A MINI-MAX APPROACH FOR FINDING THRESHOLDS TO CONTROL M/M/2 QUEUES

Within the framework of this paper, we consider an M/M/2 queuing model where a threshold –on the queue size- type control is assumed for using (or not using) the slower server. The optimization policy to control is based upon a mini-max criterion, which minimizes the maximum “first passage time to an idle period” for the servers. We derived the formulas to calculate the exact value of the optimal threshold, and we analyzed some extreme cases for the explicit expressions to connect the optimal threshold values to the queuing parameters.