Asymptotic analysis for blocking probabilities of optical buffer with general packet-length distributions

Asynchronous optical packet switching seems to be suitable as a transport technology for the next-generation Internet due to the variable lengths of IP packets. Optical buffers in the output port are an integral part for solving contention by exploiting the time domain. Fiber delay lines (FDLs) are a well-known technique for achieving optical buffers. This work aims to give a highly accurate approximation of the blocking probabilities of the optical buffers for a generally distributed packet length even when the offered load is extremely low. Such a tool is needed for investigating and designing realistic optical packet switches, which will be used for low-offered-load and low-packet-loss optical IP networks. We use the asymptotic expansion for the decay rate, resulting in a highly accurate approximation. By using the fourth order approximation of the decay rate, an accuracy within 10 % was obtained for both the exponential and uniform distribution cases of an offered load greater than 0.3. The approximations established in this work can be applied to investigate multiclass optical buffers for priority queueing.