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EasyBid: Enabling Cellular Offloading via Small Players

Zhixue Lu1, Prasun Sinha1 and R. Srikant2

1The Ohio State University 2Univ. of Illinois at Urbana-Champaign

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Cellular Data Keeps Increasing

• Mobile Data Increases more than 60% Annually• Small Cells (Femtocells) Increase Spectrum Reuse

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Femtocells: the Concept

• Small in-home Cellular Base Station – connects to the service provider’s network

through owner’s broadband network

Femtocell

Broadband Router

Internet

Core Network

Femtocell Gateway

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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

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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

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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

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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!

= ?

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Assumptions

• Sellers Can Estimate With Bounded Errors– : True Valuation of f, Hidden Value– : Perceived Valuation of f, Exposed Value

– Distribution of is known• Truthful Auctions: Sellers Submit Perceived

Valuations Truthfully

𝑉 𝑓❑𝑉 𝑓

′

𝑉𝑚𝑎𝑥❑0

𝑉 𝑓❑𝑉 𝑓

′

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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

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Negative Utility of Femtocells

• Femtocell Owners: Negative Utility when < Payment < – G=14,Uniform in [0,10] ,=2– Reserve Price: x=$7– : $8, : $6– Negative utility: 7-8 = -1– Individual Rationality Violated

𝑥𝑉 𝑓

❑𝑉 𝑓′

0 8 10642

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Address Negative Utility Issue (Naïve)

• The WSP sets a reserve price $6, payment $8• Seller f wins and receives $8 if its bid ≤ 6

• Expected Utility of WSP: 3.6– = 3.6

Worst-case IR

𝑉 𝑓❑𝑉 𝑓

′0 8 106

Reserve Price

4

Payment

2

=2

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Imprecision Loss𝑉 𝑓

New Issue (Naïve): Imprecision Loss

• For Femtocell Owners:– , No loss even if – , Loss if > 6– , Loss if > 6

• Imprecision Loss (IL): Percentage of utility loss Due to Imprecision: 100%

𝑉 𝑓

No Imprecision Loss

0 8 1064Reserve Price Payment

2

No Imprecision Loss𝑉 𝑓

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Problem Definition

• M sellers, distribution of valuations knownProblem: maximize Subject to: Sellers are comfortable to submit imprecise valuations

Imprecision Loss𝑉 𝑓𝑉 𝑓

No Imprecision Loss

0 8 1064Reserve Price Payment

2

No Imprecision Loss𝑉 𝑓

1. The Worst-case Utility of any seller ≥02. Partial Truthfulness: percent do not lose any potential utility by submitting imprecise valuations3. Imprecision Loss: The expected utility loss for each user (in red) is bounded ()

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Solution: Multiple Reserve Prices

• Example: 2-reserve-price Approach:

– 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

0 4

S1 S2

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Payments:Pi

Approval Ratios: Ri

Segments: Si

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Multiple Reserve Prices In Imprecise Valuation Auction

• Two Reserve Prices

0 4 106

No Imprecision Loss Imprecision Loss

𝑉 𝑓 𝑉 𝑓 𝑉 𝑓

No Imprecision Loss

S1 S2

WSP’s Expected Utility 4.0 vs. 3.6 (Naïve)

Imprecision Loss 25% vs. 100%

Percent of Sellers in IL Range 40% vs. 40%

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Algorithm Sketch

• Input– (Saving of WSP)– (Estimation Error) – Distribution of – (Constraints)

• Output– $N$ Reserve Prices (Si, Ri, Pi, )

• Dynamic Programming based Algorithm: Pseudo-polynomial Time Complexity

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Example

$8

Seller #1

$6

$1

$3

BC D

E

Seller #2

Seller #3

Seller #4

A

Seller Seg# Ratio Pmt

#1 S1 1 8

#2 S2 2/3 10

#3 S2 2/3 10

#4 S1 1 8

0 4 106

𝑉 𝑓 𝑉 𝑓 𝑉 𝑓

S1 S2

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Simulation Result

• Precise Valuation– Near Optimal

• Imprecise Valuation– Increasing Decreases – D Decreases

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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.