This paper considers the support of hard real-time connections in ATM netwo
rks. In an ATM network, a set of hard realtime connections can be admitted
only if the worst case end-to-end delays of cells belonging to individual c
onnections are less than their deadlines. There are several approaches to m
anaging the network resources in order to meet the delay requirements of co
nnections. This paper focuses on the use of traffic regulation to achieve t
his objective. Leaky buckets provide simple and user-programmable means of
traffic regulation. An efficient optimal algorithm for selecting the burst
parameters of leaky buckets to meet connections' deadlines is designed and
analyzed. The algorithm is optimal in the sense that it always selects a se
t of burst parameters whose mean value is minimal and by which the delay re
quirements of hard real-time connections can be met. The exponential size o
f the search space makes this problem a challenging one. The algorithm is e
fficient through systematically pruning the search space. There is an obser
ved dramatic improvement in the system performance in terms of the connecti
on admission probability when traffic is regulated using this algorithm.