Description: If a network element uses a certain amount of slack, Si, to reduce the amount of resources that it has reserved for a particular flow, i, the value Si should be stored at the network element. Subsequently, if reservation re- freshes are received for flow i, the network element must use the same slack Si without any further computation. This guarantees consisten- cy in the reservation process.

As an example for the use of the slack term, consider the case where the required end-to-end delay, Dreq, is larger than the maximum delay of the fluid flow system. In this, Ctot is the

sum of the Backlog terms end to end, and Dtot is the sum of the delay terms end to end. Dreq is obtained by setting R=r in the fluid delay formula, and is given by

b/r + Ctot/r + Dtot.

In this case the slack term is

S = Dreq - (b/r + Ctot/r + Dtot).

The slack term may be used by the network ele- ments to adjust their local reservations, so that they can admit flows that would otherwise have been rejected. A service element at an in- termediate network element that can internally differentiate between delay and rate guarantees can now take advantage of this information to lower the amount of resources allocated to this flow. For example, by taking an amount of slack s <= S, an RCSD scheduler [5] can increase the local delay bound, d, assigned to the flow, to d+s. Given an RSpec, (Rin, Sin), it would do so by setting Rout = Rin and Sout = Sin - s.

Similarly, a network element using a WFQ scheduler can decrease its local reservation from Rin to Rout by using some of the slack in the RSpec. This can be accomplished by using the transformation rules given in the previous section, that ensure that the reduced reserva- tion level will not increase the overall end- to-end delay.