On Optimal Arrangement of Stations in a Tandem Queueing System with Blocking

We consider tandem queueing networks with no waiting spaces and address the issue of ordering the stations so that the throughput (i.e., the departure rate) is maximized. Based on some theoretical and extensive empirical results, we propose two rules for ordering the stations. The first rule recommends arranging the two worst stations (according to our ordering) to the first and last stages. Numerical results show that this rule almost always agrees with the optimal ordering of stations. In cases where this rule does not agree with the optimal ordering, numerical results show that this rule leads to station arrangements that are near optimal. In addition, numerical results also indicate that the first rule is the most important one to achieve a near optimal throughput. The second rule arranges the remaining stations according to the so-called "bowl phenomenon." Numerical results illustrate that an optimal arrangement of stations need not exhibit the "bowl phenomenon," but the differences in the throughput between the optimal and the one obtained by the second rule are always very small (less than 0.5%).