We explore a dynamic approach to the problems of call admission and re
source allocation for communication networks with connections that are
differentiated by their quality of service requirements. In a dynamic
approach. the amount of spare resources is estimated on-hue based on
feedbacks from the network's quality of service monitoring mechanism.
The schemes we propose remove the dependence on accurate traffic model
s and thus simplify the tasks of supplying traffic statistics required
of network users. In this paper we present two dynamic algorithms. Th
e objective of these algorithms is to find the minimum bandwidth neces
sary to satisfy a cell loss probability constraint at an asynchronous
transfer mode (ATM) switch. We show that in both schemes the bandwidth
chosen by the algorithm approaches the optimal value almost surely. F
urthermore, in the second scheme, which determines the point closest t
o the optimal bandwidth from a finite number of choices, the expected
learning time is finite.