In this paper, we study the characteristics of dominant interference power with directional reception in a random network modelled by a Poisson Point Process. Additionally, the Laplace functional of cumulative interference excluding the n dominant interferers is also derived, which turns out to be a generalization of omni-directional reception and complete accumulative interference. As an application of these results, we study the impact of directional receivers in random networks in terms of outage probability and error probability with queue length constraint.