Jointly optimal paging and registration for a symmetric random walk

Jointly optimal paging and registration policies are identified for a cellular network composed of a linear array of cells. Motion is modeled as a random walk with a symmetric, unimodal step size distribution. Minimization of the discounted, infinite-horizon average cost is addressed. The jointly optimal pair of paging and registration policies is found. The optimal registration policy is a distance threshold type: the mobile station. registers whenever its distance from the previous reporting point exceeds a-threshold. The paging policy is ping-pong type: cells are searched in an order of increasing distance from the cell in which the previous report occurred.