their parallels to power Fernando Paganini . Universidad ORT, Uruguay - - PowerPoint PPT Presentation
Bandwidth auctions and their parallels to power Fernando Paganini . Universidad ORT, Uruguay . Outline: 1. Intro: resource allocation and pricing in comm networks. 2. Background on auctions. 3. Auctions for Internet bandwidth. 4. Connections
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LINK CAPACITY CO NSTRAINTS
SO URCE UTILITY
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Netw ork Utility M axim ization (Kelly ´98)
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Lagrange m ultiplier : congestion price" of link ( total price of route
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– Better dynamic properties (convergence, etc.) – Use other utility functions, achieving other notions of fairness.
– Routing – Medium access control (Scheduling, random access). – Physical layer control (power control, modulation,…)
– Bandwidth has been abundant, not crucial to optimally allocate it. – This control is faster than the human time-scale.
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Exam ple: sell 3 units, choose 3 highest bidders. Alternatives: Charge bid am ount: gives incentives for bidding below valuation. Vickrey-Clarke-G roves (VCG ) principle: charge users the loss
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In this case: presence of 2nd bidder changes others' total valuation from to Should charge It is shown VCG m akes it rational to reveal the true valuations. b b b b b b
Revenue Equivalence Theorem (Vickrey, M yerson, Riley-Sam uelson) Assum e: Risk neutral buyers, valuations draw n from a know n distribution. M echanism assigns objects to bidders w ith highest valuation. At Bayesian Nash equilibrium , all auction m echanism s yield the sam e expected revenue for the auctioneer.
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However, equivalence does not hold if buyers are risk averse, do not know the distribution, or do not have unbounded rationality. In such cases a first-price auction m ay give higher revenue than VCG .
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item s from low est offers (asks). e.g., buy 2 item s from offers 1, 2. VCG : pay to b buys .
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Based on 2011 paper in Computer Networks. Joint work with:
Scenario: a netw ork periodically auctions capacity. Users subm it bids for am ounts
A distributed algorithm m ust
M otivation: overlay for : ’00, ’0 , ’0 , ’0 , . ’0 prem ium services over the Internet. Related w ork Lazar Sem ret Shu Varaiya 3 Reichl W rzaczek 5 M aillé Tuffin 6 Courcoubetis et al 7.
– Optimize the value of accepted bids. – Charge 1st price, VCG would have high complexity (Maillé-Tuffin ´07). – Revenue equivalence argument.
– Bids submitted to “bandwidth brokers” distributed across the network. – Bidders need not know network topology, capacity, etc. – Brokers run a distributed algorithm to allocate the auction.
– Auctions are held periodically, for currently available capacity. – Service may be longer than the auction period, and reservations are in place: a connection, once assigned, cannot be displaced by future bids. – So the seller optimize over the risk of future bids: selling capacity now with a low bid can cause the rejection of a better bid in the future.
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Revenue from allocating bandw idth (first-price auction) piecew ise linear, concave function.
Interpolate to
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Network optim al revenue auction
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Integer program . Relaxation is a concave utility m axim ization as introduced in Kelly '98.
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Broker collects bids for this service: If w e adm it bids for a total rate the total revenue is . , 1 .
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w ith route price. Am ounts to selecting bids better than Com m unicate to links, w ho update pri argm ax ce s as
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Dual algo rithm
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n-Shroff '06, also useful for m ultipath case).
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: sell all currently available capacity. M ay m iss higher bids in the fu , ture.
M yopic policy
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W hat is the optimal policy?
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In sim ple exam ples, one-step ahead policy approxim ates well the optim al revenue.
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EXPECTED CURRENT CURRENT EXPECTED FUTURE NEXT STEP REVENUE CAPACITY CAPACITY REVENUE CONSTRAINT CONSTRAINT
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Netw ork utility m axim ization, w ith additional (step ahead) variables. Distributed im plem entation: dual algorithm , proxim al m ethod. Converges to fluid approxim ation, requires roundoff. Extends to m ultipath routing.
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D (dem and)
In deregulated wholesale electricity m arkets, auctions are carried out by the Independent System Operator (ISO) to buy power for, e.g. one day ahead dem a nd. auction of the type m entioned before, e xcept that pow er is divisible and m ay be offered in different Procur am oun e t m ent s.
quantity (M W )
unit price ($/MW h)
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Typically, a com m on m arket price is set. Possible choices:
Tw o-sided (supply-dem and) auctions also possible. Ref: Zim m erm an '2010.
– Optimize the value of accepted bids. – Charge 1st price, VCG would have high complexity (Maillé-Tuffin ´07). – Revenue equivalence argument.
– Bids submitted to “bandwidth brokers” distributed across the network. – Bidders need not know network topology, capacity, etc. – Brokers run a distributed algorithm to allocate the auction.
– Auctions are held periodically, for currently available capacity. – Service may be longer than the auction period, and reservations are in place: a connection, once assigned, cannot be displaced by future bids. – So the seller optimize over the risk of future bids: selling capacity now with a low bid can cause the rejection of a better bid in the future.
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– Offers associated with specific network buses. – ISO minimizes cost subject to meeting demand, and capacity constraints (the power being dispatchable). Prices become node-dependent (Locational Marginal Prices, LMPs). – Integer constraints present? – Underlying power flow more complex than convex constraints for the Internet case. Some papers use DC power flow. Recent developments (Lavaei-Low) on convexified OPF may be relevant here.).
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need not select cheapest If this is done, inconsistent
In Yan et al. (IEEE Pow er "Bid '08) an additive startup cost considered cost m inim izat . ion",
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to pay at the M CP (m kt clearing m arginal price). can reduce cost paid out. But, seem s an artifice of the paym ent ch oice.
"Paym ent cost m inim ization"
Startup costs do not represent correctly the m ultiple period case. Block bids for m ultiple intervals, increase auction com plexity. Perhaps a receding horizon policy can b e useful for this purpose.