Bounded-Velocity Stochastic Control for Dynamic Resource Allocation

We consider a general class of dynamic resource allocation problems within a stochastic optimal control framework. This class of problems arises in a wide variety of applications, each of which intrinsically involves resources of different types and demand with uncertainty and/or variability. The goal involves dynamically allocating capacity for every resource type in order to serve the uncertain/variable demand, modeled as Brownian motion, and maximize the discounted expected net-benefit over an infinite time horizon based on the rewards and costs associated with the different resource types, subject to flexibility constraints on the rate of change of each type of resource capacity. We derive the optimal control policy within a bounded-velocity stochastic control setting, which includes efficient and easily implementable algorithms for governing the dynamic adjustments to resource allocation capacities over time. Computational experiments investigate various issues of both theoretical and practical interest, quantifying the benefits of our approach over recent alternative optimization approaches

Admission Control for Double-ended Queues

We consider a controlled double-ended queue consisting of two classes of customers, labeled sellers and buyers. The sellers and buyers arrive in a trading market according to two independent renewal processes. Whenever there is a seller and buyer pair, they are matched and leave the system instantaneously. The matching follows first-come-first-match service discipline. Those customers who cannot be matched immediately need to wait in the designated queue, and they are assumed to be impatient with generally distributed patience times. The control problem is concerned with the tradeoff between blocking and abandonment, and its objective is to choose optimal queue-capacities (buffer lengths) for sellers and buyers to minimize an infinite horizon discounted linear cost functional which consists of holding costs, and penalty costs for blocking and abandonment. When the arrival intensities of both customer classes tend to infinity in concert, we use a heavy traffic approximation to formulate an approximate diffusion control problem (DCP), and derive an optimal threshold policy for the DCP. Finally, we employ the DCP solution to establish an easy-to-implement, simple asymptotically optimal threshold policy for the original queueing control problem