On the Performance of Matching Models with Threshold-based Policies

Overview & Synopsis

Motivated by recent optimality results in matching models, we consider the W-matching model with three costumer classes and two servers classes, and a threshold-based matching policy with finite threshold value T . Under this policy, class-2 costumers are matched to any server only when the number of servers of that class waiting is larger than T . We characterize the stationary distribution when the threshold value is T = 0, 1, 2, and show that it is of product-form. To this aim, we develop a novel technique that allows us to characterize the stationary distribution of the system with threshold values T = 0, 1, 2. Using this result, we conclude that a non-zero threshold value potentially improves the performance of the system. For general threshold values, we provide approximated analysis and show that its stationary distribution has also a product-form. For this approximation, we establish the optimal threshold value when the arrival probability of all costumer classes is the same. Furthermore, using simulations, we analyze the accuracy of the considered approximation and show that our analysis with T = 0, 1, 2 generalizes to any threshold value, i.e., a non-zero threshold value potentially minimizes the weighted mean holding cost of the system.