Optimal Design of Bus Stop Locations Integrating Continuum Approximation and Discrete Models

Optimization of bus stop locations for improving transit accessibility

Quantifying the joint impacts of stop locations, signalized intersections, and traffic conditions on bus travel time

Quantifying factors that affect bus travel time along arterials is necessary to prioritize investments to reduce bus travel time and its variability and to design advanced prediction and traveler information systems. The joint effects of bus stop location (near vs. far side), intersection delay and traffic conditions on travel time have not been addressed in the literature. To fill this researc...

Discrete approximations to continuum optimal flow problems

Problems in partial differential equations with inequality constraints can be used to describe a continuum analog to various optimal flow/cut problems. While general concepts from convex optimization (like duality) carry over into continuum problems, the application of ideas and algorithms from linear programming and network flow problems is challenging. The capacity constraints are non-linear ...

Incremental bus service design: combining limited-stop and local bus services

Long in-vehicle travel times resulting from frequent stops make bus service an unattractive choice for many commuters. Limited-stop bus services however have the advantage of shorter in-vehicle times experienced by passengers. In this work, we seek to modify a given bus service by optimally reassigning some number of bus trips, as opposed to providing additional trips, to operate a limited-stop...

Discrete Approximation of Non-compact Operators Describing Continuum-of-alleles Models

We consider the eigenvalue equation for the largest eigenvalue of certain kinds of non-compact linear operators given as the sum of a multiplication and a kernel operator. It is shown that, under moderate conditions, such operators can be approximated arbitrarily well by operators of finite rank, which constitutes a discretization procedure. For this purpose, two standard methods of approximati...