A performance metric called receptivity is introduced for quantifying
the degree of concurrent communication possible in high-speed wide are
a networks (WAN's). Given a stochastic demand pattern model, receptivi
ty is defined to be the probability that all requested connections can
be established concurrently. Because calculation of the exact value o
f receptivity is shown to (generally) have an exponential complexity,
an analytic estimate for its value is derived. The derived estimate is
dependent on network parameters such as the number of links, link cap
acity values, and a weighted hop distance metric (which depends on the
topological structure of the network and its relationship to paramete
r values of the stochastic model for the demand patterns). The derived
estimate for the proposed metric compares reasonably well with simula
ted values for several asymmetric topological structures ranging from
planar meshes to random graphs. The utility of the estimate is twofold
. First, it can be computed quickly, i.e., in polynomial time. Second,
its simple analytic form provides the network architect with insight
into some of the inherent limitations and consequences associated with
topological design choices for high-speed WAN's.