ABSTRACT
Here we investigate pricing of Internet connectivity services in the context of a
monopoly ISP selling broadband access to consumers. We first study the optimal
combination of flat-rate and usage-based access price components for
maximization of ISP revenue, subject to a capacity constraint on the data rate
demand. Next, we consider time-varying consumer utilities for broadband data
rates that can result in uneven demand for data-rate over time. Practical
considerations limit the viability of altering prices over time to smoothen out
the demanded data rate.
Despite such constraints on pricing, our analysis
reveals that the ISP can retain the revenue by setting a low usage fee and
dropping packets of consumer demanded data that exceed capacity. Regulatory
attention on ISP congestion management discourages such “technical” practices
and promotes economics based approaches. We characterize the loss in ISP
revenue from an economics based approach. Regulatory requirements further
impose limitations on price discrimination across consumers, and we derive the
revenue loss to the ISP from such restrictions. We then develop partial
recovery of revenue loss through non-linear pricing that does not explicitly
discriminate across consumers. While determination of the access price is
ultimately based on additional considerations beyond the scope of this paper,
the analysis here can serve as a benchmark to structure access price in
broadband access networks.
EXISTING SYSTEM
Pricing content-providers for connectivity to
end- users and setting connection parameters based on the price is an evolving
model on the Internet. The implications are heavily debated in telecom policy
circles, and some advocates of "Network Neutrality" have opposed
price based differentiation in connectivity. However, pricing content providers
can possibly subsidize the end-user's cost of connectivity, and the consequent
increase in end-user demand can benefit ISPs and content providers. The
framework generalizes the well-known utility maximization based rate allocation
model, which has been extensively studied as an interplay between the ISP and
the end-users, to incorporate pricing of content-providers. We derive the
resulting equilibrium prices and data rates in two different ISP market
conditions: competition and monopoly. Network neutrality based restriction on
content-provider pricing is then modeled as a constraint on the maximum price
that can be charged to content-providers. We demonstrate that, in addition to
gains in total and end- user surplus, content-provider experiences a net
surplus from participation in rate allocation under low cost of connectivity.
The surplus gains are, however, limited under monopoly conditions in comparison
to competition in the ISP market.
PROPOSED SYSTEM
Although Internet data flows along
multiple links on a route between source and destination, the end-user access
link is typically the most constrained for capacity, and the major contributor
to the connectivity price. Consumer data rate allocation can be determined by
socially optimal prices in a competitive market on the one hand, or the revenue
maximizing prices in a monopoly ISP market on the other hand. Access pricing is
typically in the form of a flat rate that is independent of usage, or a usage
based price, or some combination of the two pricing schemes. We quantify that a
significant component of the monopoly ISP revenue is from flat price if
consumer price sensitivity is low and through usage price if consumer
price sensitivity is high. Flat pricing is generally considered as the
preferred choice of consumers, but our analysis indicates that flat pricing can
lead to a significant loss of consumer net-utility, particularly when the
consumers have low price sensitivity.
Consumer
demand for data changes over hours of the day and days of the week, resulting
in peak usage of networks that can be significantly high compared to average
usage. Access ISPs face a mismatch between their revenue from average usage and
cost incurred from peak usage of networks. Considerations on billing management
and price simplicity discourage frequent changes in prices over time. This
limitation on ISP’s ability to manage peak aggregate demand through price
variations can result in potential loss of revenue. Our analysis reveals that,
despite the lack of flexibility to alter the time-dependent consumption of
consumers through price variations, the ISP can retain the revenue
through congestion management by dropping packets of consumer demanded
data that exceed available capacity. We quantify the intuition that the
revenue retention can be achieved through a combination of low usage fee that
ensures sufficient consumer demand at all times, and a high flat fee that
captures the remaining consumer net utility from the served data rates.
However,
ISPs face regulatory hurdles, including “network neutrality” concerns , that do
not encourage congestion management by selectively dropping packets of consumer
demanded data. The recent FCC notice proposes draft language to codify a
principle that would require a broadband ISP to treat lawful content,
applications, and services in a nondiscriminatory manner. In a related
decision, the CRTC recognizes that “economic practices are the most transparent
Internet traffic management practices”. It further notes that such economics
based congestion management practices “match consumer usage with willingness to
pay, thus putting users in control and allowing market forces to work”.
SYSTEM SETUP AND
BASIC NOTATION
The
congestion constraint faced by an ISP is on the peak aggregate consumer
data-rate. In contrast, the retail access price is based on the volume of data
(measured in megabytes or MB), consumed over a specified time period T (typically a
month). The pricing on data volume is equivalent to pricing on average data
rate over time T.
Therefore, ISPs face a mismatch, where revenue is accrued on average data rate
but congestion cost is incurred on the peak data rate. To address this
disparity, we note that the difference between peak data rate and the average
data
rate is reduced when measured over smaller time periods. Consider a unit time
interval that is sufficiently small so that the peak data rate demand of a
consumer in that time interval is a close approximation to the average data
rate for that consumer in that interval1. Let f Î F be
a consumer data flow with F denoting the set of all flows. Let data
rate for flow f in
the interval
[(t − 1), t] be given by xt f .
The data volume consumption over time T is then given by
xf = åT t =1
xt f,
and the capacity constraint applies at every time instant t:
åf xt f ≤ C, ∀t
A
qualitative observation is that the shape of the utility function depends on
the response of the content or application to varying data-rates, and the
utility level represents the consumer’s need for the application or content.
This motivates us to assume that the consumer’s utility level varies in time,
but the shape of the utility function does not. The observation will have to be
verified through analysis of real data. Let σtf uf (xt f ) be the utility to a
consumer associated with flow f at time instant t, with factor σtf denoting
the time dependency of consumer’s utility level.
We assume that the revenue maximizing ISP, through network measurements, has
complete knowledge of the either the consumer utility function parameters or
the probabilistic distribution of the parameters.
Faced with time-varying consumer
utilities, the ISP can charge a time-dependent price for connectivity rtf(xt f ) as a function of the
allocated data rate xt f .
Consumers maximize the net utility for each flow f:
maximize σtf uf (xt f) – rtf (xt f )
variable xt f
The consumer demand function is the data
rate that maximizes the net-utility in . One form of the price with linear
increase in data-rate is given by:
rtf (xt f) = gtf + htf xt f .
The
flat price gtf is fixed for the
duration of the time interval, irrespective of the allocated data rate. The
usage based component involves a price htf per
unit data consumption. The demand function for
this form of the price can be shown to be given by:
The condition σtf uf (xt f ) – gtf – htf xt f ≥ 0 ensures that consumers have non-negative
utility. To simplify notation, we often use ytf (htf) = uf t-1(htf / σtf ) with
the implicit assumption that the flat price is low enough to ensure
non-negative consumer net-utility. We do not consider an explicit penalty to
consumer utility, as considered in [10], [11], from congestion due to aggregate
data-rate demand. However, we note that the such a penalty can be easily
incorporated into the consumer utility function, in which case ytf (gtf , htf) is the best-response
update at a Nash-equilibrium of consumer data-rate demands.
The elasticity of demand ηtf is a standard measure of the sensitivity of the
consumer demand to price fluctuations , and is defined as
Often, we specialize the utility function
to the standard alphafair utility form:
for which we have ηtf = 1/αf : the price sensitivity is inversely proportional to
the parameter αf and independent of utility level σtf..
BASIC PRICE
STRUCTURES
We first analyze the structure of the price
rtf (xt f) = gtf + htf xt f that
allows the ISP to manage congestion while maximizing revenue. The revenue
maximization problem for the monopoly ISP can be defined by the following:
Maximize åtå
f (gtf + htf xt f)
subject to åf xt f ≤ C, ∀t
xt f ≤ u f t-1 (htf / σtf )
σtf uf (xt f ) – gtf – htf xt f ≥ 0, ∀t
variable { gtf , htf, xt f }
Obviously, the revenue increases
with higher flat fee component gtf ,
which can be set so that the consumer net utility is zero. The revenue
from each flow is then
gtf + htf xt f = σtf uf (xt f ), which can be realized
by any combination of flat and usage fee that can support a data-rate of xtf . If the usage
fee htf is such that the
consumer demand ytf (htf ) is strictly greater than the ISP
provisioned data rate xt f , then flow data
packets have to be dropped. However, the ISP can avoid packet drops by setting
a sufficiently high usage price to reduce the consumer demand so that the
aggregate demand is within the available capacity. It follows that xt f = ytf (htf) and the ISP revenue
maximization problem can be re-written as:
Maximize åtå
f σtf uf (ytf (htf ))
subject
to å ytf (htf ) ≤ C, ∀t
variable { htf }
Let the maximized revenue in problems and
from unrestricted pricing be R∗ u, which will be
contrasted with maximized revenue under restrictions on pricing in later
sections. Problem can be easily decomposed into sub-problems at each time
instant t,
and has a solution given by the following,
Theorem
1:
An
optimal pricing scheme that achieves the maximum in is given by setting for each t:
ht * = μt
xtf* = u f t-1 (μt / σtf )
åf xtf*= C
gtf = σtf u f (xtf*) −μtxtf*
The proof follows
directly from the observation that the optimal price structure represents the
KKT conditions [21] for the decomposed sub-problems of the optimization
problem.
The optimal usage fee ht * is the time dependent congestion price μt, which is the same
across all flows f, and the optimal flat
fee gtf = σtf u f (xtf*) −μtxtf* is flow dependent,
allowing the ISP to fully extract the consumer net-utility.
Let R∗f be the revenue from flat component of the
price and R∗s the revenue from usage component so that R∗ u = R∗f + R∗s. It can be shown that
In an exemplary
special case, we have the following result, whose proof is straightforward and
is omitted.
Theorem
2:
If utility functions
are alpha-fair (4) with af=a for all f, the ratio of flat revenue to usage
dependent revenue is given by
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