Stability of single‐wavelength optical buffers

Abstract

AbstractOptical burst switching (OBS) provides a future‐proof alternative to the current electronic switching in the backbone, but has buffering implemented with a set of fiber delay lines (FDLs). The resulting buffering system fundamentally differs from a classic one, in that the set of possible waiting times is not a continuum (like in the classic case) but rather a denumerable set, each value corresponding to the length of a delay line. As a result, arriving bursts in general have to wait longer than they would in a classic buffer, since their waiting time has to be in that denumerable set. The additional delay results in overall longer waiting times, when compared to a classic infinite buffer system with a continuous waiting room.While previous work already focused on the performance evaluation of finite optical buffers, the stability problem of the infinite system received only little attention. This contribution is the first to present a complete proof of sufficient stability conditions in the case of a general infinite FDL set, general arrival process and general service times. The key elements of analysis is the exploiting of the regenerative property of the waiting‐time process and a characterisation of the limiting forward renewal time process. The given bound on the traffic load guarantees stability for a wide class of GI/G/1 optical buffers, and poses no restriction on the FDL lengths. Copyright © 2009 John Wiley & Sons, Ltd.