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Traffic, Choice, and Queue Theory

While most routes do not have travel times posted, there are certain routes that do, including the George Washington bridge into NYC from New Jersey, or the wait time of the line for an amusement park ride or museum. How do this new information impact the network/system? Three professors at Cornell, Jamol Pender, Richard H. Rand, and Elizabeth Wesson, studied how delay or queue length information can impact people’s decision whether or not to join the queue. They found that when accurate and up-to-date information is provided, the system balances out as most people choose the route with the shortest time. However, when there is a lag or the system does not update quickly enough, the routes oscillate back and forth between congested areas and open ones. For example, even if a route becomes crowded and the travel time increases, but the time is not updated, more people will continue choosing this route and amplify the problem.

In class, we assumed that the dominant strategy would be to choose the route with the shortest travel time. However, in a more realistic situation where the true travel time may be unknown, our dominant strategy is not as clear. For example, if we also know that times are not updated in real time for a certain system, it may be a dominant strategy to choose a route with a longer reported travel/wait time. Thus, the network becomes more complicated as we have to account for other factors as well. In addition, the effect of an inaccurate time could confound with any potential effects from Braess’ Paradox. If we are told that a route is supposedly faster, but it is not, then this could have resulted from either or both.

We don’t even necessarily have to think of traffic as people traveling along routes, we can apply what we’ve learned in class about Nash Equilibriums in traffic networks with the ideas from this paper as well as queueing theory to other situations. One possible situation would be waiting times for calls such as waiting for customer service. Not only are you in a queue waiting for a representative, but it could also be a matching market where you were first matched to someone in the correct department. Instead of creating a constricted set, you would simply get put into a queue. Other applications include estimating the wait times for hospital ERs, which could have a serious impact on the time until treatment.



Mathematical models predict how we wait in line, traffic

Pender, J., Rand, R.H., & Wesson, E. (2017). Queues with Choice via Delay Differential Equations. I. J. Bifurcation and Chaos, 27, 1-20.


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October 2018