Accommodation of Second-Class Traffic

Situations exist in which a facility performs a primary function but is available, during otherwise idle periods between primary jobs, to service secondary tasks as well. Such is the case at side-street intersections with a main highway, aspects of this particular problem have been considered by many authors, recently by Weiss and Maradudin and Oliver in this journal. In this paper the durations of the secondary tasks are taken to be random variables, independently sampled for each “second-class” task, and held fixed until an adequate gap (idle period) appears. The model thus differs from that of Weiss and Maradudin in that it reflects between-task variability. For this model we investigate the long-run rate of task completion, the time for completion of a task that is “first in line,” and the waiting time of a task that arrives to find a queue of tasks ahead of him at the facility.