Bounds for different arrangements of tandem queues with nonoverlapping service times

The authors bound the difference in performance measures among different orders of tandem queues when service times are nonoverlapping. Two types of nonoverlapping service times, with respect to (w.r.t.) tasks and w.r.t. customers, are defined; it is not required that service times be independent. For nonoverlapping service times w.r.t. tasks, the authors bound the sample-path difference in number of customers in system by one, and bound the corresponding time-average difference by the traffic intensity of the longest station. For nonoverlapping service times w.r.t. customers, they bound the difference in mean sojourn time when the service times are bounded random variables. While the authors are motivated by probabilistic results, the present methods and results are entirely deterministic.