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 made for free-flow versus peak traffic to reflect a steep, non-linear incline between the number of peak hour vehicles and road congestion. Schulz finds that his two initial questions are theoretically linked-- knowing the first optimization helps reach the second one, namely the outcome from closing roads. He notes that the equations can enumerate savings from closing roads that handle different levels of traffic volumes. But he adds, these equations cannot tell the researcher “which roads to close ”.
While solving for full optimization, Schulz also proposes there can be a different path, namely to provide a constraint system optimization. Here, individual drivers are assigned to paths that are in his words “ not too long”. Instead, there is a ‘fairness’ applied to the path allocation, so that most drivers are generated a travel route within normal driving ranges or boundaries. Using this constraint systems approach, the optimizations reveal that 75% of the road users would experience less travel time in lieu of their individual route choice.
The take-away, says Schulz, is that we can actually route traffic much better than we currently do and adding additional roadways to a system will not necessarily make it better or alleviate traffic. The simulations made for Boston’s Big Dig bear this out, and he proposes that there are many other practical applications, particularly using the constraint systems. Current navigation systems, programmed at a system wide level, show great promise for shortening our travel time, if not occasionally lengthening our travel path....Read the full article/Watch Video
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 made for free-flow versus peak traffic to reflect a steep, non-linear incline between the number of peak hour vehicles and road congestion. Schulz finds that his two initial questions are theoretically linked-- knowing the first optimization helps reach the second one, namely the outcome from closing roads. He notes that the equations can enumerate savings from closing roads that handle different levels of traffic volumes. But he adds, these equations cannot tell the researcher “which roads to close ”.
While solving for full optimization, Schulz also proposes there can be a different path, namely to provide a constraint system optimization. Here, individual drivers are assigned to paths that are in his words “ not too long”. Instead, there is a ‘fairness’ applied to the path allocation, so that most drivers are generated a travel route within normal driving ranges or boundaries. Using this constraint systems approach, the optimizations reveal that 75% of the road users would experience less travel time in lieu of their individual route choice.
The take-away, says Schulz, is that we can actually route traffic much better than we currently do and adding additional roadways to a system will not necessarily make it better or alleviate traffic. The simulations made for Boston’s Big Dig bear this out, and he proposes that there are many other practical applications, particularly using the constraint systems. Current navigation systems, programmed at a system wide level, show great promise for shortening our travel time, if not occasionally lengthening our travel path....Read the full article/Watch Video
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