Zhang, F., Verma, P. K., & Cheng, S. (2011). Pricing, resource allocation and quality of service in multi-class networks with competitive market model. [Article]. IET Communications, 5(1), 51-60. doi: 10.1049/iet-com.2009.0694
This study considers a multi-class network resource in a competitive market where each user endowed with an initial budget will purchase bandwidth from each class of the network resource to maximise its utility function. The authors use revenue as the utility function for the service provider, and enhance Kelly’s utility function by including delay as the quality of service (QoS) parameter for users. A competitive equilibrium is reached when the total bandwidth is allocated, each user spends all its budget and the utility functions are independently and simultaneously maximised. The authors prove that such equilibriums always exist and, under fixed bandwidth supply for each class of service, the equilibrium is also unique. Furthermore, the authors discuss how to adjust the initial endowment of each user to meet his or her individual bandwidth constraint, either from constraint on the access network or the limitation of the user equipment. Under this bandwidth constraint condition, the proposed competitive equilibrium yields the price for each class of service, budget redistribution and bandwidth allocation among all users. The competitive market model presented provides a solution for pricing a multi-class network resource and allocating the resource that achieves both higher social utility and better individual satisfaction whereas maintaining the QoS of each class.