Selfish routing in the presence of side constraints

The natural approach for describing network flow problems is to introduce side constraints that capture restrictions of a logical or technological nature, e.g., capacity or budgetary constraints. We study the traffic equilibria arising from selfish routing of individual users in networks with side constraints. For the problem without side constraints the classic Wardrop principle suggests that in equilibrium for each origin-destination pair the latency on all the used routes is equal or less to the latency on all unused routes. In this paper we use a natural extension of the Wardrop principle [13] in order to obtain results on selfish routing with side constraints. The extended Wardrop principle suggests that in equilibrium flow is routed along paths of minimal latency according to a modified function that essentially incorporates penalty terms for the side constraints. This approach provides a basis for the systematic application of relevant optimization theory to selfish routing problems.