Bulk service queues with deviations from departure schedules: The problem of correlated headways

The usual approach to studying bulk service queues is to assume that successive headways are independent. This assumption is frequently violated in systems where vehicles depart according to a fixed schedule, but where deviations from the schedule may occur. A late departure implies there is one long headway followed by a shorter one. This problem is solved exactly using both classical transform techniques and iterative numerical methods. Experiments with the latter approach are presented, and comparisons between the exact results and those obtained by ignoring correlations between headways are performed. The results suggest that upper and lower bounds may be developed using existing results, where the upper bound is accurate in light traffic while the lower bound is accurate in heavy traffic.