation theory), the cut-and-twist method (simulating timeslot by timeslot), and the sequential twist method (simulating source by source). The asymptotic efficiency of these three methods is investigated as $n oinfty$: for instance, a necessary and sufficient condition is derived for the efficiency of the method based on a single exponential twist. It turns out that this method is asymptotically inefficient in practice, but the other two methods are asymptotically efficient. We evaluate the three methods by performing a simulation study

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

Self-Similarity in a multi-stage queueing ATM switch fabric

Recent studies of digital network traffic have shown that arrival processes in such an environment are more accurately modeled as a statistically self-similar process, rather than as a Poisson-based one. We present a simulation of a combination sharedoutput queueing ATM switch fabric, sourced by two models of self-similar input. The effect of self-similarity on the average queue length and cell loss probability for this multi-stage queue is examined for varying load, buffer size, and internal speedup. The results using two self-similar input models, Pareto-distributed interarrival times and a Poisson-Zeta ON-OFF model, are compared with each other and with results using Poisson interarrival times and an ON-OFF bursty traffic source with Ge ometrically distributed burst lengths. The results show that at a high utilization and at a high degree of self-similarity, switch performance improves slowly with increasing buffer size and speedup, as compared to the improvement using Poisson-based traffic

Queuing delays in randomized load balanced networks

Valiant’s concept of Randomized Load Balancing (RLB), also promoted under the name ‘two-phase routing’, has previously been shown to provide a cost-effective way of implementing overlay networks that are robust to dynamically changing demand patterns. RLB is accomplished in two steps; in the first step, traffic is randomly distributed across the network, and in the second step traffic is routed to the final destination. One of the benefits of RLB is that packets experience only a single stage of routing, thus reducing queueing delays associated with multi-hop architectures. In this paper, we study the queuing performance of RLB, both through analytical methods and packet-level simulations using ns2 on three representative carrier networks. We show that purely random traffic splitting in the randomization step of RLB leads to higher queuing delays than pseudo-random splitting using, e.g., a round-robin schedule. Furthermore, we show that, for pseudo-random scheduling, queuing delays depend significantly on the degree of uniformity of the offered demand patterns, with uniform demand matrices representing a provably worst-case scenario. These results are independent of whether RLB employs priority mechanisms between traffic from step one over step two. A comparison with multi-hop shortest-path routing reveals that RLB eliminates the occurrence of demand-specific hot spots in the network