# Blocking probabilities in large circuit-switched networks

**
F. P. Kelly
**

Advances in Applied Probability 18 (1986), 473-505.

## Abstract

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.

paper

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.

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