An Auction Mechanism for Bandwidth Allocation Over Paths

1. An Auction Mechanism for Bandwidth Allocation Over Paths Costas Courcoubetis, Manos Dramitinos, and George D. Stamoulis (gstamoul@aueb.gr) Department of Informatics, Athens University of Economics and Business and Institute of Computer Science, Foundation for Research and Technology Hellas ITC-17, Salvador da Bahia, Brazil - December 2001 Work supported by EU's IST project “Market Managed Multiservice Internet” - M3I

2. Motivation • Internet’s growth has increased the need for bandwidth • Traditional, long-term, static bandwidth contracts are not so popular anymore • Increased need for short-term, dynamically requested bandwidth contracts • A new market-aware bandwidth trading mechanism is needed

3. Auctions • Popular trading mechanism • Fast, fair, possibly efficient, reliable and transparent way of setting “market” price • They reveal the actual market demand • Ideal for diverse and scattered users • e.g. users around Internet • There exist various single and multi-unit auction mechanisms • English, Dutch, Vickrey, 1st price sealed bid, etc

4. Open Single-unit Auctions • English auction: • ascending bids, open-outcry • terminates when only one bidder is left • much information regarding demand is revealed • Dutch auction: • descending price, open-outcry • terminates when some bidder shouts “mine” • limited information regarding demand is revealed

5. reserve equalbandwidth The Problem • Develop an auction mechanism for allocation of bandwidth over paths of a network, aiming to: • exploit and satisfy demand for bandwidth, as much as possible • for path-bidders: reserve the same quantity of bandwidth at alllinks of the path • Assumption: • usage of bandwidth by different users is synchronized

6. Possible Approaches and Choices • Independent auctions for individual links was preferred to Combinatorial networkwide auction • due to simplicity and scalability reasons • Open format was preferred to Sealed bid • due to information revelation, path bidders can develop an effective strategy • Descending-price formatwas preferred toAscending-price format • for several reasons

7. Link 1 Link 2 Ascending vs Descending Auctions • Ascending auctions: bidders place bids as price per Mbps increases • Uncertainty for bidders w.r.t. final outcome until the end • Wasteful for path-bidders • Descending (Dutch) auctions:as price per Mbps drops, the bids placed are directly translated to allocations • no uncertainty for bidders w.r.t. final outcome Unknownoptimal pair of prices p1 p2

8. Our Solution: MIDAS • Multi-unit Independent Dutch AuctionS • A high initial price (per Mbps) is set at each link, depending on its capacity • All prices are progressively reduced asymmetrically, according to the demand already expressed • When a bid is placed, the network resources demanded are immediately allocated • Assume“pay-your-bid” payments to be revisited Path formation facilitated

9. Price Reduction Policies (I) • “Variable Reduction Rates”: • The price reduction rate at each link depends on spare capacity • Reduction rates at different links are ordered inversely than spare capacities • Faster decrease of prices at links with lower demand expressed so far

10. Price Reduction Policies (II) • “Price Freezing”: • The price at each link is reduces at fixed rate, but • after an allocation, the price “freezes” for time proportional to the quantity of bandwidth allocated • Prices of different links are ordered inversely than spare capacities, except for periods of freezing • prices reflect market demand better than under the Variable Reduction Rates policy

11. Example: Auction Trajectory under the VRR and the PF Policies Prices Prices Link 1 Link 2 Link 1 Link 1 Link 2 VRR PF Spare capacities Spare capacities Time Time

12. Link 1 Link 2 Our Policies Improve Social Welfare • Assumption: truth-telling bidders • Symmetric Pricing  winners: A, B, D • VRR and PF  winners: A, C, D higher social welfare (A) 3V Link 1 users: valuation 3V, total demand = C0/3 Mean valuation per Mbps and per hop V (B) Link 1 users: valuation V, total demand = 2C0/3 Path users: valuation 2V – ε, total demand = 2C0/3 (C) V – ε/ 2 ε' (D) Link 2 users: valuations ε’, total demand = C0

13. Network topologies Linear Hierarchical Bidders’ utilities guaranteed linear elastic Experiments’ Set-up

14. Evaluation of MIDAS Policies with Truth-telling Bidders (I)

15. Evaluation of MIDAS Policies with Truth-telling Bidders (II) • “Price Freezing” policy • More efficient w.r.t. social welfare • “Variable Reduction Rates” policy • Faster • Small sacrifice in efficiency • The optimal (most efficient) outcome for a network of 2links can be computed exactly • MIDAS policies approach optimal social welfare, typically within 5%

16. Work in Progress: Payment Rules and their Impact • The payment rule affects: • bidders’strategies, especially when there they receive feedback on auction trajectory • efficiency and seller’s revenue • An incentive compatible payment rule is needed • bidders do not benefit when not truthful • Pay-your-bid: simple but leads to bid-shading • Stop-out pricing: Each bidder is charged per link at the price of the last winning bid for this link • currently under investigation, both analytically and experimentally

17. Conclusions • Presented an auction-based approach (MIDAS) for bandwidth allocation over paths. MIDAS: • solves simply and fairly a complicated problem • has low message- and computational overhead • performs very well in terms of efficiency • is transparent and scalable • was already implemented in a software prototype • Work in progress concerns payment rules and their impact on MIDAS due to strategic bidding