On the performance of matching models with threshold-based policies

Abstract

Abstract Motivated by recent optimality results in matching models, we consider the symmetric W -matching model with three demand classes and two supply classes, and a threshold-based matching policy with finite threshold value T . Under this policy, class-2 demand items are matched to any supply item only when the number of supply items of that class waiting is larger than T . We characterize the stationary distribution of the system for threshold values $$T=0,1,2$$ T = 0 , 1 , 2 , and show that it admits a product-form solution. To this end, we develop a novel technique for deriving the stationary distribution for these threshold values. Moreover, our analysis shows that using a nonzero threshold can improve system performance. For general threshold values, we develop an approximate analysis and show that the resulting stationary distribution also has a product-form. Using this approximation, we determine the optimal threshold when all demand classes have identical arrival probabilities. Finally, through simulation experiments, we evaluate the accuracy of the approximation and provide evidence that the insights obtained for $$T=0,1,2$$ T = 0 , 1 , 2 extend to arbitrary threshold values; in particular, a nonzero threshold may minimize the weighted mean holding cost of the system.