ITS Berkeley

This paper proves that a class of first order partial differential equations, which include scalar conservation laws with concave (or convex) equations of state as special cases, can be formulated as calculus of variations problems. Every well-posed problem of this type, no matter how complicated, even in multi-dimensions, is reduced to the determination of a tree of shortest paths in a relevant region of space-time where "cost" is predefined. Thus, problems of this type can be practically solved with fast network algorithms. The new formulation automatically identifies the unique, single-...

This paper studies the possible integration of long-haul operations by transportation mode and service level (defined by guaranteed delivery time) for package delivery carriers. Specifically, we consider the allocation of deferred items to excess capacity on alternative modes in ways that allow all transportation modes to be utilized better. Model formulation and solution techniques are discussed. The solution techniques presented produce solutions for large-scale problem instances with up to 141 consolidation terminals and 17 breakbulk terminals. Allowing deferred items to travel by air...

Observations of freeway traffic flow are usually quite scattered about an underlying curve when plotted versus density or occupancy. Although increasing the sampling intervals can reduce the scatter, whenever an experiment encompasses a rush hour with transitions in and out of congestion, some outlying data stubbornly remain beneath the “equilibrium” curve. The existence of these nonequilibrium points is a poorly understood phenomenon that appears to contradict the simple kinematic wave (KW) model of traffic flow. This paper provides a tentative explanation of the phenomenon, based on...

This paper presents improved solution methods for kinematic wave trafficc problems with concave flow-density relations. As explained in part I of this work, the solution of a kinematic wave problem is a set of continuum least-cost paths in space-time. The least cost to reach a point is the vehicle number. The idea here consists in overlaying a dense but discrete network with appropriate costs in the solution region and then using a shortest-path algorithm to estimate vehicle numbers. With properly designed networks, this procedure is more accurate than existing methods and can be applied...