Bill Lloyd-Smith

Household size and the poisson distribution

Household size distributions for 104 countries are examined. It is shown that a Poisson distribution truncated at zero can be used to derive models of household size distribution. An improved fit is obtained by adding a linear term to the truncated Poisson model. This distribution depends only on average household size which in turn is shown to be related to modified dependency ratios. This method can be used for comparisons of household size distributions across nations and for long-term forecasting.

Dynamic Weight Changes for Traffic Matrix Estimation

A method of link weight changes has been previously proposed to overcome the under-constrained problem in traffic matrix estimation. In this paper, a new weight change algorithm is developed using the dual formulation of the multi-commodity flow problem to enable traffic matrix estimation

A note on an analytic model for slow start in TCP

Sikdar et al. [B. Sikdar et al., 2001] has provided a formula to model the window increase pattern given the mechanics of delayed acknowledgements. In this paper, we show that their sum formula significantly underestimates the iterated sum for rounds greater than seven. The approximation error grows exponentially. We also derive a more accurate sum formula whose approximation error is linearly bounded. We show that with use of the incorrect sum formula, cases arise where it is impossible to time out as the initial loss indication in slow start, which can have significant impact on TCP latency, assuming a correlated loss model. We show that our more accurate sum formula greatly reduces the number of cases showing this behaviour, further improving upon the accuracy of the model.

Shortest paths in stochastic networks

This paper discusses the sensitivity of network flows to uncertain link state information for various routing protocols. We show that the choice of probability distribution for the link metrics for a given network can have markedly different effects on the probabilities of path selection. Exact results are obtained for these probabilities but their computation is NP-hard. We provide simulation results for three networks to illustrate the sensitivity of shortest paths to different link metric distributions. We provide results for mean path costs and the k-shortest path algorithm as a comparison.

Internet Pooling: Routing for load distribution in access networks

A variety of Internet access technologies are used in private as well as commercial environments. Local access is often limited by technological advances, and at the same time wireless meshed network equipment has become very affordable. This work proposes a concept called Internet Pooling. Neighbouring sites can be connected using meshed network technology. Internet resources are shared between sites; forming an Internet access pool rather than a single access link. Such a method could be used in urban as well as rural areas. Internet pooling requires two mechanisms; a flow-based routing strategy that routes packets, belonging to the same flow on the same interface and a mechanism that allows the sharing of available resource information. This paper gives a basic overview of the general mechanism and discusses a number of mathematical models, helping to address the question of how many local resources can be shared without any negative impact on local performance and how often such load information would need to be updated. Appropriate performance measures for such a setup are also discussed.

Link and Path Metrics for Broadband Networks: Simulation Studies using the Encourager Program

We consider the implementation of a broadband system using digital crossconnect switches or ATM where a variety of paths may be established between the source and destination nodes. A heuristic path selection approach based on encouragement factors [2] is considered for implementation. We suggest a mathematical basis for this heuristic and study its performance using a PC-based tool, the Encourager program. The design of this tool and the results obtained from it for typical networks are presented. Future work will permit the testing of a number of extension strategies..