Revisiting the Performance of the Modular Clock Algorithm for Distributed Blind Rendezvous in Cognitive Radio Networks

We reexamine the modular clock algorithm for distributed blind rendezvous in cognitive radio networks. It proceeds in rounds. Each round consists of scanning twice a block of generated channels. The modular clock algorithm inspired the creation of the jump-stay rendezvous algorithm. It augments the modular clock with a stay-on-onechannel pattern. This enhancement guarantees rendezvous in one round. We make the observation that as the number of channels increases, the significance of the stay-on-one-channel pattern decreases. We revisit the performance analysis of the two-user symmetric case of the modular clock algorithm. We compare its performance with a random and the jump-stay rendezvous algorithms. Let m be the number of channels. Let p be the smallest prime number greater than m. The expected timeto-rendezvous of the random and jump-stay algorithms are m and p, respectively. Theis et al.’s analysis of the modular clock algorithm concludes a maximum expected time-to-rendezvous slightly larger than 2p time slots. Our analysis shows that the expected time-to-rendezvous of the modular clock algorithm is no more than 3p/4 time slots.