1. Price Discovery at Network Edges G. S. Arora, M. Yuksel, S. Kalyanaraman, T. Ravichandran and A. Gupta Rensselaer Polytechnic Institute, Troy, NY

2. SPECTS 2002 Overview Motivation Edge-to-Edge Concepts Price Discovery Framework Pricing Schemes Simulations Summary

3. SPECTS 2002 Motivation Need for new economic models Adaptive, particularly congestion, pricing is necessary Implementation problems need to be solved: Upgrades should be limited Administrative access is necessary Can we do it only at network edges?

4. SPECTS 2002 Edge-to-Edge Concepts A generic view and the trend for the Internet. Administrative access is available at edges. So, possible to coordinate ingress and egress edge stations. A more complex version of Clark’s Edge Pricing is possible..

5. SPECTS 2002 Price Discovery Framework Given edge-to-edge coordination, estimate edge-to-edge capacity. Congestion pricing  Pricing of edge queue. Severity of congestion is the ratio. Is this ratio really a good parameter? Formulate objective function Regression analysis for unknown variables of the objective function

6. SPECTS 2002 Price Discovery Framework (cont’d) Let there be k observations in a contract period. User adaptation: Actual spent budget for user with reservation price :

7. SPECTS 2002 Price Discovery Framework (cont’d) Objective: Minimize non-utilized capacity while keeping edge queue less than a pre-defined value. Formulation: subject to

8. SPECTS 2002 Price Discovery Framework (cont’d) Other than B k everything else is known. For k=1000, q max =50, C k ~ N(98,2) truncated in the range [96,100]: Regression analysis for B k ~ U(20,50) and B k ~ U(30,150) verified that q i /C i,mean is strongly associated with optimal price p i *. So, we can use the predictor q i /C i,mean to determine p i in adaptive pricing at the edge.

9. SPECTS 2002 Pricing Schemes Assuming that ISP wants to keep edge queue in the range [q l, q h ]. Proportional Increase Proportional Decrease (PIPD): Proportional Increase Additive Decrease (PIAD):

10. SPECTS 2002 Pricing Schemes (cont’d) Additive Increase Additive Decrease (AIAD): Additive Increase Proportional Decrease (AIPD):

11. SPECTS 2002 Simulations Define user demand according to reservation price and : Initial parameters: Step increase in demand: In times (50, 100), i.e.

12. SPECTS 2002 Simulations (cont’d)

13. SPECTS 2002 Simulations (cont’d)

14. SPECTS 2002 Simulations (cont’d) PIPD and PIAD performs significantly better than AIPD and AIAD. Compared to PIPD, PIAD has less variation in price but utilization is slightly less too. So, the best one is either PIAD or PIPD, depending on value of utilization.

15. SPECTS 2002 Simulations (cont’d) Investigated effect of several parameters on PIAD performance. We run two users with different and reservation prices: =

16. SPECTS 2002 Simulations (cont’d)

17. SPECTS 2002 Summary Adaptive (particularly congestion) pricing is necessary for enabling better economic models. Price Discovery: Deployable over diff-serv Possible to implement congestion pricing at edges Possible to develop variety of pricing schemes: PIPD, PIAD, AIPD, AIAD.