Simulated Annealing for Optimal Resource Allocation in Wireless Networks with ImperfectCommunications

Simulated annealing (SA) method has had significant recent success in designing distributed control algorithms for wireless networks. These SA based techniques formed the basis of new CSMA algorithms and gave rise to the development of numerous variants to achieve the best system performance accommodating different communication technologies and more realistic system conditions. However, these algorithms do not readily extend to networks with noisy environments, as unreliable communication prevents them from gathering the necessary system state information needed to execute the algorithm. In recognition of this challenge, we propose a new SA algorithm that is designed to work more robustly in networks with communications that experience frequent message drops. The main idea of the proposed algorithm is a novel coupling technique that takes into account the external randomness of message passing failure events as a part of probabilistic uncertainty inherent in stochastic acceptance criterion of SA. As a result, the algorithm can be executed even with partial observation of system states, which was not possible under the traditional SA approach. We show that the newly proposed algorithm finds the optimal solution almost surely under the standard annealing framework while offering significant performance benefits in terms of its computational speed in the presence of frequent message drops.Comment: 12 pages. A short version (8-page) of this paper has been published in Annual Allerton Conference on Communication, Control, and Computing (Allerton) in 201