Highway Merging Problem with Acceleration Area.

We study the highway merging problem with acceleration area. We suppose there is an acceleration area beside a highway and that a vehicle which arrives at an entrance from a rampway wails for a chance to merge as it accelerates on the acceleration area. The velocity of the merging vehicle at time t is a known function v(t), where the time origin is the moment when the merging vehicle arrives at the entrance. We derive the probability density function of the delay to the merging vehicle, i.e., the time between its arrival at the entrance and the moment it merges into the highway. We also discuss a properly of the probability density function of the delay. [ABSTRACT FROM AUTHOR]