Under use of the regulated radio spectrum is being addressed using a cognitive radio network approach termed dynamic spectrum access. Primary users have priority over the regulated radio spectrum. Secondary users may use the residual air time. We focus on the problem of meeting on a common channel by a group of secondary users. Under the asymmetric model, the secondary users have different sets of available channels. If the sets are not disjoint, they can eventually make rendezvous. The goal is to make the secondary users rendezvous on a common channel in a minimum amount of time. The jump-stay rendezvous algorithm has been created by Lin et al. to solve this problem. We develop a new analysis for the two-user expected time to rendezvous in the jump-stay rendezvous algorithm, under the asymmetric model, that better reflects its performance