An Approximation for Blocking Probabilities and Delays of Optical Buffer With General Packet-Length Distributions

An all-optical network still remains a long way from realistic deployment. However, all-optical packet switches, in which optical packets are buffered and routed in optical form, are still expected to solve the problems of electronic bottlenecks and large power consumption in electronic routers. An approximation is presented for blocking probabilities and delays of optical buffers, where optical packet arrival process is Poisson and packet-length distribution is general. The approximation aims at providing a simple calculation tool for optical buffer design without requiring computer simulations or extensive iterative computations. An approximation for the cumulative distribution function of the waiting time for general packet-length distributions was obtained that holds when the waiting time is sufficiently large and the traffic load is heavy. The difference in the blocking probabilities between the approximation and the simulation results was found to be less than 10% when the offered load was greater than 0.7. The approximation can be applied to investigate multiclass optical buffers for priority queueing and to design wavelength-division-multiplexing optical packet switches and networks with the maximum throughput.