Paging and Registration in Cellular Networks: Jointly Optimal Policies and an Iterative Algorithm

This paper explores optimization of paging and registration policies in cellular networks. Motion is modeled as a discrete-time Markov process, and minimization of the discounted, infinite-horizon average cost is addressed. The structure of jointly optimal paging and registration policies is investigated through the use of dynamic programming for partially observed Markov processes. It is shown that there exist policies with a certain simple form that are jointly optimal, though the dynamic programming approach does not directly provide an efficient method to find the policies. An iterative algorithm for policies with the simple form is proposed and investigated. The algorithm alternates between paging policy optimization and registration policy optimization. It finds a pair of individually optimal policies, but an example is given showing that the policies need not be jointly optimal. Majorization theory and Rieszs rearrangement inequality are used to show that jointly optimal paging and registration policies are given for symmetric or Gaussian random walk models by the nearest-location-first paging policy and distance threshold registration policies.