Markov Models of Signpost Sensor AVL Systems

Certain cities are installing signpost sensor AVL (automatic vehicle location) systems. Such systems provide a fixed signpost sensor at a fraction ρ of intersections; when a vehicle drives through one of these intersections, its position is detected (usually by electronic means) and updated on a master file of estimated vehicle locations. In applications one is interested in system performance as a function of ρ, sensor layout, and vehicle turning behavior. Thin paper develops Markov models for computing (as a function of these characteristics) the probabilistic behavior of the distance traveled between successive passings of sensors. The measure of performance used to compare alternative systems is the coefficient of variation of distance traveled between passings. It is shown that intuitively appealing rectangular sensor layouts are often dominated by other layouts, including (in some cases) totally random positioning of sensors.