Channel utilization and loss rate in a single-wavelength fibre delay line (FDL) buffer

We present a detailed analysis of the maximum channel utilization and loss performance in an optical buffer having access to a single outgoing channel. Such a system, consisting of a number of fiber delay lines, can only realize a discrete set of delays to resolve output port contention. This leads to an underutilization of the channel capacity, which reduces overall performance. The framework considered in this paper greatly simplifies the assumptions made in previous work, which allows us to study the impact of a variety of new parameters on the performance, e.g., the burstiness of the arrival process and the correlation of consecutive burst lengths. Moreover, we present exact results for both the channel utilization and loss rate in such a system using matrix analytic methods. We show that carefully choosing the granularity parameter can, in some cases, make a substantial difference when trying to realize lower buffer losses or a high channel utilization. Optimal values of the granularity parameter are shown to be closely related to the optical burst length distribution.