Dynamic pricing in a two-class queueing system with arrival and service rate control

Abstract

Abstract Dynamic pricing in a two-class queueing system with adjustable arrival and service rates is considered. We initially take adjustable rates into account to maximize the long-run average social welfare and further establish matched dynamic prices. For the rate-setting problem, we apply sensitivity-based optimization theory and an iterative algorithm to investigate the optimal arrival and service rates of the two classes of customers. Next, we apply the results obtained from the rate-setting problem to find the expected delay time using a recursive algorithm and explicitly determine formulae for the optimal prices of the two classes of customers. Finally, we carry out numerical experiments to illustrate our findings and the performance between two classes of customers at different levels of the holding cost. It appears that for a low holding cost, the optimal prices for the two classes of customers are monotonically increasing in the number of customers regardless of the class, but for a high holding cost, the optimal prices for the customers who have low waiting cost may drop when the number of the other class rises.