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Paris Metro Pricing for QoS in Wireless Networks An SAIC Company Ravi Jain, Tracy Mullen and Rob Hausman April 19, 2001 {rjain,mullen,hausman}@telcordia.com Copyright ©2001 Telcordia Technologies. All Rights Reserved.
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Ravi Jain / 18-Apr-01/ 2 Copyright ©2001 Telcordia Technologies. All Rights Reserved. Outline Motivation Paris Metro Pricing (PMP) Basic PMP Model PMP for Profit Conclusions
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Ravi Jain / 18-Apr-01/ 3 Copyright ©2001 Telcordia Technologies. All Rights Reserved. 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?
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Ravi Jain / 18-Apr-01/ 4 Copyright ©2001 Telcordia Technologies. All Rights Reserved. Paris Metro Pricing (PMP) Odlyzko, 1999 Basic idea: 1 st and 2 nd class train cars are identical except 1 st class tickets cost twice as much User selection: Only users who want seats, fresher air, etc., pay the premium QoS model: Assurance (1 st class typically less crowded) but no guarantees Self-regulating: As 1 st class gets crowded, users stop paying premium and travel 2 nd 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
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Ravi Jain / 18-Apr-01/ 5 Copyright ©2001 Telcordia Technologies. All Rights Reserved. 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
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Ravi Jain / 18-Apr-01/ 6 Copyright ©2001 Telcordia Technologies. All Rights Reserved. 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
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Ravi Jain / 18-Apr-01/ 7 Copyright ©2001 Telcordia Technologies. All Rights Reserved. Basic PMP Model C High QoS, Price P H, Capacity (1 - ) C Low QoS, Price P L, Capacity C P H = R P L Channel & price User QoS preference [0, 1] QoS preference for users has distribution cdf F( ) Number of users (jobs) in low and high channel J L, J H Obtained QoS in low channel Q L = C J L User utility function U( , c) = V - w - P c Q c
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Ravi Jain / 18-Apr-01/ 8 Copyright ©2001 Telcordia Technologies. All Rights Reserved. 0 0.2 0.4 0.6 0.8 1.0 Q c Obtained QoS 10 8 6 4 2 = 0.1 = 0.5 = 1 Utility User utility function U( , c) = V - w - P c e.g. V = 10, w = 1, P c = C = 1 Q c - Lower curves rise faster - Diminishing returns with Q c - Relative values of curves are not significant
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Ravi Jain / 18-Apr-01/ 9 Copyright ©2001 Telcordia Technologies. All Rights Reserved. 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, 2 nd 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 1 st and 2 nd class
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Ravi Jain / 18-Apr-01/ 10 Copyright ©2001 Telcordia Technologies. All Rights Reserved. 1 1001 2001 3001 4001 5001 6001 7001 8001 9001 10000 Job ID 1 0.8 0.6 0.4 0.2 0 *, and Fraction of jobs in Low channel Simulation results Theoretical equilibrium * Fraction of jobs in Low channel Instantaneous value of * calculated by each job J = 1000, P H = 1.25 P L = 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
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Ravi Jain / 18-Apr-01/ 11 Copyright ©2001 Telcordia Technologies. All Rights Reserved. 0 0.2 0.4 0.6 0.8 1.0 43214321 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 P L vs. P L J L + P H (J - J L ) 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 , P L = 1, S = C = 1 wJ PMP for profit Service provider with Low channel of capacity at least
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Ravi Jain / 18-Apr-01/ 12 Copyright ©2001 Telcordia Technologies. All Rights Reserved. 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
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Ravi Jain / 18-Apr-01/ 13 Copyright ©2001 Telcordia Technologies. All Rights Reserved. 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
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