Pricing and congestion management with different users´ Utility functions in the networks

It presents an economic model for a communication network with utility-maximizing elastic users who adapt to congestion by adjusting their flows. Users are heterogeneous with respect to both the utility they attach to different levels of flow and their sensitivity to delay or other measures of congestion. It shows that allowing heterogeneity with respect to delay sensitivity introduces a fundamental non-convexity into the congestion cost functions. As a result, there are typically multiple stationary points. Hence marginal-cost pricing equates users´ marginal utilities to their marginal costs may identify a local maximum or even a saddle point, rather than a global maximum. It gives an example to show that heterogeneity of users can lead to class dominance: a situation in which the system is dominated by a single user or class of users under an optimal flow allocation. However, that can be settled by choosing some proper net utility functions and making the sensitivity of the users´ to delay is same.