Traffic Paradoxes and Route Guidance: Effective Ways of Reducing Congestion Effects?

It is well know that we cannot engineer our way out of traffic congestion by building new roads. In fact, expanding the road network may paradoxically attract new traffic, and increase gridlock. Andreas Schulz provides a mathematical explanation for this conundrum. Using Nash equilibria and related game-theoretic concepts he explores two issues, namely: “how much fuel and time can we save if we route traffic optimally, and secondly, can we save fuel and time by actually closing streets or rearranging vehicle flow on our existing road network?” The answers to these questions have significant value. It is calculated by the Texas Transportation Institute (TTI) the cost of congestion, in fuel and time losses, is $87 billion annually (in 2007 dollars). Schulz uses the TTI estimate as a launching point, to ask how much we could save if we routed more optimally. The optimization is based on a complex set of algorithms with Wardrop’s Principle as a theoretical background, and total travel time as the variable. Wardrops principle says that the journey times on all the routes actually used are equal and less than those that would be experienced by a single vehicle on an unused route. From this user optimum/equilibrium, Schulz branches to a key concept called the “price of anarchy”. Applied to traffic, it is a ratio of the journey time of the individual transport user (represented in the numerator) to the value of a system optimization (in the denominator). The so-called “price of anarchy’ relationship, numerically expresses what is lost in terms of travel efficiency when each driver acts on their selfish interests (autonomously) instead of using the optimized network. Schulz uses scenarios about traffic delay and travel times and the mathematical proof shows that the price of anarchy can be measured and valued. A simple graphic establishes the relationship between the travel time function for individual actors vis-à-vis those of the collective. An adjustment is ...

Channel: MIT World Video Length: 0s Date Found: Sat, Oct 23 2010 8:02 PM Category: Science Date Produced: Mon, Sep 13 2010 12:00 AM View Count: 0