Many proposed network resource allocation algorithms in existing literature, especially those in practical networking, are designed based on heuristics and then validated by (limited) prototyping and experimentation or numerical simulations. These algorithms usually perform poorly in either responsiveness or convergence, and lack a principled way to trade off between the convergence and the optimality of resource allocation. This paper shows that for a very general resource allocation problem, algorithms based on the proportional control achieve both fast response and convergence. We establish the convergence of the proportional control algorithms with inter-task and spatial couplings, and quantify their performance under estimation error. We further establish the convergence of the algorithms when operating asynchronously with bounded delays. Numerical experiments are provided to complement the theoretical analysis.