Klimov'sModel

Abstract

The Klimov model concerns the optimal dynamic scheduling of a multiclass M/G/1 queue with general Bernoulli feedback of jobs and linear holding costs. In his seminal 1974 paper, Klimov established the optimality of a static priority‐index rule for such a model under the average cost criterion and gave an adaptive‐greedy index algorithm, via a novel linear programming approach. The model has rich and insightful connections with stochastic scheduling and bandit problems, and has found use in a wide variety of applications, most notably in time‐sharing computer‐communication and flexible manufacturing systems.

A Fast-Pivoting Algorithm for Whittle’s Restless Bandit Index

“…This has its early roots in Klimov's algorithm in [36] for calculating the optimal priority indices for scheduling a multiclass queue with Bernoulli feedback, which was extended in [37] to a framework of stochastic scheduling systems satisfying so-called generalized conservation laws, such as the classic (non-restless) multi-armed bandit problem and branching bandits. See also [38,39]. Yet, the aforementioned work has not addressed the efficient computational implementation of such an algorithm, which is necessary for its actual deployment and widespread application.…”