A novel use of value iteration for deriving bounds for threshold and switching curve optimal policies

Abstract

AbstractIn this article, we develop a novel role for the initial function v0 in the value iteration algorithm. In case the optimal policy of a countable state Markovian queueing control problem has a threshold or switching curve structure, we conjecture, that one can tune the choice of v0 to generate monotonic sequences of n‐stage threshold or switching curve optimal policies. We will show this for three queueing control models, the M/M/1 queue with admission and with service control, and the two‐competing queues model with quadratic holding cost. As a consequence, we obtain increasingly tighter upper and lower bounds. After a finite number of iterations, either the optimal threshold, or the optimal switching curve values in a finite number of states is available. This procedure can be used to increase numerical efficiency.