Paging Multiple Users in Cellular Network: Yellow Page and Conference Call Problems

Abstract

Mobile users are roaming in a zone of cells in a cellular network system. The probabilities of each user residing in each cell are known, and all probabilities are independent. The task is to find any one, or all, of the users, by paging the cells in a predetermined number of rounds. In each round, any subset of the cells can be paged. When a cell is paged, the list of users in it is returned. The paging process terminates when the required user(s) are found. The objective is to minimize the expected number of paged cells. Finding any one user is known as the yellow page problem, and finding all users is known as the conference call problem. The conference call problem has been proved NP-hard, and a polynomial time approximation scheme exists. We study both problems in a unified framework. We introduce three methods for computing the paging cost. We give a hierarchical classification of users. For certain classes of users, we either provide polynomial time optimal solutions, or provide relatively efficient exponential time solutions. We design a family of twelve fast greedy heuristics that generate competitive paging strategies. We implement optimal algorithms and non-optimal heuristics. We test the performance of our greedy heuristics on many patterns of input data with different parameters. We select the best heuristics for both problems based on our simulation. We evaluate their performances on randomly generated Zipf and uniform data and on real user data.