A mathematical model of the Paris Metro Pricing scheme for charging packet networks
Pricing has become one of the main challenges of the networking community and is receiving a great deal of interest in the literature. In this paper, we analyze the so-called Paris Metro Pricing scheme which separates the network into different and independent subnetworks, each behaving equivalently, except that they charge their customers at different rates. In our model, each subnetwork is represented by a single bottleneck queue, and the "customers" (data packets) choose their subnetwork taking into account not only the prices, but also the expected delay, which is supposed to have an economic impact. We obtain some necessary and sufficient conditions for the stability of the system; we analyze the problem of maximizing the network revenue and compare it with the case of a single network, and present a multiapplication extension of the model. Numerical results illustrating some key aspects of the system are provided throughout the paper.