Optimizing Traffic in Virtual and Real Space

We show how optimization methods from economics known as portfolio strategies can be used for minimizing download times in the Internet and travel times in freeway traffic. While for Internet traffic, there is an optimal restart frequency for requesting data, freeway traffic can be optimized by a small percentage of vehicles coming from on-ramps. Interestingly, the portfolio strategies can decrease the average waiting or travel times, respectively, as well as their standard deviation (“risk”). In general, portfolio strategies are applicable to systems, in which the distribution of the quantity to be optimized is broad. Virtual Traffic in the World Wide Web Anyone who has browsed the World Wide Web has probably discovered the following strategy: whenever a web page takes too long to appear, it is useful to press the reload button. Very often, the web page then appears instantly. This motivates the implementation of a similar but automated strategy for the frequent “web crawls” that many Internet search engines depend on. In order to ensure up-to-date indexes, it is important to perform these crawls quickly. More generally, from an electronic commerce perspective, it is also very valuable to optimize the speed and the variance in the speed of transactions, automated or not, especially when the cost of performing those transactions is taken into account. Again, restart strategies may provide measurable benefits for the user. The histogram in Figure 1 shows the variance associated with the download times for the text on the main page of over 40,000 web sites. Based on such observations, an economics-based strategy has recently been proposed for quantitatively managing the time of executing electronic transactions [1]. It exploits an analogy with the modern theory of financial portfolio management by associating cost with the time it takes to complete the transaction and taking into account the “risk” given by the standard deviation of that time. Before, such a strategy has already been successfully applied to the numerical solution of hard computational problems [2]. In modern portfolio theory, risk averse investors may prefer to hold assets from which they expect a lower return if they are compensated for the lower return with a lower level of risk exposure. Furthermore, it is a non-trivial result of portfolio theory that simple diversification can yield portfolios of assets which have higher expected return as well as lower risk. In the case of latencies (waiting times) on the Internet, thinking of different restart strategies is analogous to asset 2 Dirk Helbing, Bernardo A. Huberman, and Sebastian M. Maurer