paris metro pricing for qos in wireless networks an saic company ravi jain, tracy mullen and rob...

Paris Metro Pricing for QoS in Wireless Networks

An SAIC Company

Ravi Jain, Tracy Mullen and Rob HausmanApril 19, 2001{rjain,mullen,hausman}@telcordia.com

Copyright ©2001 Telcordia Technologies. All Rights Reserved.

Ravi Jain / 18-Apr-01/ 2Copyright ©2001 Telcordia Technologies. All Rights Reserved.

Outline

Motivation Paris Metro Pricing (PMP) Basic PMP Model PMP for Profit Conclusions


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?


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


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


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


Basic PMP Model

C

High QoS, Price PH, Capacity (1 - ) C

Low QoS, Price PL, Capacity C

PH = R PL

• Channel & price

• 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 QL = C JL • User utility function U(, c) = V - w - Pc

Qc


0 0.2 0.4 0.6 0.8 1.0 QcObtained QoS

10

8

6

4

2

= 0.1

= 0.5

= 1

Utility

User utility function

U(, c) = V - w - Pc e.g. V = 10, w = 1, Pc = C = 1 Qc - Lower curves rise

faster - Diminishing

returns with Qc

- Relative values of curves are

not significant


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


1 1001 2001 3001 4001 5001 6001 7001 8001 9001 10000Job ID

1

0.8

0.6

0.4

0.2

0

*, andFractionof jobs inLowchannel

Simulation results

Theoretical equilibrium * Fraction of jobs in Low channel Instantaneous value of * calculated by each job

J = 1000, PH = 1.25 PL

= 0.5, Uniform

• 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


0 0.2 0.4 0.6 0.8 1.0

4

3

2

1

Max Profit

Undifferentiated

PMP

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 + PH (J - JL)

For any given , the service

provider can charge a premium to maximize profit

As 0, Profit i.e., a minimum basic service clause is essential Uniform , PL = 1, S = C = 1 wJ

PMP for profitService provider with Low channel of capacity at least


PMP for profitService 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


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

paris metro pricing for qos in wireless networks an saic company ravi jain, tracy mullen and rob...

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