Verification of the stability region of the workload process in a single-wavelength optical buffer

In current networks, packets/customers travel from host to host in the form of light. A buffering of customers is a specific problem, since light cannot be frozen. Optical burst switching is an advanced alternative to the current electronic switching, which has buffering by means of a set of fiber delay lines (FDL). So the set of possible waiting times is not a continuum (like in a classic queueing system), but a denumerable set, where each value corresponding to the length of a delay line. As a result, in general arriving customers have to wait for service longer than in a classic case, since their waiting times has to be in that denumerable set.

A sufficient stability condition for the systems with optical buffers has been recently obtained. It holds for a wide class of GI/G/1-like optical systems. Besides it poses no restriction on the FDL lengths. This condition implies negative drift of the workload process and involves the difference between FDL lengths and the first moments of the interarrival and service times.

The purpose of this work is to verify by simulation the sharpness of the proposed sufficient condition. We realize a few scenarios to observe how a relaxation of the stability condition may influence the dynamics of the workload process. We simulate a low-loaded GI/G/1-like systems using various distributions of the interarrival and service times and a constant difference between the adjacent FDL lengths.