Optimal aggregation factor and clustering under delay constraints in aggregate sequential group paging schemes

This paper considers several optimization problems of sequential paging with aggregation mechanism which has been shown to reduce significantly the paging cost of a wireless communication system. An important problem is to find the optimal aggregation factor subject to a constraint on the average paging delay. Another problem is, given a cost function that depends on both paging cost and paging delay, how to find the optimal aggregation factor to minimize that cost function. We have formulated and shown that these can be solved nicely due to the monotonicity and convexity of the average paging cost function and paging delay function. We demonstrate that the optimization problems of the aggregate factor and subnet clustering are not separable. This leads to joint optimization problems of aggregation factor and clustering that are investigated in this paper. The paper presents different algorithms to solve these joint optimization problems using the monotonicity in the aggregation factor and the number of clusters of the average paging cost and delay with the unconstrained optimal clustering and the structures of the constrained optimal clustering.