Recently Rajasekaran and Ross [1] presented an algorithm that takes an expected 0(1) time to generate a nonuniform discrete random variate. In this paper we discuss how this algorithm can be employed in the efficient simulation of large-scale telephone networks. In a simulation based upon a standard event-list approach, the generation of a new event in the systems take 0(log n) time. With this new algorithm, event generation becomes an 0(1) process, and simulation times for large networks can be reduced.