Create Presentation
Download Presentation

Download Presentation

Simplification of Network Dynamics in Large Systems

Download Presentation
## Simplification of Network Dynamics in Large Systems

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Simplification of Network Dynamicsin Large Systems**Xiaojun Lin, Ness Shroff Presented by Shengbo Chen 5/6/2011**Outlines**• Introduction • System model • Problem statement • Main result • Conclusion**Introduction**• Large Networks • Internet • Power network • Network Pricing • Dynamic pricing: charge different prices to the users according to the current utilization level of the network and also other factors • Better performance • Static pricing: price is independent of the current network utilization • Do not require instantaneous load information • Only depends on average parameters • Less overhead and computation**System model**• Network with L links • Link capacity • I users • Price • Poisson arrivals with rate • Resource cost • Feasible States where is the number of flows, and is the routing matrix**System model (contd’)**• Service time • Dynamic pricing function where is an increasing sequence of positive numbers**Problem Statement**• Revenue maximization where pik is the probability that the service time Ti is in the segment [ak-1,ak)**Upper and Lower Bounds**• Upper bound • Lower bound**Scaling Laws**• Scaling Laws 1 • Scaling factor c: increasing sequence to infinity • Scaling Laws 2 • Scaling with topology changes Number of links, number of classes, routing matrix**Main Result**• Under the scaling law 1 • Under the scaling law 2 • Dynamic routing does not help The static prices induced by the upper bound are in fact asymptotically optimal The static prices induced by the upper bound is not asymptotically optimal**Intuition & Implication**• The upper bound has the average constraint, which is the loosest. • Strong Law of Large Number • Sands in a can • Implications • An appropriately chosen static scheme can approach that of the optimal dynamic scheme when the system is large • Telephone networks • Smart grid**Future work**• Delay tolerant task?**Conclusion**• An appropriately chosen static scheme can approach that of the optimal dynamic scheme when the system is large • Static pricing scheme: lack of adaptivity • Dynamic pricing scheme: different from the duality-based scheme**Thank you!**13