Queueing analysis of a single-wavelength Fiber-Delay-Line buffer

We present in rather mathematical detail the queueing analysis of a single-wavelength Fiber-Delay-Line buffer. Such optical buffer system cannot realize all possible delay values, but only a limited set, typically multiple integers of some basic unit called the granularity. This leads to an under-utilization of the available channel capacity, and a bad design choice for the granularity can seriously impair performance. The analysis makes extensive use of generating functions and focusses on the scheduling horizon as seen by arriving bursts and the waiting time these incur in an infinite system. From the expressions obtained, several measures of interest are derived, notably heuristics for the burst loss probability and the mean waiting time in finite systems, which can be used to evaluate performance for any given value of the input load. The model we propose allows for rather general burst-size distributions, but for special instances thereof, the formulae can be made more explicit. A number of numerical examples highlight some of the peculiar aspects of Fiber-Delay-Line buffers.