Sequential Hypothesis Testing With Spatially Correlated Presence-Absence Data and the Corridor Problem
Firstly, we develop a sampling methodology for making pest treatment decisions based on mean pest density. Previous research assumes pest densities are uniformly distributed over space, and advocates using sequential, presence-absence sampling plans for making treatment decisions. Here we develop a spatial sampling plan which accommodates pest densities which vary over space and which exhibit spatial correlation, and we demonstrate the effectiveness of our proposed methodology using parameter values calibrated from empirical data on Oligonychus perseae, a mite pest of avocados. To our
knowledge, this research is the first to combine sequential hypothesis testing techniques with presence-absence sampling strategies which account for spatially correlated pest densities.
Secondly, we investigate "The Corridor Problem", a model of morning traffic flow along a corridor to a central business district (CBD). We consider travel time cost and schedule delay (time early) cost, and we assume that a fixed number of identical commuters have the same desired work start-time at the CBD and that late arrivals are prohibited. Traffic flow along the corridor is subject to LWR flow congestion with Greenshields' Relation (i.e., mass conservation for a fluid coupled with a negative linear relationship between velocity and density), and we seek to characterize the no-toll equilibrium or user optimum (UO) solution, in which no commuter can reduce their trip cost, and the social optimum (SO) solution, in which the total population trip cost is minimized.
Allowing for a continuum of entry-points into the corridor we develop a numerical algorithm for constructing a UO solution. Restricting to a single entry-point we provide complete characterizations of the SO and UO, with numerical examples and quasi-analytic solutions. Finally, we develop a stochastic model of incident occurrence on a corridor, calibrated using a recently developed change-point detection algorithm
applied to traffic data along a San Diego freeway over the course of a year, coupled with Hierarchical Generalized Linear Model (HGLM) fitting techniques. We use the calibrated incident model in a simulation study to determine the effect of stochastic incidents on the equilibrium solutions to the single-entry point Corridor Problem.