Learning the Scheduling Policy in Time-Varying Multiclass Many Server Queues with Abandonment
Abstract
We consider a learning variant of a canonical scheduling problem in a multiclass many server queue with abandonment (specifically, the M_t/M/N+M and the GI/GI/N+GI queues). The objective is to minimize the long-run average class-dependent expected linear holding and abandonment costs when the class-dependent model parameters (arrival rates, service rates, and abandonment rates) are a priori unknown. The difficulty is that even when parameters are known, characterizing an optimal scheduling policy appears intractable. Fortunately, the simple cμ/θ rule, that prioritizes classes in accordance with a static ranking that depends on the costs, the service rates, and the abandonment rates, is asymptotically optimal as the arrival rates and number of servers become large, under certain conditions. Then, our task is to learn the service and abandonment rates well enough to determine an optimal static priority ranking for the classes, and we can benchmark our performance by defining the regret relative to the cμ/θ rule.
Bio
Amy is the Rothman Family Professor of Operations Management at the University of Chicago Booth School of Business. She received her Ph.D. from Stanford University in 2001. She is the Editor-in-Chief of Operations Research Letters (since April 2021) and was the Area Editor for the Stochastic Models Area of Operations Research (2018-2021). Her main interest is in developing queueing theory methodology to support efficient service operations.
