Worst Case Arrivals of Leaky Bucket Constrained Sources: The Myth of the On-Off source

We have simulated a set of independent connections limited by leaky bucket shapers and fed into a buffered multiplexer. This scenario is typical of an ATM switch or in a looser sense of an RSVP capable router. We found periodic traffic patterns which result in much worse loss rates than the on-off or tristate patterns found in literature to date. We give an intuitive justification for what we believe is the worst case and back this with an extensive set of simulations. Our results are important for Connection Acceptance Control when connections are known to be statistically independent. They clearly invalidate the widespread belief that on-off patterns are the worst case traffic of independent leaky bucket constrained sources.