Algorithms for Flows over Time with Scheduling Costs

Abstract

Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering the arc; flows are time-varying. We consider a setting which is very standard within the transportation economic literature, but has received little attention from an algorithmic perspective. The flow consists of users who are able to choose their route but also their departure time, and who desire to arrive at their destination at a particular time, incurring a scheduling cost if they arrive earlier or later. The total cost of a user is then a combination of the time they spend commuting, and the scheduling cost they incur. We present a combinatorial algorithm for the natural optimization problem, that of minimizing the average total cost of all users (i.e., maximizing the social welfare). Based on this, we also show how to set tolls so that this optimal flow is induced as an equilibrium of the underlying game. * Partially supported by NWO TOP grant 614.001.510 and NWO Vidi grant 016.Vidi.189.087.

Teaching Quality of College Students’ Mental Health Based on Mathematical Programming Algorithm

“…Frascaria and Olver proposed a mathematical programming algorithm for natural optimization problems to minimize the average total cost of all users. He also demonstrated the optimal setting of tolls on an algorithmic basis [10]. Cannelli et al proposed a new asynchronous parallel block descent algorithm framework.…”

Side-Constrained Dynamic Traffic Equilibria

“…Finally, it is worth mentioning that our model and the subsequent characterization and existence results require only mild continuity properties of the walk-delay operator and the edge load functions, respectively, and thus apply for several realistic and well-studied network loading models including the Vickrey queueing model with point queues [6,7,30,37,44], with spillback [41] with departure-time choice [12,23], the Lighthill-Whitham-Richards (LWR) model [16], the LWR model with spillback [25] and the classical link-delay model of Friesz et al [13].…”

The Price of Anarchy for Instantaneous Dynamic Equilibria

“…Bhaskar, Fleischer and Anshelevich [1] devised Stackelberg strategies in order to improve the efficiency of dynamic equilibria. Recently, Frascaria and Olver [6] considered a flexible departure choice model from an optimization point of view and derived insights into devising tolls for improving the performance of dynamic equilibria.…”