Price Discovery at Network Edges

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

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

3. 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? SPECTS 2002

4. 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.. SPECTS 2002

5. 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 SPECTS 2002

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

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

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

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

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

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

12. Simulations (cont’d) SPECTS 2002

13. Simulations (cont’d) SPECTS 2002

14. 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. SPECTS 2002

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

16. Simulations (cont’d) SPECTS 2002

17. 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. SPECTS 2002