Competitive on-line paging strategies for mobile users under delay constraints

A mobile user is roaming in a zone of n cells in a cellular network system. When a call for the mobile arrives, the system pages the mobile in these cells since it never reports its location unless it leaves the zone. A delay constraint paging strategy must find the mobile after at most 1 ≤ D ≤ n paging rounds each pages a subset of the n cells. The goal is to minimize the number of paged cells until the mobile is found. Optimal solutions are known for the off-line case, for which an a priori probability of a mobile residing in any one of the cells is known. In this paper we address the on-line case. An on-line paging strategy makes its decisions based only on past locations of the mobile while trying to learn its future locations. We present deterministic and randomized on-line algorithms for various values of D (number of paging rounds) as a function of n (number of cells) and evaluate them using competitive analysis. In particular, we present a constant competitive on-line algorithm for the two extreme cases of D = 2 and D = n. The former is the first nontrivial delay constraint case and the latter is the case for which there are no delay constraints. We then show that the constant competitiveness can be attained already for D ≥ log₂ n. All of the above algorithms are deterministic. Our randomized on-line algorithm achieves a near optimal performance for all values of D. This algorithm is based on solutions to the best expert problem.