The independence of volume–capacity ratio of private toll roads in general networks

In a general traffic network under some widely used assumptions, this paper proves that the level of service, represented by the volume–capacity (v/c) ratio, offered by a profit-maximizing private firm on a private toll road is independent of another competitor’s choice of capacity and toll rate for another private toll road. The v/c ratio will be the same as the one provided by a centralized welfare-maximizing traffic authority. Moreover, the ratio remains the same even in a regulated market where the authority imposes a cap for the generalized travel cost on the private toll road.