Recent measurements of network tra c have s h o wn that self-similarity is an ubiquitous phenomenon present i n b o t h local area and wide area tra c traces. In previous work, 1 we h a ve s h o wn a simple, robust application layer causal mechanism of tra c self-similarity, namely, the transfer of les in a network system where the le size distributions are heavy-tailed. In this paper, we study the e ect of scale-invariant burstiness on network performance when the functionality of the transport layer and the interaction of tra c sources sharing bounded network resources is incorporated.First, we s h o w that transport layer mechanisms are important factors in translating the application layer causality into link tra c self-similarity. Network performance as captured by throughput, packet loss rate, and packet retransmission rate degrades gradually with increased heavy-tailedness while queueing delay, response time, and fairness deteriorate more drastically. The degree to which h e a vy-tailedness a ects self-similarity is determined by h o w well congestion control is able to shape a source tra c into an on-average constant output stream while conserving information.Second, we s h o w that increasing network resources such as link bandwidth and bu er capacity results in a superlinear improvement in performance. When large le transfers occur with nonnegligible probability, the incremental improvement in throughput achieved for large bu er sizes is accompanied by long queueing delays vis-a-vis the case when the le size distribution is not heavy-tailed. Bu er utilization continues to remain at a high level implying that further improvement in throughput is only achieved at the expense of a disproportionate increase in queueing delay. A similar trade-o relationship exists between queueing delay and packet loss rate, the curvature of the performance curve being highly sensitive to the degree of self-similarity.Third, we i n vestigate the e ect of congestion control on network performance when subject to highly self-similar tra c conditions. We implement an open-loop congestion control using unreliable transport on top of UDP where the data stream is throttled at the source to achieve a xed arrival rate. Decreasing the arrival rate results in a decline in packet loss rate whereas link utilization increases. In the context of reliable communication, we compare the performance of three versions of TCP|Reno, Tahoe, and Vegas|and we nd that sophistication of control leads to improved performance that is preserved even under highly self-similar tra c conditions. The performance gain from Tahoe to Reno is relatively minor while the performance jump from TCP Reno to Vegas is more pronounced consistent with quantitative results reported elsewhere.

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This paper proposes a dynamic vehicle routing problem (DVRP) model with nonstationary stochastic travel times under traffic congestion. Depending on the traffic conditions, the travel time between two nodes, particularly in a city, may not be proportional to distance and changes both dynamically and stochastically over time. Considering this environment, we propose a Markov decision process model to solve this problem and adopt a rollout-based approach to the solution, using approximate dynamic programming to avoid the curse of dimensionality. We also investigate how to estimate the probability distribution of travel times of arcs which, reflecting reality, are considered to consist of multiple road segments. Experiments are conducted using a real-world problem faced by Singapore logistics/delivery company and authentic road traffic information.Index Terms-Dynamic vehicle routing problem, approximate dynamic programming, uncertain travel times, rollout algorithm.