Optical buffers, batch arrivals and synchronization

We present the analysis of a single-wavelength fiber-delay-line buffer fed by a batch arrival process, and apply the results to study the influence of (internal) synchronization on performance. We rely on generating functions to develop a discrete-time queueing model that, unlike previously obtained results, is able to cope with concurrent arrivals. Without making any special assumptions on the burst or batch size distribution, we derive an expression for the scheduling horizon as seen by arriving batches in a system of infinite size. From that, we are able to derive e.g. a maximum tolerable arrival intensity. For finite systems, we use a heuristic to calculate the burst loss probability which is validated against simulations. Consequently, we employ the model assuming a Poisson batch size distribution, and investigate the influence of synchronization. Whether or not this turns out beneficial is shown to relate strongly to the burst size distribution