A polynomial algorithm for minimizing travel time in consistent time‐dependent networks with waits

International audience; We consider a time-dependent shortest path problem with possible waiting at some nodes of the graph and a global bound W on the total waiting time. The goal is to minimize the time traveled along the edges of the path, not including the waiting time. We prove that the problem can be solved in polynomial time when the travel time functions are piecewise linear and continuous. The algorithm relies on a recurrence relation characterized by a bound ω on the total waiting time, where 0 ≤ ω ≤ W . We show that only a small number of values ω 1 , ω 2 , . . . , ω K need to be considered, where K depends on the total number of breakpoints of all travel time functions.