EasyBid: Enabling Cellular
Offloading via Small Players
Zhixue Lu1, Prasun Sinha1 and
R. Srikant2
1The
Ohio State University
2Univ. of Illinois at Urbana-Champaign
1
Cellular Data Keeps Increasing
• Mobile Data Increases more than 60% Annually
• Small Cells (Femtocells) Increase Spectrum Reuse
2
Femtocells: the Concept
• Small in-home Cellular Base Station
– connects to the service provider’s network
through owner’s broadband network
Femtocell
Internet
Broadband Router
Femtocell
Gateway
Core Network
3
Femtocells: the Facts
• To Deploy Cellular Base Stations
– Site, Backbone and Power Supply
– Costly to deploy
• 7.9 Million Femtocells Deployed by 2013
– Almost all are residential and enterprise (small
owners) Femtocells
• Acquiring Access to these Femtocells is
Important
4
Proposed Incentive Mechanism:
Auction
• Why Auction? : Fair and Efficient
• Two Types of Auctions
– Forward Auction: buyers bid
– Reverse Auction: sellers bid
• Consider a Reverse Auction Model
– Buyer: the wireless service provider (WSP)
– Sellers: the femtocell owners
– Reason: most owners have only one femtocell
5
Background
• Desired Properties of Auctions
– Truthfulness: bidders cannot get higher utility by
lying
– Individual Rationality: utility of any bidder ≥0
• Common Auction Mechanisms
– Secondary price auction
– Reserve price based secondary auction
6
Imprecise Valuation: an Ignored
Problem
• Existing Works Assume Precise Valuations
• Valuations of Femtocell Owners Depend On:
– Cost of extra broadband traffic, electricity usage
– Degree of overload/delay tolerance
– Wiliness to provide service
– May vary over time
• Hard to Precisely Estimate
+
= ?
+
No Delay!
7
Assumptions
• Sellers Can Estimate With Bounded Errors
– 𝑉𝑓 : True Valuation of f, Hidden Value
– 𝑉𝑓′ : Perceived Valuation of f, Exposed Value
– |𝑉𝑓′ − 𝑉𝑓 | ≤ 𝜀, ∀𝑓
– Distribution of 𝑉𝑓 is known
𝑉𝑓′
0
𝑉𝑓
𝑉𝑓′
𝑉𝑓
𝑉𝑚𝑎𝑥
• Truthful Auctions: Sellers Submit Perceived
Valuations Truthfully
8
Basic Form of Auctions in the Paper
• Consider Reserve-Price based Secondary Auction
– Secondary auction: truthful with precise valuations
– Reserve price: eliminate errors (uncertainties) in
payments
• How It Works
–
–
–
–
–
Consider one seller a time
WSP sets a reserve price x
The Femtocell owner places its bid
Auction succeeds and pay x to the owner if the bid ≤ x
Utility of WSP is G-x, G: the savings of the WSP on
each unit of data offloading
9
Negative Utility of Femtocells
• Femtocell Owners: Negative Utility when
𝑉𝑓′ < Payment < 𝑉𝑓
– G=14, 𝑉𝑓 Uniform in [0,10] , 𝜀=2
– Reserve Price: x=$7
– 𝑉𝑓 : $8, 𝑉𝑓′ : $6
– Negative utility: 7-8 = -1
– Individual Rationality Violated
𝑥
0
2
4
𝑉𝑓′
6
𝑉𝑓
8
10
10
Address Negative Utility Issue (Naïve)
• The WSP sets a reserve price $6, payment $8
• Seller f wins and receives $8 if its bid ≤ 6
Worst-case IR
• Expected Utility of WSP: 3.6
– 𝐸(𝑈𝑤𝑠𝑝 ) =
8−2
10
× (14 − 8) = 3.6
Reserve Price
0
2
4
6
𝑉𝑓′
Payment
10
8
𝜀=2
𝑉𝑓
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New Issue (Naïve): Imprecision Loss
• For Femtocell Owners:
– 𝑉𝑓 ∈ 0,4
⇨ 𝑉𝑓′ ≤ 6, No loss even if 𝑉𝑓′ ≠ 𝑉𝑓
– 𝑉𝑓 ∈ 4,8
∃ 𝑉𝑓′ > 6, Loss if 𝑉𝑓′ > 6
– 𝑉𝑓 ∈ 8,10 ⇨ 𝑉𝑓′ ≥ 6, Loss if 𝑉𝑓′ > 6
Imprecision Loss
No Imprecision Loss
𝑉𝑓
𝑉𝑓
4
6
0
2
Reserve Price
No Imprecision Loss
𝑉𝑓
8
Payment
10
• Imprecision Loss (IL): Percentage of utility loss
Due to Imprecision: 100%
12
Problem Definition
• M sellers, distribution of valuations known
Problem:
maximize 𝑈𝑤𝑠𝑝
Subject to: Sellers are comfortable to submit
imprecise valuations
1. The Worst-case Utility of any seller ≥0
2. Partial Truthfulness: 𝛼 percent do not lose any
potential utility by submitting imprecise valuations
3. Imprecision Loss: The expected utility loss for each
user (in red) is bounded (𝛽)
Imprecision Loss
No Imprecision Loss
𝑉𝑓
𝑉𝑓
4
6
0
2
Reserve Price
No Imprecision Loss
𝑉𝑓
8
Payment
10
13
Solution: Multiple Reserve Prices
Segments: Si
• Example: 2-reserve-price Approach:
S1
0
S2
Payments:
Pi
10
4
– if bid ∈ [0,4), approve and pay $8
– if bid ∈ [4,10], approve with probability 2/3 and
pay $10 if it is approved
• Truthful and IR with Precise Valuations
Approval
Ratios: Ri
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Multiple Reserve Prices In Imprecise
Valuation Auction
• Two Reserve Prices
No Imprecision Loss
𝑉𝑓
No Imprecision Loss
𝑉𝑓
Imprecision Loss
𝑉𝑓
0
4
10
6
S1
𝑅1 = 1, 𝑃1 = 8
S2
2
𝑅2 = 3 , 𝑃2 = 10
WSP’s Expected Utility
4.0 vs. 3.6 (Naïve)
Imprecision Loss
25% vs. 100%
Percent of Sellers in IL Range 40% vs. 40%
15
Algorithm Sketch
• Input
– 𝐺 (Saving of WSP)
– 𝜀 (Estimation Error)
– Distribution of 𝑉𝑓
– 𝛼 and 𝛽 (Constraints)
• Output
– $N$ Reserve Prices (Si, Ri, Pi, ∀ 𝑖 ∈ {1 … 𝑁})
• Dynamic Programming based Algorithm:
Pseudo-polynomial Time Complexity
16
Example
𝑉𝑓
𝑉𝑓
𝑉𝑓
4
0
10
6
S1
S2
2
𝑅1 = 1, 𝑃1 = 8
𝑅1 = 3 , 𝑃2 = 10
Seller #2
Seller #4
$6
A
$1
C
B
$8
$3
D
E
Seller
Seg#
Ratio
Pmt
#1
S1
1
8
#2
S2
2/3
10
#3
S2
2/3
10
#4
S1
1
8
Seller #1
Seller #3
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Simulation Result
• Precise Valuation
– Near Optimal
• Imprecise Valuation
– Increasing 𝛼 Decreases 𝑈𝑤𝑠𝑝
– Decreasing 𝛽 Decreases 𝑈𝑤𝑠𝑝
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Summary
• EasyBid: A Reverse Auction Mechanism for
Acquiring Access to Femtocells
– Introduce the notion of Perceived Valuation,
Partial Truthfulness, and Imprecision Loss to
characterize the quality of auctions with imprecise
valuations.
– Present heuristic algorithms to maximize the
WSP’s utility while satisfying given constraints on
partial truthfulness and imprecision loss.
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