  The goal of traffic management is efficiently utilizing network resources via
adapting of source sending rates and routes selection. Traditionally, this
problem is formulated into a utilization maximization problem. The single-path
routing scheme fails to react to instantaneous network congestion. Multi-path
routing schemes thus have been proposed aiming at improving network efficiency.
Unfortunately, the natural optimization problem to consider is concave but not
strictly concave. It thus brings a huge challenge to design stable multi-path
congestion control algorithms.
  In this paper, we propose a generalized multi-path utility maximization model
to consider the problem of routes selection and flow control, and derive a
family of multi-path dual congestion control algorithms. We show that the
proposed algorithms are stable in the absence of delays. We also derive
decentralized and scalable sufficient conditions for a particular scheme when
propagation delays exist in networks. Simulations are implemented using both
Matlab and NS2, on which evaluation of the proposed multi-path dual algorithms
is exerted. The comparison results, between the proposed algorithms and the
other two existing algorithms, show that the proposed multi-path dual
algorithms with appropriate parameter settings can achieve a stable aggregated
throughput while maintaining fairness among the involved users.
