Klimov's Model

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.

Keywords: multiclass queues with feedback; dynamic scheduling; index policies; queueing networks; achievable performance