Average Number of Recirculations in SDL Constructions of Optical Priority Queues

In this letter, we derive the average number of times an optical packet recirculates through the optical switch and the fiber delay lines in our previous constructions of optical priority queues (see Figure 1 in Section I) under Bernoulli arrival traffic, Bernoulli control input, and uniform priority assignment. The analytical results on the average number of recirculations are further verified through simulations. Through simulations, we also find that these analytical results are useful in choosing the number of fiber delay lines in our constructions of optical priority queues when there is a limitation on the number of times an optical packet can be recirculated through the optical switch and the fiber delay lines.