The authors discuss the broad issue of bandwidth allocation and call a
dmission control (CAC) in high-speed networks, focusing on asynchronou
s transfer mode technology. It is maintained that despite the consider
able amount of high-quality work carried out in this area, the debate
surrounding these issues is not yet resolved. The complexity of dealin
g with a wide variety of as yet unknown user traffic types. as well as
the evolving architecture of networks, means that currently proposed
solutions are only an intermediate step of the design process. The aut
hors discuss the nature of user traffic and illustrate how it can impa
ct the debate on quality of service, concentrating on some ''equivalen
t bandwidth'' type CAC strategies. Also discussed is a recently introd
uced method which uses diffusion approximations. Finally, the authors
discuss the novel issue of evaluating the overload created by the CAC
procedure itself on network nodes. The presentation is complemented by
several numerical and simulation results which illustrate the discuss
ion.