We analyze a cell with a fixed number of users in a time period network. The base station schedules to serve at most one user in a given time period based on information about the available data rates and other parameter(s) for all the users in the cell. We consider infinitely backlogged queues and model the system as a Markov Decision Process (MDP) and prove the monotonicity of the optimal policy with respect to the \"starvation age\" and the available data rate. For this, we consider both the discounted as well as the long-run average criterion. The proofs of the monotonicity properties serve as good illustrations of analyzing MDPs with respect to their optimal solutions.
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L. Georgiadis, M. J. Neely and L. Tassiulas, “Resource Allocation and Cross-Layer Control in Wireless Networks,” Foundations and Trends in Networking, Vol. 1, No. 1, 2006, pp. 1-144. doi:10.1561/1300000001