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_at_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

• Internets 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
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 all links 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 format was preferred to
  Ascending-price format
• for several reasons

7
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
PF
VRR
Spare capacities
Spare capacities
Time
Time
12
Our Policies Improve 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 e, total
demand 2C0/3
(C)
V e/ 2
e'
(D)
Link 2 users valuations e, total demand C0

• Assumption truth-telling bidders
• Symmetric Pricing ? winners A, B, D
• VRR and PF ? winners A, C, D ? higher social
  welfare

13
Experiments Set-up

• Network topologies
• Linear
• Hierarchical
• Bidders utilities

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 2 links 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 sellers 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