The area of broadband communication networks

gives rise to a large number of
on-line problems.

One of the most extensively studied problem in this area is the

on-line processing of calls;

two classes of problems have been considered: call control and load

balancing.
In the first case a sequence of

requests for calls is given on-line to an algorithm which can be

either accepted or rejected; the algorithm

has to select a virtual circuit between the communicating parties

of an accepted call,
obeying the network constraints, with the

goal of maximizing the total benfit of accepted calls.

In load balancing the goal of the algorithm is to find virtual

circuits for all calls that minimize the use

of network resources.

Algorithms for on-line problems are usually analysed in terms of

their competitive ratio, i.e., the worst case, over all input

sequences, of the ratio between the values of the solution found by

an optimal off-line algorithm (that knows the whole sequence in

advance) and by the on-line algorithm.

In this talk we review the main results that have been proposed in

the literature by presenting both deterministic and randomized

algorithms for various kind of network topologies and discussing

lower bounds.

**CV****:**