Since it was found that real mobility processes exhibit significant degree of correlation (correlated mobility) and nodes are often heterogeneously distributed in clustered networks (cluster scalability), there has been a great interest in studying their impact on network performance, such as throughput and delay. However, limited works have been done to investigate their impact jointly, which may due to the challenges in capturing both features under a unified network model. In this paper, we focus on their impact on asymptotic connectivity and propose correlated mobile k-hop clustered network model. Two connectivity metrics are considered. One is network connectivity with probability (w.p.). The other is connectivity almost surely (a.s.), which requires a stronger condition than connectivity with probability. With mobility correlation and cluster scalability vary, we show that there are three distinct states for network connectivity, i.e., cluster-sparse, cluster-dense state, and cluster-inferior dense state, respectively. We first prove the exact value of the critical transmission range for each state, respectively, and then further generalize the three states into a unified one, which we call it cluster mixed state. The critical transmission range for connectivity almost surely is √2 times the range for connectivity with probability. Our main contribution lies in how to group correlated nodes into independent ones in various settings, and reveals the interrelated relationship between correlated mobility and cluster scalability through state transitions.

We propose the correlated mobile k-hop clustered networks model to implement correlated node movements and scalable clusters. We divide network states into three categories, i.e., cluster-sparse state, cluster-dense state and cluster-inferior dense state, and achieve the critical transmission range for the last two states. Furthermore, we find that correlated mobility and cluster scalability are closely related with each other and the impact of these two properties on connectivity is mainly through influencing network state transition.

Cognitive radio networks (CRN) is a promising technology for the efficient utilization of spectrum resource. However, how to dynamically allocate the spectrum combining with the characteristics of CRN is a crucial challenge for the mechanism design. In this paper, from the perspective of frequency-time characteristics of the spectrum opportunity in CRN and the secondary users' flexible requirements, we model the dynamic spectrum allocation problem as a knapsack problem and prove that maximizing the social welfare is NP-hard. Therefore, a spectrum auction mechanism is developed to approximate the optimal social welfare, and we prove its approximate ratio. Further, to guarantee the truthfulness, we devise a corresponding payment scheme. In simulation results, we show that no matter how many SUs are in the CRN, our scheme can approximate the maximal social welfare perfectly, and the spectrum utilization can be improved to over 96.5% or even larger.