Extending the Network Calculus Pay Bursts Only Once Principle to Aggregate Scheduling

The Differentiated Services framework allows to provide scalable network Quality of Service by aggregate scheduling. Services, like a Premium class, can be defined to offer a bounded end-to-end delay. For such services, the methodology of Network Calculus has been applied successfully in Integrated Services networks to derive upper bounds on the delay of individual flows. Recent extensions allow an application of Network Calculus even to aggregate scheduling networks. Nevertheless, computations are significantly complicated due to the multiplexing and de-multiplexing of micro-flows to aggregates. Here problems concerning the tightness of delay bounds may be encountered. A phenomenon called Pay Bursts Only Once is known to give a closer upper estimate on the delay, when an end-to-end service curve is derived prior to delay computations. Doing so accounts for bursts of the flow of interest only once end-to-end instead of at each link independently. This principle also holds in aggregate scheduling networks. However, it can be extended in that bursts of interfering flows are paid only once, too. In this paper we show the existence of such a complementing Pay Bursts Only Once phenomenon for interfering flows. We derive the end-to-end service curve for a flow of interest in an arbitrary aggregate scheduling feed forward network for rate-latency service curves, and leaky bucket constraint arrival curves, which conforms to both of the above principles. We give simulation results to show the utility of the derived forms.