System-optimal trip scheduling and routing in commuting networks

A time-space network formulation is presented for the system-optimal assignment to departure times and routes of traffic flows from multiple origins to a common destination. Time is discretized, and congestion is represented using simplified deterministic queuing stations. The solution minimizes total travel time in the system subject to arrivals at the destination taking place within a specified time interval. Alternatively, a formulation is presented for the minimization of a total cost measure consisting of a weighted sum of the users' travel time and schedule delay. The solution can be obtained using efficient and widely available pure network optimization algorithms. A numerical application is presented to illustrate the methodology, including a network generator developed for this purpose.