Paris Metro Pricing for QoS in Wireless
Networks
Ravi Jain, Tracy Mullen and Rob Hausman
April 19, 2001
{rjain,mullen,hausman}@telcordia.com
An SAIC Company
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Outline
 Motivation
 Paris Metro Pricing (PMP)
 Basic PMP Model
 PMP for Profit
 Conclusions
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 2
Motivation
 QoS is increasingly important as diverse applications proliferate
 Two basic approaches to QoS
– Integrated Services: QoS guarantees (e.g. with RSVP), but costly
– Differentiated Services (Diff-Serv): probabilistic assurances
 Wireless networks particularly require low-overhead schemes
 Most previous work on QoS focuses on protocols, messages, policies
and algorithms for resource allocation
 However, discussing QoS without the user’s willingness to pay is only
half the story
– Critical to integrate economics and pricing with QoS
 Our approach: Diff-Serv QoS integrated with low-overhead pricing
– Question: When can this be profitable to the service provider?
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 3
Paris Metro Pricing (PMP)
Odlyzko, 1999
 Basic idea: 1st and 2nd class train cars are identical except 1st
class tickets cost twice as much
 User selection: Only users who want seats, fresher air, etc., pay
the premium
 QoS model: Assurance (1st class typically less crowded) but no
guarantees
 Self-regulating: As 1st class gets crowded, users stop paying
premium and travel 2nd
 Low-overhead: No reservations, no seat assignments, etc – only
a ticket checker (possibly random spot check) and deterrent
(fine)
 Our approach: PMP for Diff-Serv in wireless networks, with a
simple policing function at the base station
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 4
Implementing PMP in an enterprise wireless PCS
system
 Enterprise wants low-cost in-building wireless voice and data
 For low cost, the design would use
– the unlicensed band spectrum
– simple TDMA scheme
– low-power, low-mobility air interface
– Example: T-PACS-UB indoor wireless TDMA system at isochronous
unlicensed band (1920-1930 MHz)
 T-PACS-UB has an 8-slot TDD frame (typically 4 slots up, 4
down)
 Divide into two channels: high QoS and low QoS in ratio 1:1,
1:3, 3:1
 Network layer
– Mobile station marks IP Type-of-Service (TOS) field with QoS
desired
– Sampling or counting at edge routers to bill user for QoS used
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 5
PMP Modeling
 Gibbens et al (1999)
– Developed an analytical economic model comparing PMP with
Undifferentiated pricing
– With two competing service providers, PMP is unstable, i.e., both providers
would have an incentive to switch to undifferentiated pricing
 We build on Gibbens model for the single-provider case
 We focus on enterprises where
– network services are outsourced to a third party
– accounting is used to track costs and discourage waste
– service provider seeks to maximize profit while ensuring customers are
satisfied with QoS
 We show
– Gibbens model overlooks number of jobs in the system
– PMP is profitable for the service provider, even when users can opt out of the
system
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 6
Basic PMP Model
• Channel & price
PH = R PL
High QoS, Price PH,
Capacity (1 - ) C
C
Low QoS, Price PL,
Capacity  C
• User QoS preference
  [0, 1]
• QoS preference for users has distribution cdf
F()
• Number of users (jobs) in low and high channel
JL, JH
• Obtained QoS in low channel
• User utility function
QL =  C
JL
U(, c) = V - w  - Pc
Qc
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 7
User utility function
 U(, c) = V - w  - Pc
e.g. V = 10, w = 1, Pc = C = 1
- Lower  curves rise faster
- Diminishing returns with
Qc
Qc
- Relative values of
Utility
curves are
10
 = 0.1
significant8
not
 = 0.5
=1
6
4
2
0
0.2
0.4
0.6
0.8
Obtained QoS
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
1.0
Qc
Ravi Jain / 18-Apr-01/ 8
Basic PMP Model: User job allocation
 Gibbens: At equilibrium
– Property 1: the premium channel has lower congestion
– Property 2: users desiring high QoS (high ) join the premium channel, i.e.,
there is threshold * above which users join the premium channel
 Observation 1: (At equilibrium) The threshold * decreases as the
number of jobs in the system increases
– When the system is lightly loaded, 2nd class is good enough!
– As the system gets crowded, more users are willing to pay the premium
 For  uniformly distributed, *   as number of jobs increases
– For equal numbers of users at all QoS preferences, when the system is
crowded users distribute themselves in accordance with the capacity in 1st
and 2nd class
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 9
Simulation results
• Bootstrapping from an empty channel, PMP does converge, and to the
threshold value of * predicted by the analytical model
• As the Low channel gets crowded, the new incoming jobs calculate a lower
threshold to enter the High channel
Theoretical equilibrium *
Fraction of jobs in Low channel
Instantaneous value of * calculated by each job
J = 1000, PH = 1.25 PL
 = 0.5, Uniform 
1
0.8
*, and
Fraction 0.6
of jobs in 0.4
Low
channel
0.2
0
1
1001 2001 3001 4001 5001 6001 7001 8001 9001 10000
Job ID
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 10
PMP for profit
Service provider with Low channel of capacity at least 
 Question: Is it worthwhile for the provider to add a premium
channel?
 Compare the service provider’s profit with and without Diff-Serv
– Profit = J PL vs.
PL JL + PHMax
(J - JProfit
L)
4
3
 For any given , the service
2
provider can charge a
premium to maximize profit 1
PMP
Undifferentiated
 As   0, Profit  
0
i.e., a minimum basic service
clause is essential
0.2
0.4
0.6
0.8
1.0

Uniform , PL = 1, S = C =
1
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
wJ
Ravi Jain / 18-Apr-01/ 11
PMP for profit
Service provider where users can opt out of the service
 Users have three choices: basic channel, premium channel, or
opt out
 Price premium can be set to maximize profit for any given 
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 12
Conclusion
 Integrating economics and pricing into QoS investigation is essential
 PMP offers a simple and low-overhead method for Diff-Serv
– Particularly important for wireless networks
 In the single-provider case, Diff-Serv using PMP allows the provider to
maximize profit
– This holds even if users can opt out of the service altogether
 Simulation experiments validate the model and show that the system
does reach equilibrium from a bootstrap situation
 Analytical model shows the importance of taking the number of jobs in
the system into account
 Future work: Multiple competing providers where user demand is
bundled
– Users with a bundle of jobs (some high QoS, some low QoS) choose
between a provider who offers Diff-Serv vs. a provider who does not
Copyright ©2001 Telcordia Technologies. All Rights Reserved.
Ravi Jain / 18-Apr-01/ 13