Asynchronous Blind Rendezvous Algorithms for Anonymous Users

Abstract

In this chapter, we present symmetric algorithms for the blind rendezvous problem between two asynchronous, anonymous users. In the rendezvous setting, we fix Alg, Time, and ID as follows: $$\begin{aligned} RS = \end{aligned}$$ (8.1) where \(Port \in \{Port-S, Port-AS\}\), which implies that we will design efficient algorithms that have good performance for both symmetric and asymmetric port situations. In this chapter, we will introduce a commonly used technique in designing rendezvous algorithms for cognitive radio networks, which is called Channel Hopping (CH) [1, 2, 11, 13, 14]. The intuitive idea is: in order to guarantee rendezvous for asynchronous users, the rule to access the licensed channels (in the network) should be periodic. Thus, we should construct a sequence of fixed length, such as \(S = \{s_0,s_1,\ldots ,s_{T-1}\}\) where \(s_i\) is an available channel and the user hops among the channels by repeating the sequence, i.e. they access \(s_{t ~\text {mod}~ T}\) at time t. Rendezvous in the distributed system is similar to rendezvous in the cognitive radio networks, and we can use the Channel Hopping technique to design efficient algorithms. In a distributed system, the available port sets for asymmetric users could be different, and different users may construct different hopping sequences. Therefore, it is difficult to design efficient algorithms (or short hopping sequences) that are suitable for all users. Moreover, the lower bound of such sequence cannot be derived directly when the sequences for different users vary, which is important for evaluating and verifying the efficiency of any proposed rendezvous algorithm. Therefore, we introduce Global Sequence (GS) based rendezvous algorithms to alleviate the impact of asymmetry in the ports’ occupancy; the intuitive idea is: design a fixed sequence \(S = \{s_0,s_1,\ldots ,s_{T-1}\}\) for all users based on the full port set \(U=\{1,2,\ldots ,N\}\) and each user hops among the ports by repeating the sequence (modification on the sequence may exist when some ports are not available for communication). Specifically, the GS based rendezvous algorithms work in two phases: Phase 1: Assume all users have the same available port set U and design the GS on the basis of U; Phase 2: Each user modifies the sequence according to its own available port set, i.e. when the user should access an unavailable port by the original hopping sequence, replace it with an available one that is picked randomly or by some pre-defined rules.