  IEEE 802.11 has evolved from 802.11a/b/g/n to 802.11ac to meet rapidly
increasing data rate requirements in WLANs. One important technique adopted in
802.11ac is the channel bonding (CB) scheme that combines multiple 20MHz
channels for a single transmission in 5GHz band. In order to effectively access
channel after a series of contention operations, 802.11ac specifies two
different CB operations: Dynamic Channel Bonding (DCB) and Static Channel
Bonding (SCB). This paper proposes an optimal channel allocation algorithm to
achieve maximal throughputs in DCB WLANs. Specifically, we first adopt a
continuous-time Markov Chain (CTMC) model to analyze the equilibrium
throughputs. Based on the throughput analysis, we then construct an integer
nonlinear programming (INLP) model with the target of maximizing system
throughputs. By solving the INLP model, we then propose an optimal channel
allocation algorithm based on the Branch-and-Bound Method (BBM). It turns out
that the maximal throughput performance can be achieved under the channel
allocation scheme with the least overlapped channels among WLANs. Simulations
show that the proposed channel allocation algorithm can achieve the maximal
system throughput under various network settings. Our analysis on the optimal
channel allocation schemes brings new insights into the design and optimization
of future WLANs, especially for those adopting channel bonding technique.
