Arbitrary Instants Research Articles

A Comprehensive Control Concept for Merging of Automated Vehicles Under a Broad Class of Traffic Conditions

The paper presents basic theoretical ideas and simulation results of a new and comprehensive control concept for the automatic merging of two streams (A and B) of automated surface vehicles. Extending previous work in this field this concept can cope with vehicles entering a merge-control region (.5km in length) with arbitrary differing entering velocities 0<v(tE)≤30m/s in both lanes and at arbitrary instants of time tE.

On the Bound of First Excursion Probability

Method has been developed to improve the lower bound of the first excursion probability that can apply to the problem with either constant or time-dependent barriers. The method requires knowledge of the joint density function of the random process at two arbitrary instants.

Overflow Traffic from a Trunk Group with Balking*

A stream of telephone calls is submitted to a group of trunks, the first-choice group, according to a recurrent process. We allow balking on this trunk group; i.e., if a call finds k of the first-choice trunks busy it may be served, with probability p k , or may fail to be served, with probability q k . A call which fails to receive immediate service on the first-choice trunk group is submitted to a second-choice trunk group, the overflow group. We also allow balking on the overflow group. Calls which fail to receive immediate service on the overflow group are lost to the system. Holding times have negative-exponential distribution. We give methods for finding the joint distributions of numbers of busy trunks on the first-choice and overflow groups, at overflow instants (i.e., instants at which calls are submitted to the overflow group), at arrival instants, and at arbitrary instants. We consider the transient as well as the limiting distributions (and demonstrate the existence of the limiting distributions). The methods developed are illustrated by several examples. Numerical results are given for the blocking in the particular case that the first-choice group constitutes a random slip, while the overflow group is full-access (common).