Braess’ paradox: Some new insights

This paper examines some properties of the well-known Braess’ paradox of traffic flow, in the context of the classical network configuration used by Braess. The paper shows that whether Braess’ paradox does or does not occur depends on the conditions of the problem; namely, the link congestion function parameters and the demand for travel. In particular, this paper shows that for a given network with a given set of link congestion functions, Braess’ paradox occurs only if the total demand for travel falls within a certain intermediate range of values (the bounds of which are dependent on the link congestion function parameters). The paper also shows that, depending on the problem parameters, adding a new link might not lead to a reduction in total system travel time, even if users are charged the marginal cost of traveling. On the other hand, there are ranges of values for the problem parameters for which the new link reduces total system travel time, as long as marginal cost pricing is implemented.