In the design and analysis of circuit-switched alternate-routing networks a fundamental and important problem is the decomposition of the overflow traffic from a given trunk-group (or link) into its component traffic streams. Decomposition is required because the individual streams corresponding to different sources of traffic can in principle be routed to different links depending upon the routing algorithms. Because the exact solution of this problem is intractable, several approximate methods have been given in the past. However, these approximate methods yield either incomplete solutions or solutions that are not tractable enough to be implementable in today's large networks. In this paper, we describe a model which provides a complete solution for the individual streams overflowing a group of trunks when this group of trunks is offered a number of independent traffic streams with varying peakedness values (peakedness=variance/mean, where mean and variance are the first two moments of a given traffic stream (or distribution); these moments adequately describe a given traffic distribution for teletraffic calculations). The derived formulas are simple and easily implementable in algorithms for the design of today's networks which can require large amounts of computation.