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A set of hard real time (HRT) connection scan can be admitted only if the worst-case end-to-end delays of cells belonging to individual connections are less than their deadlines. Using a new optimal leaky bucket regulator algorithm to provide simple and user programmable mean of traffic regulation to meet the delay requirements of the hard real time connections, by selecting the burst parameters (β) of the leaky bucket to meet connections deadline is designed and analyzed. The implemented algorithm is optimal in the sense that it always selects a set of burst parameters whose mean value is minimal and by which the delay requirements of the hard real time connections can be met. As well as, improving the system performance, in terms of connection admission probability. The implemented algorithm is new in the sense that it uses the leaky bucket regulator as a method for guaranteeing the end-to-end deadline of hard real time networks not as it was traditionally used as a policing mechanism when the source traffic does not conform to network characteristics.