In this paper a particular loss network consisting of two links with C 1 and C 2 circuits, respectively, and two fixed routes, is investigated. A call on route 1 uses a circuit from both links, and a call on route 2 uses a circuit from only the second link. Calls requesting routes 1 and 2 arrive as independent Poisson streams. A call requesting route 1 is blocked and lost if there are no free circuits on either link, and a call requesting route 2 is blocked and lost if there is no free circuit on the second link. Otherwise the call is connected and holds a circuit from each link on its route for the holding period of the call.

The case in which the capacities C 1, and C 2, and the traffic intensities v 1, and v 2, all become large of O(N) where N » 1, but with their ratios fixed, is considered. The loss probabilities L 1 and L 2 for calls requesting routes 1 and 2, respectively, are investigated. The asymptotic behavior of L 1 and L 2 as N→ ∞ is determined with the help of double contour integral representations and saddlepoint approximations. The results differ in various regions of the parameter space (C 1, C 2, v 1, v 2). In some of these results the loss probabilities are given in terms of the Erlang loss function, with appropriate arguments, to within an exponentially small relative error. The results provide new information when the loss probabilities are exponentially small in N. This situation is of practical interest, e.g. in cellular systems, and in asynchronous transfer mode networks, where very small loss probabilities are desired.

The accuracy of the Erlang fixed-point approximations to the loss probabilities is also investigated. In particular, it is shown that the fixed-point approximation E 2 to L 2 is inaccurate in a certain region of the parameter space, since L 2 « E 2 there. On the other hand, in some regions of the parameter space the fixed-point approximations to both L 1 and L 2 are accurate to within an exponentially small relative error.