Advances in Applied Probability 18 (1986), 473-505.
This paper is concerned with blocking and loss probabilities in circuit-switched networks. We show that when the capacity of links and the offered traffic are increased together, a limiting regime emerges in which loss probabilities are as if links block independently, with blocking probabilities given by the solution of a simple convex programming problem. We then show that an approximate procedure, based on solving Erlang's formula under the assumption of independent blocking, produces a unique solution when routes are fixed, and that under the limiting regime the estimates of loss probabilities obtained from the procedure converge to the correct value.
Keywords: loss probabilities; network flow; local limit theorems; Erlang's formula; fixed routing; dynamic routing; cellular radio.
Note: for the example around Figure 7, see also
D. L. Pallant and P. G. Taylor, Modeling Handovers in Cellular
Mobile Networks with Dynamic Channel Allocation, Operations Research
43 (1995) 33-42, and
J. Kind, T. Niessen and R. Mathar, Theory of maximum packing and related channel assignment strategies for cellular radio networks, Math Meth Oper Res 48(1998), 1-16.