  This paper studies distributed resource allocation problem in multi-agent
systems, where all the agents cooperatively minimize the sum of their cost
functions with global resource constraints over stochastic communication
networks. This problem arises from many practical domains such as economic
dispatch in smart grid, task assignment, and power allocation in robotic
control. Most of existing works cannot converge to the optimal solution if
states deviate from feasible region due to disturbance caused by environmental
noise, misoperation, malicious attack, etc. To solve this problem, we propose a
distributed deviation-tracking resource allocation algorithm and prove that it
linearly converges to the optimal solution with constant stepsizes. We further
explore its resilience properties of the proposed algorithm. Most importantly,
the algorithm still converges to the optimal solution under the disturbance
injection and random communication failure. In order to improve the convergence
rate, the optimal stepsizes for the fastest convergence rate are established.
We also prove the algorithm converges linearly to the optimal solution in mean
square even with uncoordinated stepsizes, i.e., agents are allowed to employ
different stepsizes. Simulations are provided to verify the theoretical
results.
