On a class of time varying shapers with application to the renegotiable variable bit rate service

A shaper is a system that stores incoming bits in a bu er and delivers them as early as possible, while forcing the output to be constrained with a given arrival curve. A shaper is time invariant if the tra c constraint is de ned by a xed arrival curve; it is time varying if the condition on the output is given by a time varying tra c contract. This occurs, for example, with renegotiable variable bit rate (RVBR) services. We focus on the class of time varying shapers called time varying leaky bucket shapers; such shapers are de ned by a xed numbers of leaky buckets, whose parameters (rate and bucket size) are changed at speci c transition moments. We assume that the bucket levels are kept unchanged at those transition moments (\no reset" assumption). Our main nding is an input-output characterisation for this class of time varying shapers. Then we apply it to the tradeo in optimising the RVBR service, assuming that a perfect prediction of future tra c can be made. We provide two algorithms that solve the problem of nding, at any renegotiation, the parameters for a RVBR service, respectively when the Contact author: Email. silvia.giordanoep .ch Tel. +41 21 693 67 48 Fax. +41 21 693 6610