Optimal Admission Control for Multiclass Queues with TimeVarying Arrival Rates via State Abstraction
Abstract
We consider a novel queuing problem where the decisionmaker must choose to accept or reject randomly arriving tasks into a no buffer queue which are processed by $N$ identical servers. Each task has a price, which is a positive real number, and a class. Each class of task has a different price distribution and service rate, and arrives according to an inhomogenous Poisson process. The objective is to decide which tasks to accept so that the total price of tasks processed is maximised over a finite horizon. We formulate the problem as a discrete time Markov Decision Process (MDP) with a hybrid state space. We show that the optimal value function has a specific structure, which enables us to solve the hybrid MDP exactly. Moreover, we prove that as the time step is reduced, the discrete time solution approaches the optimal solution to the original continuous time problem. To improve the scalability of our approach to a greater number of task classes, we present an approximation based on state abstraction. We validate our approach on synthetic data, as well as a real financial fraud data set, which is the motivating application for this work.
 Publication:

arXiv eprints
 Pub Date:
 March 2022
 DOI:
 10.48550/arXiv.2203.08019
 arXiv:
 arXiv:2203.08019
 Bibcode:
 2022arXiv220308019R
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Artificial Intelligence;
 Mathematics  Optimization and Control
 EPrint:
 7+1 pages main text, 16 pages supplementary material, accepted to AAAI 2022