Buffer dimensioning for rate adaption modules

In a telecommunication network, information (represented by fixed-length packets) sent by a source typically passes through a number of nodes before reaching its final destination. In a variety of networks, the communication links that interconnect multiple nodes do not necessarily transmit the same amount of information per time unit. In particular, when the speed of an incoming link(s) in a node exceeds the speed of the outgoing link(s), buffering of packets must be provided in order to avoid excessive packet loss. In this report, we examine the problem of dimensioning such a rate-adaptation buffer. The packet arrival stream is described by characterizing the length of consecutive active and passive periods (i.e., a series of consecutive slots during which packets, respectively no packets, are generated); the former quantities can have any distribution, while the latter are assumed to be geometrically distributed. Using a generating-functions approach, an expression for the steady-state probability generating function of the buffer occupancy is derived. From this result, a closed-form expression for the tail distribution of the buffer occupancy is derived, that is practical and easy to evaluate, this latter quantity is especially useful for buffer dimensioning purposes. In addition, an accurate approximations for this quantity, that reduces all numerical calculations to an absolute minimum, is established as well.