A mathematical model of the Paris Metro Pricing scheme for charging packet networks

Abstract

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 several extensions of the model. Numerical results illustrating some key aspects of the system are provided throughout the paper.

Wireless Service Pricing under Multiple Competitive Providers and Congestion-Sensitive Users

“…However, as telecommunication networks have progressively switched from a monopolistic network to a oligopolistic one with competitive service providers, more attention has been given to price competition among service providers, see for example, (Gibbens et al, 2000) (Cao et al, 2002) (Sakurai et al, 2003) (Armony & Haviv, 2003) (Ros & Tuffin, 2004) (Khan, 2005) (Zhang et al, 2008). In practice, markets are often partly regulated and partly competitive.…”

An economic model for pricing tiered network services

“…The feasible area is represented by the shaded triangle formed by the linear constraints (10)- (12). As the value of Ω increases, the curve moves upwards, and vice versa.…”

“…Pricing of Internet services using concepts from economic theory has been a subject of research for more than a decade [3], [5]- [7], [9], [10], [12], [14]. This is a broad area that encompasses issues from calculating the cost of resources to determining the services to offer and setting appropriate prices, and from dealing with the realities and economics of layered networks to interconnection agreements between ISPs.…”

Demand management for telecommunications services

“…Regarding static pricing, in the "Paris Metro Pricing" (PMP) scheme [15] [22] two classes of services exist in the network, and each one has its own queue. Calls of the high class cost more than calls of the low class.…”

“…In order to find the optimal solution to the problem, we need the values in (21), (22) to be equal to zero. We now focus on what would these equations mean.…”