On the Viability of Paris Metro Pricing for Communication and Service Networks

Abstract

Paris Metro Pricing (PMP) is a simple multi-class flat-rate pricing scheme already practiced by transport systems, specifically by the Paris Metro at one time. The name is coined after Andrew Odlyzko proposed it for the Internet as a simple way to provide differentiated services. Subsequently, there were several analytical studies of this promising idea. The central issue of these studies is whether PMP is viable, namely, whether it will produce more profit for the service provider, or whether it will achieve more social welfare. The previous studies considered similar models, but arrived at different conclusions. In this paper, we point out that the key is how the users react to the congestion externality of the underlying system. We derive sufficient conditions of congestion functions that can guarantee the viability of PMP, and provide the relevant physical meanings of these conditions.

On Optimal Two-Sided Pricing of Congested Networks

“…Besides, different forms of the congestion function Φ can be adopted to capture the congestion metric based on different models of network services. For example, the function Φ(λ, µ) = 1/(µ − λ) models the M/M/1 queueing delay for network services and Φ(λ, µ) = λ/µ captures the capacity sharing [5] nature of general network congestion.…”

“…In particular, we adopt the congestion functions Φ(λ, µ) = λ/µ and Φ(λ, µ) = 1/(µ − λ). The former models the capacity sharing [5] nature of network services and was used in much prior work [6,9]; the latter models the M/M/1 queueing delay, which was also widely used in prior work [5,24]. We adopt the gain functions ρ(ϕ, s) = 1/(ϕs + 1) and ρ(ϕ, s) = (s + 1) −ϕ for s > 0, which were used in prior work [13,15].…”

Rethinking Business Model in Cloud Computing: Concept and Example

“…Among these efforts, Expected Capacity Charging [10] model is popularly applied in mobile markets, where each user pays for the expected capacity profile based on her general usage. Paris-Metro Charging [11], [12] allows ISPs to auction their service when the Internet is in congestion. Edge Pricing [13] proposes to charge Internet at the access point.…”

Subscription dynamics and competition in communications markets

“…There is a continuum of users, as in [6], that can potentially subscribe to one of the NSPs for communications services. The continuum model approximates well the real user population if there are a sufficiently large number of users in the market so that each individual user is negligible [2]. As in [7][11], we assume throughout this paper that each user can subscribe to at most one NSP at any time instant.…”

“…1 In other words, the QoS provided by NSP S1 is the same regardless of the number of its subscribers, whereas the QoS provided by NSP S2 degrades with the number of its subscribers [1] [2]. Let λi be the fraction of users subscribing to NSP Si for i = 1, 2.…”