| Motivated by flow allocation in communication and transportation networks we examine user equilibrium and system optimal flows on networks of parallel links. User equilibrium is achieved when the journey times on all the used routes are equal and less than any other unused route. On the other hand the system optimal flow minimizes the average journey times for all used routes. In this paper we study the connection between user equilibrium and system optimums and investigate networks that have identical user equilibrium and system optimal flows. We identify a correspondence between the system optimum of a network and the user equilibrium of the associated Pigovian network and use it to show uniqueness of the system optimum. Using a characterization of Wardrop optimal flows for differentiable convex networks, we show that they are preserved via continuous, strictly increasing and convex functions, uniform increase or decrease of the latency functions and network addition and multiplication. |
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