In this paper we propose a new unified approach to address simultaneously the issues of traffic policing (using leaky buckets), admission control and network dimensioning. First we compute the effective bandwidth of the output of the leaky bucket. We find a surprising result that effective bandwidth of the output of a leaky bucket is independent of the token pool size. Furthermore, the output effective bandwidth exhibits discontinuous behavior as the token pool size approaches infinity. We use these results in an optimization model to find the 'optimal' leaky bucket parameters. We explain how this optimization program can be used to do network dimensioning if the input traffic characteristics are known, or to do connection admission control if the network parameters are fixed.