optimizing providers’ profit in peer networks …...optimizing providers’ profit in peer...

OptimizingOptimizingOptimizingOptimizingProviders’ Profit in Peer NetworksProviders’ Profit in Peer NetworksProviders’ Profit in Peer NetworksProviders’ Profit in Peer Networks

ApplyingApplyingApplyingApplyingAutomatic Pricing and Game TheoryAutomatic Pricing and Game TheoryAutomatic Pricing and Game TheoryAutomatic Pricing and Game Theory

PhD Defense Presentation

Sohel KhanOctober 24, 2005

2

1. Introduction2. Automatic Price Transaction Architecture3. Providers’ Profit Optimization Method

• Select Strategic Price by Game Theory• Minimize Congestion Cost by Optimum Routing• Guarantee QoS by Traffic Engineered Network Design

4. Result5. Conclusion6. Appendix

Outline of the PresentationOutline of the PresentationOutline of the PresentationOutline of the Presentation

3

• Existing Customer-Provider peer architecture and protocols do not support – Automatic price transaction – Customers’ option to select any provider based on competitive service

price– Customers’ option to broadcast their budget– Providers’ automatic mechanism to compute price and optimize Profit

• In competitive market• In dynamic Internet traffic demand

• Therefore, the problem is to develop– Automatic price-transaction based network architecture – A provider’s model that compute competitive price and optimize Profit– Demonstrate the advantages of the architecture and the model through

analysis

Introduction: Problem StatementIntroduction: Problem StatementIntroduction: Problem StatementIntroduction: Problem Statement

4

• This research proposes– A new Price transaction Architecture

• “Automatic Price Transaction-based One-to-Many Peer Network Architecture”

– A new providers’ Profit optimization model• “Providers Optimized Game in Internet Traffic Model”

– An algorithm • That implements the model in the architecture

• This research demonstrates– The validity of the model– Advantage of the model

• Customer Benefit• Providers’ Benefit

– Providers’ Profit optimization method– Examples of TE applications

Introduction: Proposed SolutionIntroduction: Proposed SolutionIntroduction: Proposed SolutionIntroduction: Proposed Solution

5

This Research:• Develops the Architecture

– Wire-line and wireless options– Study only wire-line option

• Develops the Model and Algorithm– Determines strategically appropriate price

• By Game Theory

– Minimizes the network congestion sensitive cost• By optimum Routing technique

– Non-linear optimization method» The Gradient Projection Algorithm and the Golden Section Line Search

– Guarantees service quality• By Designing Traffic Engineered Network

• Evaluates performance by– Mathematical Analysis – Simulation Study

• Studies the followings:– Advantages– Profit Optimization Strategies – Applications

Introduction: Research MethodIntroduction: Research MethodIntroduction: Research MethodIntroduction: Research Method

6

• Significant Internet pricing research– In monopoly market– Congestion sensitive pricing

• Service per Customer’s bid • Static Congestion Game

– Game theory • Internet Pricing: Monopoly market• Congestion Issues: Monopoly market• Peer providers in Series

• Industry Standard Activity– 3GPP Wireless Price Model– ATIS/PTSC wireline IP Peering– IETF wireline VoIP Peering

• On-line Exchange Research (Bandyopadday model)– We extend this model (Details later)

• Price-Transaction based mechanism– One provider network

Related ResearchRelated ResearchRelated ResearchRelated Research

7

• Automatic price transaction in one-to-many peer network– New idea of pricing in peer networks– Extends various industry standards

• Majority research are in monopoly market– We study Oligopoly market

• Provider’s Profit optimization in oligopoly market– New method in internet pricing and Profit optimization

• Network Model– A complex network, bi-directional links, multiple paths, OD&DO call legs

• Oligopoly Model– Bandyopadhyay et al. model

• Based on Bertrand Model and “Model of Sale” example• Symmetric market

– All parameters are fixed• Commodity is not internet bandwidth• Two step static game of incomplete information• Homogeneous service• Uses Reinforcement Learning (RL) in simulation to determine best strategy

– Our model• Extension to Bandyopadhyay et al. model• Asymmetric market

– Some parameters are sensitive to the dynamic nature of Internet traffic• Commodity bandwidth• “Myopic” Markovian static game of incomplete information• Heterogeneous service• An analytical framework to determine the best strategy in dynamic internet traffic

Distinguishing Characteristics of our ApproachDistinguishing Characteristics of our ApproachDistinguishing Characteristics of our ApproachDistinguishing Characteristics of our Approach

8

• Developed a New price transaction architecture that benefits customers and providers

– By Automation– By providing options to select any provider based on competitive price– By allowing customer power to specify budget– By introducing new price transaction research in one-to-many architecture

• Developed a mathematical model for providers to– To compute competitive price through the best strategy– Optimize Profit in dynamic internet traffic demand

• Developed an algorithm and simulation model– To verify and study providers’ game in flexible environment

• Introduced a New framework to determine Bayesian-Nash equilibrium – In dynamic internet traffic demand

• Demonstrated that:– Providers improved their Profit

• Our approach yielded relative advantages over the existing Bertrand Oligopoly Model– Providers determined Best strategies (Bayesian-Nash equilibrium and Pareto-efficient

outcome) using our approach– Providers was able to obtain fair market share of Profit and throughput– Providers could implement TE applications such as optimized load balancing in the network– Customers could enjoy market price lower than their budgets.

• Introduced new area in Internet pricing research– Our research is the first in Internet Oligopoly pricing research for disjoint providers– Existing research are for monopoly market

• Introduced pricing research in a complex network model– Bi-directional links, multiple paths, Origin-Destination and Destination-Origin Call Legs.

Introduction: ContributionsIntroduction: ContributionsIntroduction: ContributionsIntroduction: Contributions

9

Blue.com

Red.com

Chicago.Enterprise.com

[email protected]

NewYork.Enterprise.com

Atlanta.Enterprise.com

SIP User Agents (UA)

SIP Phone

PCSIP Mobile


SIP Phone

PCSIP Mobile

[email protected]

Dallas.Enterprise.com

Session Control Function (e.g. SIP proxy)

Bearer Function (e.g. IP Router)

Security Function (e.g. Firewall)

Peering

Does Not SupportAutomatic Price Transaction Functions

Enterprises do not gain pricing advantage in provider selection

Current Managed IP Peering ArchitectureCurrent Managed IP Peering ArchitectureCurrent Managed IP Peering ArchitectureCurrent Managed IP Peering Architecture

RR

10

Blue.com

Red.com


[email protected]




SIP Phone

PCSIP Mobile


SIP Phone

PCSIP Mobile

[email protected]

Dallas.Enterprise.comPeering

Analyst

Analyst

Price Broker

Price Broker

Price Broker

Price Broker

Presence server

Proposed Proposed Proposed Proposed Automatic Price TransactionAutomatic Price TransactionAutomatic Price TransactionAutomatic Price Transaction----based 1:M Peer Network Architecturebased 1:M Peer Network Architecturebased 1:M Peer Network Architecturebased 1:M Peer Network Architecture




Our architecture allows an enterprise customer Our architecture allows an enterprise customer Our architecture allows an enterprise customer Our architecture allows an enterprise customer to automatically shop from multiple providers to automatically shop from multiple providers to automatically shop from multiple providers to automatically shop from multiple providers based on the service price they offer.based on the service price they offer.based on the service price they offer.based on the service price they offer.

11

Architecture: ATIS/PTSC IP (wireline) Peering Reference DiagramArchitecture: ATIS/PTSC IP (wireline) Peering Reference DiagramArchitecture: ATIS/PTSC IP (wireline) Peering Reference DiagramArchitecture: ATIS/PTSC IP (wireline) Peering Reference Diagram

ProviderA

ProviderA

ProviderB

ProviderB

CCFE CCFECRFE CRFEBFE BFE

CCFE: Call Control Functional EntityCRFE: Call Routing Functional EntityBFE: Bearer Functional Entity

Signaling Plane

Routing Plane

Bearer Plane

Current ATIS PTSC IP NNI Architecture specifies:• One-to-one peer interface• No pricing architecture is supported

12

Blue.comBlue.com

Red.comRed.com

CustomerRegion#1

CustomerRegion#1

CustomerRegion#3

CustomerRegion#3

Enterprise C

CCFEE-LSR

CCFEE-LSR

CCFEE-LSR

CustomerRegion#2

CustomerRegion#2

Enterprise B

CustomerRegion#4

CustomerRegion#4

Enterprise A

CCFEE-LSR

Enterprise D

CCFEE-LSR

Analyst

BrokerPresence

Analyst

CCFEE-LSR

Broker

CCFEE-LSR

Broker

CCFEE-LSR

Broker

Presence

Presence

Presence

Current ATIS PTSC IP NNI Architecture specifies:• One-to-one peer interface• No pricing architecture is supported

Our extension enhances ATIS Architecture to• One-to-Many peer interface• Automatic Price Transaction

Our Extension to ATIS ArchitectureOur Extension to ATIS ArchitectureOur Extension to ATIS ArchitectureOur Extension to ATIS Architecture

Red.comRed.comEnterprise C

CCFEE-LSR

CustomerRegion#4

CustomerRegion#4

Enterprise D

CCFEE-LSR

Analyst

CCFEE-LSR

Broker

CCFEE-LSR

Broker

Presence Presence

Red.comRed.comEnterprise C

CCFEE-LSR

CustomerRegion#4

CustomerRegion#4

Enterprise D

CCFEE-LSR

Analyst

CCFEE-LSR

Broker

CCFEE-LSR

Broker

Presence Presence

13

P -C S C F

P C S to w e r

P C S to w e r

P C S to w e r

O th e rIM S

F u n c t io n s

O n lin eC h a r g in g

S y s te m

P -C S C F

P C S to w e r

P C S to w e r

P C S to w e r

O th e rIM S

F u n c t io n s

O n lin eC h a r g in g

S y s te m

SessionChargingFunction

RatingFunction

EventChargingFunction

BearerChargingFunction

CorrelationFunction

SessionChargingFunction

RatingFunction

EventChargingFunction

BearerChargingFunction

CorrelationFunction

3GPP On-line Charging System (WOP)

Charging Architecture

Current 3GPP Architecture specifies One-to-one customer-providerOnline charging architecture (work on progress)Does not support one-to-many model

Current 3GPP (Wireless) IMS Charging Architecture Current 3GPP (Wireless) IMS Charging Architecture Current 3GPP (Wireless) IMS Charging Architecture Current 3GPP (Wireless) IMS Charging Architecture

14

Our Extension supportsOur Extension supportsOur Extension supportsOur Extension supports• OneOneOneOne----totototo----many modelmany modelmany modelmany model• Allows automatic price negotiationAllows automatic price negotiationAllows automatic price negotiationAllows automatic price negotiation• Allows providers to compute competitive price Allows providers to compute competitive price Allows providers to compute competitive price Allows providers to compute competitive price

P-CSCF: Proxy-Call Session Control FunctionIMS: Internet Multi-media subsystem

Current 3GPP Architecture supports• One-to-one model• Does not allow price negotiation• Does not allows providers to compute competitive price

Our Extension to the 3GPP (Wireless) IMS ArchitectureOur Extension to the 3GPP (Wireless) IMS ArchitectureOur Extension to the 3GPP (Wireless) IMS ArchitectureOur Extension to the 3GPP (Wireless) IMS Architecture

P - CSCF

PCS tower

PCS tower

OtherIMS

Functions

OnlineCharging

System

Blue.Com

P - CSCF

PCS tower

PCS tower

OtherIMS

Functions

OnlineCharging

System

AnalystAnalystBlue.Com

P - CSCF

PCS tower

PCS tower

OtherIMS

Functions

OnlineCharging

System

AnalystRed.Com

P - CSCF

PCS tower

PCS tower

OtherIMS

Functions

OnlineCharging

System

AnalystRed.Com

PriceBroker

15

The Protocol is analogous to theThe Protocol is analogous to theThe Protocol is analogous to theThe Protocol is analogous to theSealedSealedSealedSealed----BidBidBidBid----Reverse Auction.Reverse Auction.Reverse Auction.Reverse Auction.Customers has power to specify the highest priceCustomers has power to specify the highest priceCustomers has power to specify the highest priceCustomers has power to specify the highest price

EnterpriseBroker

Presence(CCFE)

Presence(CCFE)

Presence(CCFE)

(1)

I Want a Price of a Session

Class: S, BW: B;

I am willing to Pay ?

(1)I Want a Price of a Session

Class: S, BW: B;



Class: S, BW: B; I am willing to Pay ?

(4)Enterprise

SelectsBlue.comBecause

P2=Min(P 1, P2, P3)

Analyst

Analyst

Analyst

Provider: Red.com

Provider: Blue.com

Provider: Green.com

CustomerBroker

Presence(CCFE)

Presence(CCFE)

Presence(CCFE)

(1)

I Want a Price of a Session

Class: S, BW: B;



Class: S, BW: B;



Class: S, BW: B; I am willing to Pay ?

(3)

The Price is P 11

(3)The Price is P 2

(3)The Price is P 2

(3)The Price is P3

(3)The Price is P3

(4)Enterprise

SelectsBlue.comBecause

P2=Min(P 1, P2, P3)

(5)Enterprise

InitiatesSession

With Blue.com

(5)Enterprise

InitiatesSession

With Blue.com

Analyst

Analyst

AnalystAnalyst

Provider: Red.com

Provider: Blue.com

Provider: Green.com

Proposed Price Transaction ProtocolProposed Price Transaction ProtocolProposed Price Transaction ProtocolProposed Price Transaction Protocol

(2)Compute Price P1

by proposedGame of Oligopoly

(2)Compute Price P2


(2)Compute Price P3


16

BobUA

Region Jayhawk CCFE(Broker, Forking Proxyand B2BUA)

Provider CCFE(Presence andProxy Server)

AliceUA

Region WildcatProxy Server

Blue.com

Red.com

EnterpriseRegion

JayhawkEnterpriseRegion

Wildcat

(1) INVITESIP: [email protected]

(2) 200 OK (3) SUBSCRIBE Class: Platinum,BW: 10 Mbps, Res Price: $100

Provider Analyst

(4) 200 OK

(4) 200 OK

(5) NOTIFY Price: $85

(5) NOTIFY Price: $75

(6) INVITE SIP: [email protected]

(7) 200 OK

(8) INVITESIP: [email protected]

(9) 200 OK(10) INVITESIP: [email protected]

(3) SUBSCRIBE Class: Platinum,BW: 10 Mbps, Res Price: $100

(11) 200 OK(12) 180 Ringing

(13) ACK

Media Session(14) BYE

(15) 200 OK

Query

Response

Query

Response

Example: Session Initiation Protocol (SIP) Call Flow (sketch)Example: Session Initiation Protocol (SIP) Call Flow (sketch)Example: Session Initiation Protocol (SIP) Call Flow (sketch)Example: Session Initiation Protocol (SIP) Call Flow (sketch)

17

Blue.comBlue.com

Red.comRed.com

CustomerRegion#1

CustomerRegion#1

CustomerRegion#3

CustomerRegion#3

Enterprise C

E-LSR

E-LSR

E-LSR

CustomerRegion#2

CustomerRegion#2

Enterprise B

CustomerRegion#4

CustomerRegion#4

Enterprise A

E-LSR

Enterprise D

E-LSR

Analyst

Analyst

E-LSR

E-LSR

E-LSR

Many other variants of the proposed Architecture are possible(See Table 2.1)

Computes Price P1By Proposed

Game of Oligopoly( = Maximum Price)

Computes Price P2By Proposed

Game of Oligopoly( = Maximum Price)

Border Gateway Protocol (BGP)

updates routing table with price as a routing cost

parameter

E-LSR performs Least cost routing

Based on min(p1, p2)

Architecture: BGP ImplementationArchitecture: BGP ImplementationArchitecture: BGP ImplementationArchitecture: BGP Implementation

18

Blue.com

Red.com


[email protected]




SIP Phone

PCSIP Mobile


SIP Phone

PCSIP Mobile

[email protected]

Dallas.Enterprise.comPeering

Analyst

Analyst

Price Broker

Price Broker

Price Broker

Price Broker

Presence server

Proposed Proposed Proposed Proposed Automatic Price TransactionAutomatic Price TransactionAutomatic Price TransactionAutomatic Price Transaction----based 1:M Peer Network Architecturebased 1:M Peer Network Architecturebased 1:M Peer Network Architecturebased 1:M Peer Network Architecture




Our architecture allows an enterprise customer Our architecture allows an enterprise customer Our architecture allows an enterprise customer Our architecture allows an enterprise customer to automatically shop from multiple providers to automatically shop from multiple providers to automatically shop from multiple providers to automatically shop from multiple providers based on the service price they offer.based on the service price they offer.based on the service price they offer.based on the service price they offer.

19

NSP1NSP1

1

3 4

2100

100

100 100

100

100

CustomerRegion#1(Chicago)

CustomerRegion#1(Chicago) 300

300

CustomerRegion#3

(Dallas)

CustomerRegion#3

(Dallas)

300

300

CustomerRegion#2

(NewYork)

CustomerRegion#2

(NewYork)

300

CustomerRegion#4

(Atlanta)

CustomerRegion#4

(Atlanta)

300

300

NSP1NSP1

1

3 4

2100

100

100 100

100

100

1

3 4

2100

100

100 100

100

100



300

CustomerRegion#3

(Dallas)

CustomerRegion#3

(Dallas)

300

300

CustomerRegion#2

(NewYork)

CustomerRegion#2

(NewYork)

300

CustomerRegion#4

(Atlanta)

CustomerRegion#4

(Atlanta)

300

300

E-LSR

E-LSRE-LSR

E-LSR

Internal Network of Each Provider of our studyInternal Network of Each Provider of our studyInternal Network of Each Provider of our studyInternal Network of Each Provider of our studyNodes are fully meshedEach O-D Pair is connected with five alternative LSPsThere are 60 LSPs in each networkEach call has two legs: O-D and D-O

Single Integrated Queue per output linkFirst-in-First-Out (FIFO) non-preemptive Scheduling scheme

20

• Packet:– Arrival Pattern: Poisson Distributed– Mean Service Rate: Exponentially Distributed– Aggregate arrival distribution: Poisson– Aggregate mean service rate distribution: Hyper-exponential– Queue Theory Model

• M/G/1

• For Traffic Engineering, we will use M/G/1• For Cost Analysis, we will approximate with M/M/1

• Session: (No Queuing)– Arrival Pattern: Poisson Distributed– Mean Service Rate: Exponentially Distributed

• Assumed Traffic Mix– Homogeneous: Gold– Heterogeneous Class: Platinum, Gold, and Silver

• The service class is differentiated by cost coefficient parameter.• Cost coefficient parameter depends on the type of protocol and Intelligence used• Example: Level of Security guarantees, addressing (IPv4 vs. IPv6), type of DSP• Cost coefficient parameter distinguishes Service Class (Plat, Gold, Silver)

Traffic ModelTraffic ModelTraffic ModelTraffic Model

21

• Our method of Providers’ Profit Optimization:

– Design Traffic-Engineered Network to Guarantee QoS

– Minimize congestion sensitive cost (Y)

– Select strategically appropriate price by Game Theory

• to maximize revenue (pY)

: ( ) ( )Unit Utility at steady state u p p Yω= −

( )( ) ( )

( )

( ) ( )

Max p Y

Max pY Max Y Max p

Maximize u p

Maximize pY Minimize Y Maximiz

Y

e u pω

ωω ω

= −

+ − −+

Profit OptimizationProfit OptimizationProfit OptimizationProfit Optimization

, , , , , , , ,( )n s t k n s t k n k n s kk

profit p d yω∀

= −p: call unit price: call marginal costd: call durationy: call bandwidth

Price (p(.))

Time (t)

Marginal Cost ((.))

Network Throughput (Y)

Time (t)

Profit ( u(.))

dt dt

dt dt

Unit-Profit

Price (p(.))

Time (t)

Marginal Cost ((.))

Network Throughput (Y)

Time (t)

(.))

dt dt

dt dt

-

Maximize u(.)Network Architecture Constraint

s.t. Internet Traffic Pattern and Queue System ConstraintGame Strategy Constraint

Mar

ket P

rice

M

argi

nal C

ost

Thr

ough

put

Prof

it

22

Enforce Traffic Engineering RuleBased on

Queuing Theory (e.g. M/G/1)

Minimize Marginal Cost

byPerform Optimum Traffic Routing

Approximate Optimum

Mean Number of Packets (M*) for Y (Based on Queuing Theory (e.g. M/M/1))

Based onMathematical

Non-Linear Programming(Gradient Projection Method and

Golden Section Line Search)

Perform Non-Cooperative Game of Oligopoly to developBelief Function: F(p) = G(…)

Find bid price based on providersStrategy: P = H(F(p))

QoS Guarantee Enforce Traffic Engineering RuleBased on Queuing Theory (e.g. M/G/1)

Minimize Marginal Costby

Optimum Traffic RoutingApproximate

OptimumMean Number of Packets (M*) for Y

(Based on Queuing Theory (e.g. M/M/1))

Based on Non-Linear Programming

(Gradient Projection Method and Golden Section Line Search)

Perform Game of Oligopoly to develop

Belief Function: F(p) = G(… , ,)

Find bid price based on providersStrategy: pb = H(F(p))

A.com

B.com

CustomerDomain

Sealed Bid Reverse AuctionProtocol

(Signaling & Control Layer)

BearerLayer

AlgorithmAlgorithmAlgorithmAlgorithm

Develop CongestionSensitive Cost: (M*)

Develop DemandFunction: (Y)

23

• We develop TE Rules to guarantee mean delay less than 1 msec.– Homogeneous services

• Link Load (Green) < 90%– Heterogeneous Services

• Link Load (Blue) < 20%• Link Load (Green) < 30%• Link Load (Red) < 40%

• Based on M/G/1 System

22 22 2 2

2 2 2 2

2

[ ][ ] [ ][ ] , [ ] , [ ]

[ ][ ] [ ][ ] 2. , [ ] 2. , [ ] 2.

ˆ[ ] [ ] [ ] [ ]

ˆ[ ] [ ] [ ] [ ]

ˆ[ ] [ ][ ]

2(1

gb rb g r

gb rb g r

gb vb g r

gb vb g r

ss

E LE L E LE E E

C C C

E LE L E LE E E

C C C

E E E E

E E E E

E L EE T

C E

τ τ τ

τ τ τ

λλ λτ τ τ τλ λ λ

λλ λτ τ τ τλ λ λ

λ τλ

= = =

= = =

= + +

= + +

= +− ˆ[ ])τ

QoS GuaranteeQoS GuaranteeQoS GuaranteeQoS Guarantee

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.950

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Link Utilization (ρLINK)

Sys

tem

Del

ay: E

[ τ](m

sec)

M/G/1 System Delay

BlueGrenRed

ρb = 20%

ρg = 30%

ρr = 5% <-->45%

24

Service Cost FunctionService Cost FunctionService Cost FunctionService Cost Function

• Assumption: Following four influences on the service cost:– Congestion in the network

• Degrades the service quality– causes the delay in packet transmission.

• The degradation of service is detrimental to the revenue• Providers have to pay to the Enterprise for jitter (Expense• An indicator of network congestion

– Mean packet count (M) in the queue system

– Protocol used to provide a service• Service cost coefficient (s)

– Amount of service (commodity)• Throughput (Y)

– Providers’ fixed cost ()

, , , , , , ,ˆ( ) ( )n s t n t n t s n t n t n n tCost Y g Y M Y Yδ θ= = +

, ,( )n t n tf Y M→

25

Minimize CostMinimize CostMinimize CostMinimize Cost

,

,, ,

,

ˆˆ ( )

n t

n ts n t n t n

n t

Minimize

MMinimize Y M

Y

ω

δ θ∂

= + +∂

ˆMinimize M optimize network traffic routes applying nonlinear program⇐

,,

, ,

ˆ

ˆn t

n tn t n t

route optimization loadbalances andMMinimize Y

Y reduces change in M in low load

∂⇐

∂

A Cost Function assumption• Service cost is a functions of network congestion• Mean packet count in network queue system is a congestion indicator

• Minimize Congestion Cost by Optimum Routing Method– Minimizing Mean Packet Count

• Mean Packet Count (M/M/1 Model):

• Non-Linear Program:

We implement Gradient Projection and Golden Section line searchto satisfy Karush-Kuhn-Tucker condition In each game instance (each request for bid), this optimization is performed

(See dissertation for details, we provide highlight in next three slides)

:

:

:

( )

ˆ:

:

0

jj l j

l l jj l j

j TE lj l J

j wj J w

j

xMinimize M

C x

Subject to x C

x r

x

ρ

∈

∈

∈

∈

=−

≤

=

≥

:

:

ˆ [ ]j

j l j

l l jj l j

xM E packets

C x∈

∈

= =−

Minimize Marginal CostMinimize Marginal CostMinimize Marginal CostMinimize Marginal Cost

27

xp: BW of an LSPEach O-D pair has Five LSPs.Total: 60 LSPs in each provider networkCl: Capacity of each linkTE: TE load

NSP1NSP1

1

3 4

2100

100

100 100

100

100



300

CustomerRegion#3

(Dallas)

CustomerRegion#3

(Dallas)

300

300

CustomerRegion#2(NewYork)


300

CustomerRegion#4

(Atlanta)

CustomerRegion#4

(Atlanta)

300

300

NSP1NSP1

1

3 4

2100

100

100 100

100

100

1

3 4

2100

100

100 100

100

100



300

CustomerRegion#3

(Dallas)

CustomerRegion#3

(Dallas)

300

300



300

CustomerRegion#4

(Atlanta)

CustomerRegion#4

(Atlanta)

300

300

E-LSR

E-LSRE-LSR

E-LSR

12 123 124 1243 1234 312 3124 3412 4123 412 4312 12

21 321 421 3421 4321 213 4213 2143 3214 214 2134 21

13 134 213 413 132 1342 1324 4132 2134

0

0

G Inequality

TE

TE

x x x x x x x x x x x C


x x x x x x x x x

ρρ

+ + + + + + + + + + − ≤+ + + + +

+ + + + +

− ≤+ + + + + + + +

=

+ 2413 4213 13

31 431 312 314 231 2431 4231 2314 4312 3142 3124 31

14 142 214 314 143 1432 1423 2314 3214 3142 2143 14

41 241 412 413 341 2341 3241 4132 4

0

0

0

TE

TE

TE

x x C



x x x x x x x x x

ρρρ

+ − ≤+ + + + + + + + + + − ≤+ + + + + + + + + + − ≤+ + + + + + + + 123 2413 3412 41

42 142 342 421 423 1342 1423 3142 3421 4213 4231 42

24 241 243 124 324 2431 3241 2413 1243 3124 1324 24

23 231 234 123 423 1234 1423 231

0

0

0

TE

TE

TE

x x C



x x x x x x x x

ρρρ

+ + − ≤+ + + + + + + + + + − ≤+ + + + + + + + + + − ≤+ + + + + + + 4 2341 4123 4231 23

32 132 432 321 324 4321 3241 4132 1432 3214 1324 32

34 134 234 341 342 1342 1234 2341 2134 3421 3412 34

43 431 432 143 243 2431 4321

0

0

0

TE

TE

TE

x x x C



x x x x x x x

ρρρ

+ + + − ≤+ + + + + + + + + + − ≤+ + + + + + + + + + − ≤+ + + + + + + 1432 4312 1243 2143 43 0TEx x x x Cρ

+ + + − ≤

[ ]

12 132 142 1342 1432 12

21 231 241 2431 2341 21

13 123 143 1243 1423 13

31 321 341 3421 3241 31

14 124 134 1324 1234 14

41 421 431 4231 4321 41

42 412 43

0

0

0

0

0

0H

x x x x x r

x x x x x r

x x x x x r

x x x x x r

x x x x x r

x x x x x r

x x x

+ + + + − =+ + + + − =+ + + + − =+ + + + − =+ + + + − =+ + + + − =

=+ +

32 312 342 3

2 4132 4312 42

24 214 234 2314 2134 24

23 213 243 2143 2413 23

34 314 324 3124 3214 34

43 413 423 4213 4

412 3142

23 3

2

4

3

1

0

0

0

0

0

0

x x x x x

x x r

x x x x x r

x x x x x r

x x x x x r

x x x x x

r

r

+ + − = + + + + − =

++

+ + + − = + + + + − = + + + + − =

+ + + − =

_ . jx 0,G non neg j J = − ≤ ∈

NonNonNonNon----linear Program: Constraintslinear Program: Constraintslinear Program: Constraintslinear Program: Constraints

28

• Gradient Projection Method requires an initial feasible vector (X0)• Determine: New Session Route Vector (NV)

– Minimum Hop Routing• Step 1

– Select the shortest path (one hop route)• If fails Step 1, Step 2

– Select either of the two hop route with equal probability• If fails Step 2, Step 3

– Select either of the three hop route with equal probability

• Anticipated Route Vector = (Current Route Vector) + NV

• Initial feasible vector (X0) Anticipated Route Vector

NonNonNonNon----Linear Program: Initial Feasible PointLinear Program: Initial Feasible PointLinear Program: Initial Feasible PointLinear Program: Initial Feasible Point

29

[ ](12 60) (12 1)(60 1) 72 1

(60 60) (60 1)

G CY 0

G 0Inequaltiy TE

Non negative

ρ× ×× ×

× − ×

− ≤

Equality Constraints:Inequality Constraints:

[ ][ ] [ ] [ ][ ] [ ]

12 60 60 1 12 1 12 1

12 1 12 1

H Y R 0

H 0LSP× × × ×

× ×

− =

=

Working Matrix: [ ] ActiveGW

H

=

This working matrix is the foundation of the working surface (Aq)Direction of movement (d) is found as follows:

1( )

( )

T Tq q q qP I A A A A

d P x Tf

−= −

= − ∇

( ) ( )x x d binactive Max inactiveg gα+ =

Find Maximum distance (Max):

Use Golden Section Line search to find optimum point in each feasible segment:

[ ] [ ]( d )

. .k k kMinimize f x

s t A b

α+≤

Minimum is achieved at dk = 0 and such that the following FONC is satisfied 0λ ≥

( ) Tkf λ∇ + =k qx A 0

NonNonNonNon----Linear Program: Gradient Projection SnapshotLinear Program: Gradient Projection SnapshotLinear Program: Gradient Projection SnapshotLinear Program: Gradient Projection Snapshot

30

• Output of Non-linear program– Optimized Mean Packet Count

– Optimum Routes

– Fair Load Distribution Inside the Network

-Minimization of Cost

*M

NonNonNonNon----Linear Program: OutputLinear Program: OutputLinear Program: OutputLinear Program: Output

31

0 0.5 1 1.5 2

x 104

0

0.02

0.04

0.06

0.08

0.1

0.12

Simulation Time

With Optimization

Cha

nge

in M

ean

Num

ber o

f Pac

kets

0 0.5 1 1.5 2

x 104

0

0.02

0.04

0.06

0.08

0.1

0.12

Simulation Time

Without Optimization

Cha

nge

in M

ean

Num

ber o

f Pac

kets

Network Load (δn) = 38% Network Load (δn) = 38%

,

, ,

ˆ

ˆn t

n t n t

route optimization loadbalances andMMinimize

Y reduces change in M in low load

∂⇐

∂

Minimizing Change in CongestionMinimizing Change in CongestionMinimizing Change in CongestionMinimizing Change in Congestion

32

*,* *

, ,

* * *, 1 , 1

, ,,

,

, 1

ˆ ˆ

ˆˆ ˆ(

ˆ

( )

( )

)

n t n t n t

n t

n tns t n t s n t

OD

n n

O

tt

D

n

MM Y

M M MSimulation

Y b b

MY

ω δ θ

+ +

+

∂= +

∂ −≈

∂ +

+∂

0.4 0.5 0.6 0.7 0.80

20

40

60

80

100

120

140

160

Mar

gina

l Cos

t (ω(

Y)

Network Load (ρNetw ork(Y))0.4 0.5 0.6 0.7 0.80

20

40

60

80

100

120

140

160

Mar

gina

l Cos

t (ω(

Y)

Network Load (ρNetw ork(Y))

Marginal Cost (ω) and Cost Coefficient (δ)

Ωb = $160

δb = 1.0

δg = 0.1

δr = 0.01

Ωg = $100

Ω r = $70

Three classes (Blue, Green, Red)Cost coefficient parameterdepends on security levels(High, Medium, Low)• Cost coefficient parameterdistinguishes Service ClassMean Packet Count: M/M/1

Congestion Sensitive Optimized Marginal CostCongestion Sensitive Optimized Marginal CostCongestion Sensitive Optimized Marginal CostCongestion Sensitive Optimized Marginal Cost

We develop the Marginal Cost Functionfrom

the Optimized Mean Packet Count (M*):

Blue Green Red Provider 1

*1, *

1, 1,1,

ˆˆ1.00( ) 10t

t tt

MY M

Y

∂+ +

∂

*1, *

1, 1,1,

ˆˆ0.10( ) 10t

t tt

MY M

Y

∂+ +

∂

*1, *

1, 1,1,

ˆˆ0.01( ) 10t

t tt

MY M

Y

∂+ +

∂

Provider 2

*2, *

2, 2,2,

ˆˆ1.00( ) 10t

t tt

MY M

Y

∂+ +

∂

*2, *

2, 2,2,

ˆˆ0.10( ) 10t

t tt

MY M

Y

∂+ +

∂

*2, *

2, 2,2,

ˆˆ0.01( ) 10t

t tt

MY M

Y

∂+ +

∂

33

• Our Model is– Based on Bertrand Oligopoly Model– A Myopic Markovian-Bayesian Static Game of Incomplete Information

• Our models extends– Bandyopadhyay et al. On-Line-Exchange Model

Game Theory ModelGame Theory ModelGame Theory ModelGame Theory Model

• Bandyopadhyay et al. On-Line-Exchange Model

– Based on Bertrand Model and “ Model of Sale” example

– Symmetric market• All parameters are fixed

– Commodity is not Internet bandwidth

– Two step static game of incomplete information

– Homogeneous service

– Uses Reinforcement Learning (RL) in simulation to determine best strategy

• Our Model:

– Extension to Bandyopadhyay et al. model

– Asymmetric market• Demand and cost are functions of the

dynamic nature of Internet traffic

– Commodity is internet bandwidth

– “ Myopic” Markovian static game of incomplete information

– Heterogeneous service

– An analytical framework to determine the best strategy in dynamic internet traffic

34

Oligopoly Model SelectionOligopoly Model SelectionOligopoly Model SelectionOligopoly Model Selection

• Oligopoly– A small number of providers collectively influence

• Market condition such as price, capacity – A single provider alone cannot completely control the market

• Two well-established fundamental models of Oligopoly– Bertrand Model

• Strategic Variable: Price– Cournot Model

• Strategic Variable: Capacity (quantity)

35

Oligopoly Model Oligopoly Model Oligopoly Model Oligopoly Model

• In the Internet, providers strategically interact– Long term:

• Adds more capacity, i.e. “ bandwidth wars”– Short term:

• Price adjustment in fixed capacity, i.e., “ price wars”• Our Model is based on Bertrand Oligopoly Model

– Short term• Session arrival and departure in a relatively short time period

– Capacity does not change during the game– Providers adjust price to win over customers– Customers subscribe to the service from the lowest priced provider.

36

Game Model SelectionGame Model SelectionGame Model SelectionGame Model Selection

• Game Theory– The mathematical theory pertaining to the strategic interaction of decision makers

• There are four fundamental classes of game

Game Class Equilibrium Static Game of Complete Information Nash Equilibrium Dynamic Game of Complete Information Subgame-perfect Nash equilibrium Static Game of Incomplete Information Bayesian Nash equilibrium Dynamic Game of Incomplete Information Perfect Bayesian Equilibrium

• Complete Information:• Providers’ payoff or strategies are common knowledge

• Incomplete Information:• At least one player is unware of the payoffs or strategies of other providers

• Static Game• Players simultaneously interacts (chooses actions) without the knowledge of past

• Dynamic Game• Players repeatedly interacts based on the knowledge of game history (e.g., payoff)

37

Game ModelGame ModelGame ModelGame Model

• Our model is Myopic Markovian-Bayesian Game of Incomplete Information– Each provider is a rational player– Each provider’s payoff is private information.– All providers simultaneously select bid price without past knowledge of payoffs– “ Myopic Markovian”

• Each session is an instance of the game• Game uses one step nearsighted information

– The game is also known as Bayesian Static Game of Incomplete Information• Developed based on Bayes’ Conditional Probability Rule

38

Game ParametersGame ParametersGame ParametersGame Parameters

• Our Game Parameters– Strategic Players : A few Internet Service Providers– Strategic variable : Bid Price (pbid)– Commodity: the bandwidth of services in the Internet– Services: Homogeneous/Heterogeneous (Plat., Gold, Silv.) Services– Capacity: Peer capacity in bw (Fixed)– Demand: Sensitive to Internet traffic throughput (Variable)– Marginal Cost: Sensitive to network congestion (Variable)– Customer’s limited Budget: Reservation price (Fixed)– Payoff: Profit

39

Bayesian Static Game of Incomplete InformationBayesian Static Game of Incomplete InformationBayesian Static Game of Incomplete InformationBayesian Static Game of Incomplete Information

• Static Bayesian Game of two Providers ( A.com, B.com)– In Static Bayesian game, a provider’s strategy is to maximize its’ expected Profit– G = ActionA, ActionB; TypeA, TypeB; BeliefA(), BeliefB(); PayoffA(), PayoffB()

• Action = Bid price (pbid)• Type = Provider’s marginal cost ()• Payoff = Expected Profit (E(u(.))• BeliefA(.) = ProbA(TypeB|TypeA)

– A.com’s belief or uncertainty of B’s Type given that A.com knows own type– It is a conditional probability function – It is also referred to as the Mixed Strategy Profile

– A.com develops a set of feasible strategies from the belief function:

: (., (.))Aj A Aj Astrategy h Action h Belief←

40

• The Belief function is the main entity of this Game • Belief Function: FA(p):

– is the Rejection probability of A.com for A’s bid price p.• A.com’s belief of B.com’s winning probability for A.com’s bid price pA

• Strategy space h is the set of functions over F(p)– Strategy is identified by the rejection probability

• A Strategy, hAj = “ 95% probability of having the bid rejected”

( ) Prob( )bid bidA A B AF p p p= ≤

, , , , , , , ,: ( ) ( ) 0.95bid bid bidn s t n s t n s t n s tp F p prob p p= ≤ =

Game Model: Belief functions and StrategiesGame Model: Belief functions and StrategiesGame Model: Belief functions and StrategiesGame Model: Belief functions and Strategies

41

Belief Function (F(p))Belief Function (F(p))Belief Function (F(p))Belief Function (F(p))

• Belief function – It is a cumulative distribution function F(p)

• FA(p)– A.com’s belief of B.com’s winning probability for A.com’s bid price pA

– A.com’s probability of having its pA bid rejected• The Rejection probability of A.com

( ) Prob( ) 0.90bid bidA A B AF p p p= ≤ =

• A.com’s rejection probability = 90%

• A.com believes that B.com will select bid-prices at most pA with 90%probability• A.com’s winning probability = 10%

( ) Prob( )bid bidA A B AF p p p= ≤

42

StrategyStrategyStrategyStrategy

• Strategy space h is the set of functions over F(p)– The strategy space is constructed from the Type and Action space– A.com’s set of strategies hAj is the set of all possible functions with domain (input) TypeA and range

(output) ActionA.

• A Strategy, hAj = “ 95% probability of having the bid rejected”

• Strategy is identified by the rejection probability

: ( (..., ))Aj A Aj A Astrategy h Action h Belief Type←

, , , , , , , ,: ( ) ( ) 0.95bid bid bidn s t n s t n s t n s tp F p prob p p= ≤ =

( ) ( )my bid othersbid my bidF p Prob p p γ= ≤ =

43

• F(p) = Game(N, , (Y) , s, (M*))– N: Number of providers in the market– : Market Capacity– (Y): Market Demand (function of throughput)– s: Customer Reservation Price, function of service type (s)– (M*)): Marginal Cost (function of mean packet count, M)

1 1

,,

, ,

*,* *

, , , , ,,

*,

2,,

* * *, 1 , 1 ,

, 1

( 1) , 0( )

ˆˆ ˆ( ) ( )

ˆ

1( )

12ˆ ˆ ˆ

( )

N N

n TE TE nn n

TE n t TEn t

n t TE n t Max

n tn s t n t s n t n t n

n t

n t

n tn t

n t n t n t

n t OD DO

K K

N K NY KY

NY K NY

MM Y M

Y

M CAnalysis

Y C Y

M M MS

Y b b

ρ ρ

ρ ε ρ ερ

ω δ θ

= =

+ +

+

Γ = =

− + ≤ >∆ = < ≤ ∆

∂= + +

∂

∂=

∂ −

∂ −≈

∂ +

imulation

Game Model: Belief ParametersGame Model: Belief ParametersGame Model: Belief ParametersGame Model: Belief Parameters

44

1 1

N N

n TE TE nn n

K Kρ ρ= =

Γ = =

NSP1NSP1

1

3 4

2100

100

100 100

100

100

300

NSP1

1

3 4

2100

100

100 100

100

100

300

CustomerRegion#4(Atlanta)


300300



CustomerRegion#3(Dallas)


CustomerRegion#2

(NY)

100

100

100 100

100

100

300


EnterpriseRegion#4(Atlanta)

300300


EnterpriseRegion#1(Chicago)


EnterpriseRegion#3(Dallas)

CustomerRegion#2

(NY)

EnterpriseRegion#2

(NY)

300

300B.com

A.com

300

E-LSR

NSP1NSP1

1

3 4

2100

100

100 100

100

100

300

NSP1

1

3 4

2100

100

100 100

100

100

300



300300





CustomerRegion#2

(NY)

100

100

100 100

100

100

300


EnterpriseRegion#4(Atlanta)

300300


EnterpriseRegion#1(Chicago)


EnterpriseRegion#3(Dallas)

CustomerRegion#2

(NY)

EnterpriseRegion#2

(NY)

300

300B.com

A.com

300

E-LSR

Market Capacity ( ): Aggregate Traffic Engineered access bandwidth capacities of all providers in a market

NTEK(N-1)TEK

(Y)

Y

(N-1)TEK

= NTEK

Max

N = 2

Max

(Y) = NY

(Y) = (N-1)TEK +

,,

, ,

( 1) , 0( ) TE n t TE

n tn t TE n t Max

N K NY KY

NY K NY

ρ ε ρ ερ

− + ≤ >∆ = < ≤ ∆

Market Demand ():

45

Market DemandMarket DemandMarket DemandMarket Demand• Max Market Demand (Max)

– Aggregate Bandwidth in active session by all the customers from all the providers at a certain instant of game (t)

– An NSP cannot meet the demand () of the whole market• TEK <

– Maximum Market Demand is less than Market Capacity• Max <

– Market Demand is greater than N-1 providers’ aggregate capacity• TE(N-1)K < <= Max

• Proposed Market Demand is a function of traffic served (Network output/production)– Network is loss-less (no packet drop occurs in the network)

Yt : Sum of output (production) traffic bandwidth in all the egress ports of anNSP at a certain Instant of the game (t)

,,

, ,

( 1) , 0( ) TE n t TE

n tn t TE n t Max

N K NY KY

NY K NY

ρ ε ρ ερ

− + ≤ >∆ = < ≤ ∆

46

Reservation Price of the InstitutionReservation Price of the InstitutionReservation Price of the InstitutionReservation Price of the Institution

• Reservation price () is the price that a customer is willing to pay in the Reverse Auction

– It can be considered as customer’s budget.• We do not study the method of determining .• We assume

– Enterprises (customers) are rational• Reservation price is selected during the business agreement• Enterprises do not violate the agreement

– Do not change the reservation price during the game– for Homogeneous services, is a same fixed value for all providers– For Heterogeneous services, s depends on the type of service

• Enterprises may adopt their own strategies to determine .– This will require another larger research

• For example, Enterprise selects reservation price by considering monopoly market (assume that all providers constitute a Super-provider)

47

Price (p)

F(p)

1.0

0.8

0.5

0.2

Mixed Strategy Profile of A

pMin p

pb

If A Bids here

If B Bids here

Price (p)

F(p)

1.0

0.8

0.5

0.2


pMin p

pb

If A Bids here

If B Bids here

Price (p)

F(p)

1.0

0.8

0.5

0.2


pMin p

pb

If A Bids here

If B Bids here

Price (p)

F(p)

1.0

0.8

0.5

0.2


pMin p

pb

If A Bids here

If B Bids here

A.com’s price lower than B.com price A.com’s price higher than B.com price

This event occurs: 1-F(p)=prob(pb > p)

( ) ( (.)) ( (.))Lu p p Y p Kω ω ρ= − = −

( ) ( (.))L Min Minu p p Kω ρ= −If p = pMin

This event occurs: F(p)=prob(pb <= p)

( ) ( (.))( (.) )Hu p p Kω ρ= − ∆ −

( ) ( (.))( (.) )Hu Kω ρΩ = Ω − ∆ −

If p =

( ) ( )(1 ( )) ( ) ( )L Hu p u p F p u p F p= − +Expected Unit Profit =

Deriving Belief FunctionDeriving Belief FunctionDeriving Belief FunctionDeriving Belief Function

48

The derived Belief function for N providers is as follows:

* *, , ,

*, ,

( ( )) ( ( ))( ( ) )( )

( ( ))(2 ( ))n t TE s n t n t TE

n t TE n t

p M K M Y KF p

p M K Y

ω ρ ω ρω ρ

− − Ω − ∆ −=

− − ∆

The derived Belief function for 2 providers is as follows:

1* * * 1

, , , , , , , , ,, , , , * *

, , , , , ,

( ( )) ( ( )( ( ) ( 1) ))( )

( ( ))( ( ))

Nn s t n s t n t TE s n s t n t n t TE

n s t n s tn s t n s t n t TE n t

p M K M Y N KF p

p M N K Y

ω ρ ω ρω ρ

− − − Ω − ∆ − −= − − ∆

Game Model: Belief Function EquationsGame Model: Belief Function EquationsGame Model: Belief Function EquationsGame Model: Belief Function Equations

Dissertation presents the derivation of the belief function and associated parameters

49

Price (p)

F(p)

Price (p)

F(p)

n,s

Pt+2 Pt Pt+1

• Belief function shifts left or right on the p axis (x-axis)• due to the change in the network production and Network congestion• as a function of Mean packet count in the network• causes a bid price of a service to change

• Each service class has a distinct Belief function• For each call, each provider has a distinct Belief function

Game Model: Properties of the Belief FunctionGame Model: Properties of the Belief FunctionGame Model: Properties of the Belief FunctionGame Model: Properties of the Belief Function

50

Strategy Feasible strategies Very Low Rejection

, , , , , , , ,: ( ) ( ) 0.05bid bid bidn s t n s t n s t n s tp F p prob p p γ= ≤ = =

Low Rejection , , , , , , , ,: ( ) ( ) 0.35bid bid bid

n s t n s t n s t n s tp F p prob p p γ= ≤ = =

Rejection Neutral , , , ,( ( ))bid

n s t n s tp Mean F p=

High Rejection , , , , , , , ,: ( ) ( ) 0.65bid bid bid


Very High Rejection , , , , , , , ,: ( ) ( ) 0.95bid bid bid


Price (p)

F(p)1.00.8

0.5

0.2Very High RejectionHigh Rejection

Low Rejection

Very Low RejectionNo Rejection Absolute Rejection

Rejection Probability

A Provider finds a bid price of a service from F(p) using h(.)

Note, not all them are feasible

Feasible StrategiesFeasible StrategiesFeasible StrategiesFeasible Strategies

51

Bid PriceBid PriceBid PriceBid Price

*, , ,

** *, , , , , ,, , , ,

, , *, *

, , , * *, , , , , , , , ,

( )ln

( )( ( ) )( ( ))

(2 ( )) 1 1( )

( ) ( )

s n s t n t

Min n s t n s t n tn t TE s n s t n tNeutraln s t

TE n t

n s t n tMin n s t n s t n t s n s t n t

M

p MY K Mp

K YM

p M M

ωωρ ω

ρω

ω ω

Ω − −∆ − Ω − = − ∆ + − − Ω −

Derived Bid Price for Rejection Neutral Strategy:

( )

1

,*, , , , , * * *

, , , , , , , , , ,*,

1( )

( ) ( ( ) )( ( ))(2 ( ))

n sn s t n s t n t

Min n s t n s t n t n t TE s n s t n t

TE n t

p Mp M Y K M

K Y

γ γω

ω ρ ωρ

− = + − − ∆ − Ω − − ∆

Derived Bid Price for any Strategy (n,s):

Dissertation presents the derivation of these functions

52

Market PriceMarket PriceMarket PriceMarket Price

When Two Providers use an Identical Strategy Set:

*, , , , ,( )Market s t n s t n tp p Yγ=

When Two Providers do not use an Identical Strategy Set:• Market price can be found by solving bid price equations of both providers• Bid price equations are hyperbolic function

• Solving by algebraic method is seemingly difficult• We apply Numerical Analysis in MATLAB to solve bid price equations

We determine Analytical Market Price from the Bid Price

53

( ),

,

* * * * *

1

,*, , , , , * * *

, , , , , , , , , ,*,

* *, , , , , *

, , , , ,

,

1( )

( ) ( ( ) )( ( ))(2 ( ))

1( )

(

jA s

kB s

A B A B

jA s

A s t A s t A tMin A s t A g t A t A t TE s A s t A t

TE A t

B s t B s t A tMin B s t B s t

Y Y Y Y

p Yp Y Y K Y

K Y

p Yp Y

γ

γ

γω

ω ρ ωρ

ωω

−

≠ ∆ = +

= + − − ∆ − Ω − − ∆

= ∆ − +− ∆ −( )

1

,

* * * **, , , ,,

* *,

( ( ) )( ( )))(2 ( ))

kB s

A t TE g B s t A tA t

TE A t

Y K Y

K Y

γρ ω

ρ

− − ∆ ∆ − − Ω − ∆ − − ∆ ∆ −

* * *, , , , , , , ,( ) ( )bid bid

Market s t A s t A t B s t B tp p Y p Y= =

700 750 800 850 900 950 1000 1050 110040

50

60

70

80

90

100

110

A.com Throughput (YA)

Pric

e

Bid Price Functions Converges to Market Price

A.com Bid Price FunctionStrategy: VLR

B.com Bid Price FunctionStrategy: VLR

Market Price = $90.7YA = 984 Mbps

• Bid prices converge to market price• At a steady state market

Finding Market Price by Numerical AnalysisFinding Market Price by Numerical AnalysisFinding Market Price by Numerical AnalysisFinding Market Price by Numerical Analysis

54

ProfitProfitProfitProfit

Homogeneous Service (All strategies):

* * * *, , , ,(.) ( )n n g t n g tu p Yω= −

Heterogeneous Service (Identical Strategy Set):

* * * * * * * * * *, , , , , , , , , , , , , , ,

2 3 4(.) ( )( ) ( )( ) ( )( )

9 9 9n n b t n b t n t n g t n g t n t n r t n r t n tu p Y p Y p Yω ω ω= − + − + −

Heterogeneous Service (Non-Identical Strategy Set):

, , , , , , ,n t n b t n g t n r tY Y Y Y= + +

Throughput of each service is unknown

One equation three unknownsUnique Profit cannot be determined by math.

We study homogeneous service based market mainly by math. equations

We study heterogeneous service based market mainly by simulation

55

ResultsResultsResultsResults

56

• Validation • Advantages:

– Customer’s benefit• Is market price less than customers’ budget (reservation price)?

– Provider’s benefit• Is market price above marginal cost?• Does providers’ obtain positive Profit?• Can providers optimize in fair market share Profit?

• Profit Maximizing Strategies – Best Strategies (Bayesian-Nash and Pareto-Efficient)

• TE Application

We demonstrateWe demonstrateWe demonstrateWe demonstrate

57

Unit Profit Curve:• Monotonous• Bound • Concave:

,1 ,2 ,1 ,2( (1 ) ) ( ) (1 ) ( ), [0,1]n n n nu u uψρ ψ ρ ψ ρ ψ ρ ψ+ − ≥ + − ∈

• Simulation validates Analysis• Advantages:

• Market Price less than Reservation Price• Market Price more than Marginal Cost• Optimizes in Positive Profit in Fair share of

• Market demand and throughput• Optimum load is around 0.7704

Homogeneous Service Market:hHomogeneous Service Market:hHomogeneous Service Market:hHomogeneous Service Market:hAAAA, h, h, h, hBBBB = RN, RN = RN, RN = RN, RN = RN, RN

1 1.5 20

0.5

1

Net

wor

k Lo

ad ( ρ

Net

wor

k)

Market Demand Load (ρMarket)

Plot 1: Network Load vs. Market Demand

0.4 0.6 0.8 10

50

100

Pm

ean ($

)

Network Load (ρNetw ork)

Plot 2: Mean Market Price

0.4 0.6 0.8 10

50

100


Mar

gina

l Cos

t ($)

Plot 3: Marginal Cost

0.4 0.6 0.8 10

2

4

6x 10

4


Uni

t Pro

fit ($

)

Plot 4: Unit Profit

AnalyticalSimulated

γA = 0.5

γB = 0.5

58

• Simulation Validates Analysis• Advantages:

• Market Price less than Reservation Price• Market Price more than Marginal Cost• Optimizes in Positive Profit in Fair share of

• Market demand and throughput• Optimum Load is around 0.74 to 0.77

• VHR,VHR yields higher Profit, VHR strategy dominates

Homogeneous Service Market (Identical Strategies)Homogeneous Service Market (Identical Strategies)Homogeneous Service Market (Identical Strategies)Homogeneous Service Market (Identical Strategies)

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90

50

100

Strategy:A.com = VHR (γA = 0.95), B.com = VHR(γA = 0.95)

Mar

ket

Pric

e


0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90

50

100


A.c

om M

argi

nal C

ost

AnalyticalSimulated

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90

5

x 104


A.c

om P

rofit

A.com =B.com Profit

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90

50

100

Strategy:A.com = VLR (γA = 0.05), B.com = VLR(γA = 0.05)

Mar

ket

Pric

e


0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90

50

100


A.c

om M

argi

nal C

ost

AnalyticalSimulated

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90

5

x 104


A.c

om P

rofit A.com = B.com Profit

59

• Lower rejection strategy• causes to operate in lower optimum load

• Higher rejection strategy• causes to operate in higher optimum load

• Higher rejection strategy yields higher Profit• Higher rejection strategy is dominant

• Simulation Validates Analysis• Advantages:

• Market Price less than Reservation Price• Market Price more than Marginal Cost• Optimizes in Positive Profit

Homogeneous Service Market (NonHomogeneous Service Market (NonHomogeneous Service Market (NonHomogeneous Service Market (Non----Identical Strategies)Identical Strategies)Identical Strategies)Identical Strategies)

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.80

50

100

Market Load (ρMarket)

Mar

ket P

rice

(Gre

en)

Market Price Validation: A.com-->VLR, B.com-->VHR

AnalyticalSimulated

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.80

2

4

6

x 104


Pro

vide

rs U

nit P

rofit

Unit Profit Validation: A.com-->VLR, B.com-->VHR

Analytical A.comAnalytical B.comSimulated A.comSimulated B.com

γA = 0.05

γB = 0.95

60

• Simulation validates analysis• pb > pg > pr• Advantages:

• Market Price less than Reservation Price• Market price more than Marginal Cost• Optimizes in positive Profit in Fair market share of

• Market demand and throughput• Optimum load is around .68 to .70

Heterogeneous Service Market (Identical Strategies)Heterogeneous Service Market (Identical Strategies)Heterogeneous Service Market (Identical Strategies)Heterogeneous Service Market (Identical Strategies)

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750

100

Mar

ket

Pric

e ($

)


Market Price Validation: A.com-->RN-RN-RN, B.com-->RN-RN-RN

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750

100

Mar

gina

l Cos

t A

.com


Marginal Cost Validation: A.com-->RN-RN-RN, B.com-->RN-RN-RN

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750

5

x 104 Profit Validation: A.com-->RN-RN-RN, B.com-->RN-RN-RN

Pro

vide

rs U

nit

Pro

ift


Analytical Simulated

Blue ServiceGreen Service

Red Service

Blue Service

Green ServiceRed Service

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750

100

Mar

ket P

rice

Market Load

Market Price Validation: A.com-->VHR-RN-VLR, B.com-->VHR-RN-VLR

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750

100M

argi

nal C

ost

A.c

om

Market Load

Marginal Cost Validation: A.com-->VHR-RN-VLR, B.com-->VHR-RN-VLR

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750

5

x 104 Profit Validation: A.com-->VHR-RN-VLR, B.com-->VHR-RN-VLR

Pro

vide

rs U

nit P

roift

Market Load

AnalyticalSimulated

BlueGreen

Red

Blue

GreenRed

61

Heterogeneous Service Market (Identical Strategies)Heterogeneous Service Market (Identical Strategies)Heterogeneous Service Market (Identical Strategies)Heterogeneous Service Market (Identical Strategies)

• pb > pg > pr• Advantages:

• Market Price less than Reservation Price• Market price more than Marginal Cost• Optimizes in positive Profit

RN,RN,RN

0 1 2 3 4 5

x 104

0

50

100

150

200Plot a: Market Price of Services

Game Instant (t)

Pric

e ($

)

0 1 2 3 4 5

x 104

0

50

100

150

200Plot b: Marginal Cost (A.com)

Cos

t ω ($

)

0.4 0.5 0.6 0.7 0.80

50

100

150

Plot c: Mean Market Service Price

Pric

e ($

)

Market Load (ρMarket)0.4 0.5 0.6 0.7 0.80

50

100

150

Plot d: Mean Marginal Cost (A.com)C

ost ω

($)


Blue Service

Green Service

Red Service

Blue Service

Green Service

Red Service

Red Service

Blue Service

Green Service

Green Service

Blue Service

Red Service

ρMarket = 0.711

62

Heterogeneous Service Market (NonHeterogeneous Service Market (NonHeterogeneous Service Market (NonHeterogeneous Service Market (Non----Identical Strategies)Identical Strategies)Identical Strategies)Identical Strategies)

• Higher Priced Service May Not Bring Higher Profit• Providers’ Should Select Lower Rejection Strategy For Higher Profit Yielding Services• Providers’ Should Select Higher Rejection Strategy For Lower Profit Yielding services

0.4 0.5 0.6 0.70

50

100

Market Load

Pric

e - M

argina

l Cos

t

A.com: VHR-RN-VLR

0.4 0.5 0.6 0.70

0.5

1

Market Load

Service

Loa

d

0.4 0.5 0.6 0.70

2

4x 10

4

Market Load

Unit Proft

BlueGreenRedTotal

0.4 0.5 0.6 0.70

50

100

Market Load

Pric

e - M

argina

l Cos

t

B.com: RN-RN-RN

BlueGreenRed

0.4 0.5 0.6 0.70

0.5

1

Market LoadService

Loa

d

0.4 0.5 0.6 0.70

2

4x 10

4

Market Load

Unit Profit

Plot 1 Plot 2

Plot 3 Plot 4

Plot 5 Plot 6

63

Heterogeneous Service Market (NonHeterogeneous Service Market (NonHeterogeneous Service Market (NonHeterogeneous Service Market (Non----Identical Strategies)Identical Strategies)Identical Strategies)Identical Strategies)

Careful Strategy Selection May Allow a Provider to Optimize the Market Profit Shareby Selling Only the Lowest Valued Service

0.4 0.5 0.6 0.70

50

100

Market Load

Pric

e - M

argi

nal C

ost

A.com: VLR-RN-VHR

BlueGreenRed

0.4 0.5 0.6 0.70

0.5

1

Market Load

Ser

vice

Loa

d

0.4 0.5 0.6 0.70

1

2

3

4x 10

4

Market Load

Uni

t Pro

fit

0.4 0.5 0.6 0.70

50

100

Market Load

Pric

e - M

argi

nal C

ost

B.com: RN-RN-RN

0.4 0.5 0.6 0.70

0.5

1

Market LoadS

ervi

ce L

oad

0.4 0.5 0.6 0.70

1

2

3

4x 10

4

Market Load

Uni

t Pro

fit

BlueGreenRedTotal

Plot 1 Plot 2

Plot 3 Plot 4

Plot 5

Plot 6

640.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

Market Load (Market Demand/Physical Capacity)

% M

arke

t Sha

re o

f Pro

fit (A.c

om)

A.com: Market Share and Strategies

Very High Rejection

Very High Rejection

Very Low Rejection

Very Low Rejection

Rejection Neutral

High Rejection

Low Rejection

vs. ,j RNAj Ajh h∀ ,RN RN

Aj Ajh h

• Market share in the dynamic internet traffic demand• remains invariant for the Rejection Neutral strategy • remains close to invariant for the HR and LR strategies • changes rapidly for the VHR and VLR strategies

• Assign strategies if traffic demand does not change and known:• VHR: for High demand• VLR: for Low demand

Homogeneous Service: Market Share in different strategies and maHomogeneous Service: Market Share in different strategies and maHomogeneous Service: Market Share in different strategies and maHomogeneous Service: Market Share in different strategies and market demandrket demandrket demandrket demand

The Market Share of Profit Changes Due to the Change in Market Demand

65

* * *[ ( , )] [ ( , )]jA Aj Bj A Aj BjE u h h E u h h∀≥

Bayesian-Nash Equilibrium:Find * * , Aj Bjh h

s.t.

• Internet Traffic demand varies and pattern is unknown• We use a hypothetical market load distribution

• Gaussian Normal2( 0.65)

2(0.01)1( ) exp

2 (0.01)

Market

Marketprob

ρ

ρπ

−−

=

• Our proposal to compute the expected unit Profit as follows:

[ (.)] ( ) (.)

[ (.)] ( ) (.)Market

Market

A Market A

B Market B

E u prob u

E u prob u

ρ

ρ

ρ

ρ∀

∀

=

=

““““Best Strategy” SetBest Strategy” SetBest Strategy” SetBest Strategy” Set

0.5 0.55 0.6 0.65 0.7 0.75 0.80

0.2

0.4

0.6

0.8

1

1.2

Probability %


Pseudo-Gaussian Distribution

Mean = 0.65Variance =0.01

The “Best Strategy” Set Should Optimize Profit in all Market Load

66

FOR Aj= 0.05 to 0.95FOR Bj= 0.05 to 0.95

FOR Market = Min to MaxDevelop Belief Functions ()Find Bid_Prices_A;Find Bid_Prices_B;Find Market Price;Find Network_Load_A;Find Network_Load_B;Find Marginal Cost_AFind Marginal Cost_B;Find UA(.);Find UB(.);

END;

[ (.)] ( ) (.)

[ (.)] ( ) (.)Market

Market

A Market A

B Market B

E u prob u

E u prob u

ρ

ρ

ρ

ρ∀

∀

=

=

END;END;

* * * , . . [ ( , )] [ ( , )]jAj Bj n Aj Bj n Aj BjFind s t E u E uγ γ γ γ γ γ∀≥

Analytical Algorithm to Find Best Strategy SetAnalytical Algorithm to Find Best Strategy SetAnalytical Algorithm to Find Best Strategy SetAnalytical Algorithm to Find Best Strategy Set

67

B.com hnj VLR LR RN HR VHR

VLR (.50,.50) (.54,.55) (.57,.58) (.60,.61) (.66,.73) LR (.55,.54) (.59,.59) (.62,.62) (.65,.66) (.74,.77) RN (.58,.57) (.62,.62) (.65,.65) (.69,.69) (.79,.80) HR (.61,.60) (.66,.65) (.69,.69) (.73,.73) (.84,.85)

A.com

VHR (.73,.66) (.77,.74) (.80,.79) (.85,.84) (1.00,1.00)

0 0.5 10.65

0.7

0.75

0.8

0.85

0.9

0.95

1

B.com Strategies (γB)

Nor

mal

ized

Exp

ecte

d U

nit

Util

ity

Explaining Bayesian Nash Equilibrium

A.comB.com

0 0.5 10.65

0.7

0.75

0.8

0.85

0.9

0.95

1

A.com Strategies (γA)

Nor

mal

ized

Exp

ecte

d U

nit

Util

ityExplaining Bayesian Nash Equilibrium

A.comB.com

A.com Strategy VHR (γA) = 0.95

B.com Strategy VHR (γB) = 0.95

A.com'sVHR isdominant

B.com'sVHR isdominant

NASH

0 0.2 0.4 0.6 0.8 1

00.5

1

0.6

0.8

1

A.com Strategy(γ)

Bayesian Nash Equilibrium (Homogeneous Market)

B.com Strategy(γ)

Nor

mal

ized

Exp

ecte

d U

tility

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

0.6

0.8

1

B.com Strategy(γ)A.com Strategy(γ)

Nor

mal

ized

Exp

ecte

d U

tility

Azimuth =-37.5o

Elevation= 30o

Azimuth = 45.5o

Elevation= 30o

UniqueBayesian-Nash Equilibrium

= VHR, VHR

( ) ( _ _ , _ _ )j ju u a Very High Rejection Very High Rejection jα > = ∀VHR, VHR is also Pareto-Efficient Set because there is no other set ( ) s.t.α

Homogeneous Market: Analytical Best StrategyHomogeneous Market: Analytical Best StrategyHomogeneous Market: Analytical Best StrategyHomogeneous Market: Analytical Best Strategy

68

11.5

22.5

3 11.5

22.5

3

0.65

0.7

0.75

0.8

0.85

0.9

0.95

B .com S trategy S et

Illus trat ing Nas h-E quilibrium by 3D P lot

A .c om S trategy S et

No

rma

lize

d E

xp

ec

ted

Uti

lity

Nas h E quilibrium #1

Nash E quilibrium #2

Nas h E quilibrium #3

P areto-effic ient outc om e

Heterogeneous Market: Best Strategy Set from SimulationHeterogeneous Market: Best Strategy Set from SimulationHeterogeneous Market: Best Strategy Set from SimulationHeterogeneous Market: Best Strategy Set from Simulation

40%

20%20%

10% 10%

20%

Market Load

Probability of Market Load Probability of Market Load

Market Load

Scenario 1 Scenario 2

0.80.4 0.4 0.80.6 0.6

40%

20%20%

10% 10%

20%

Market Load

Probability of Market Load Probability of Market Load

Market Load

Scenario 1 Scenario 2

0.80.4 0.4 0.80.6 0.6

1 = VHR-RN-VLR2 = RN-RN-RN3 = VLR-RN-VHR

Hypothetical Market Load

• Three Bayesian-Nash Equilibriums• Existence of Pareto-Efficient Outcome

69

• Not All Nash-equilibrium is preferred• Market price of lower priority service may exceed higher priority service

• May confuse customers• The highest Nash equilibrium that meets customers’ preference should be selected• In our study, it is RN,RN,RN which is also the same for homogeneous service

Care in Adopting the Best Strategy Set Care in Adopting the Best Strategy Set Care in Adopting the Best Strategy Set Care in Adopting the Best Strategy Set

Price (p)

F(p)

0.95Very High Rejection (Red)

pRed

Green

(Green)

pGreenPrice (p)

0.95

p

Rejection Neutral

Red

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750

50

100

150


Mea

n M

arke

t Pric

e (P

Mea

n)

Market Price of Strategy set: VLR-RN-VHR vs VLR-RN-VHR

BlueGreenRed

700 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (Second) -->

Net

wor

k Lo

ad (

ρ Net

wor

k)

Load Balancing by the Assignment of Strategies

A.com: Very High Rejection Strategy (γA =0.95)

B.com: Very Low Rejection Strategy (γB = 0.05)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

B.com Strategy (γB)

Net

wor

k Lo

ad (

ρ Net

wor

k)

Analytical Load Adjustment by Changing B.Com Strategy

Market Load (ρMarket) = 0.7

A.com Strategy: VLR (γ = 0.05)

A.com

B.com

• Load Distribution can be performed• By changing strategies

• Assign lower rejection strategy• For Higher load in the network

• Assign higher rejection strategy• For Lower load in the network

• Assign identical strategy for fair share of load

TE Application: Load DistributionTE Application: Load DistributionTE Application: Load DistributionTE Application: Load Distribution

ConclusionConclusionConclusionConclusion

72

• Developed a New price transaction architecture that benefits customers and providers

– By automation– By providing options to select any provider based on competitive price– By allowing customer power to specify budget– By introducing new price transaction research in one-to-many architecture

• Developed a mathematical model for providers to– To compute competitive price through the best strategy– Optimize Profit in dynamic internet traffic demand

• Developed an algorithm and simulation model– To verify and study providers’ game in flexible environment

• Introduced a New framework to determine Bayesian-Nash equilibrium – In dynamic internet traffic demand

• Demonstrated that:– Providers improved their Profit

• Our approach yielded relative advantages over the existing Bertrand Oligopoly Model– Providers determined Best strategies (Bayesian-Nash equilibrium and Pareto-efficient

outcome) using our approach– Providers was able to obtain fair market share of Profit and throughput– Providers could implement TE applications such as optimized load balancing in the network– Customers could enjoy market price lower than their budgets.

• Introduced new area in Internet pricing research– Our research is the first in Internet Oligopoly pricing research for disjoint providers– Existing research are for monopoly market

• Introduced pricing research in a complex network model– Bi-directional links, multiple paths, Origin-Destination and Destination-Origin Call Legs.

ContributionsContributionsContributionsContributions

73

– Automatic Price-based Services– Profit Optimization and Determining Optimum Throughput– Traffic Load Distribution– Least Price Routing– Forecasting and Capacity Planning– Service Provisioning

Practical ApplicationPractical ApplicationPractical ApplicationPractical Application

74

• Limitations– Traffic Distribution Pattern– The Cost Function– Network Queue Model

• Future Work– Variable Reservation Price– Experiment on 3GPP Network– Priority based Queue System– Extend model beyond Duopoly

Limitations and Future WorkLimitations and Future WorkLimitations and Future WorkLimitations and Future Work

AppendixAppendixAppendixAppendix

76

Marginal Cost FunctionMarginal Cost FunctionMarginal Cost FunctionMarginal Cost Function

Marginal Cost ():*

, ,* *, , , ,

, ,

ˆ( )ˆ ˆ( ) ( )n t n tns t n t s n t n t n

n t n t

g Y MM Y M

Y Yω δ θ

∂ ∂= = + +

∂ ∂

* * *, 1 , 1 ,

, 1 , 1 ,

* * *, 1 , 1 ,

, 1

ˆ ˆ ˆ

ˆ ˆ ˆ

( )

n t n t n t

n t n t n t

n t n t n t

n t OD DO

M M M

Y Y Y

M M M

Y b b

+ +

+ +

+ +

+

∂ −≈

∂ −

∂ −≈

∂ +

Simulation:

This use of nearsighted one-step history extends the game to a Myopic Markovian-Bayesian Game

, , , , , , ,ˆ( ) ( )n s t n t n t s n t n t n n tCost Y g Y M Y Yδ θ= = +

, ,( )n t n tM f Y←

*, ,

2,, ,,

ˆ

1( )

1212

n t n t

n tn t n tn t

M Y CYY Y C YC

∂ ∂ = =

∂ ∂ −−

Analysis:

• Service cost coefficient (s)• Mean Packet Count (M)• Network Throughput (Y)• Provider’s Fixed Cost (n)

Cost ():

77

=100

100

100 100

100

100

1

3 4

2=100

100

100 100

100

100



CustomerRegion#3

(Dallas)

CustomerRegion#3

(Dallas)

yDallas



yNewyork

CustomerRegion#4

(Atlanta)

CustomerRegion#4

(Atlanta)

yAtlanta

yChicago

Y = yChicago + yDallas + yAtlanta + yNewyork

Y/12

Y/12

Y/12

, , , , ,

,,

12: ,*

,1 ,

:

, ,

,

, , ,

*, ,

,, ,

12

ˆ

12 12...

12 12 12

ˆ

12

Chicago Dallas Atlanta Newyorkn t n t n t n t n t

n tl t

pp l p l t

n tl ll p l l t

p l p

n t n t

n t

n t n t n t

n t n t

n tn t n t

Y y y y y

Yy

xy

MC x C y

Y YY

Y Y YC C C

M Y CYY Y

C

∈

=∈

= + + +

≈

= =− −

= + + =− − −

∂ ∂ = =

∂ ∂ −

2,

2,

,*

, , , ,2

,

1( )

12

212ˆ( ) ( )

1( )

12

n t

n tn t

n s t n t s n t n

n t

C Y

YCY

M YC Y

ω δ θ

−

−= +

−

Analytical Marginal Cost Function

Assumption and verified by simulation:Optimum routing by Gradient Projection,equally load balance network traffic across all links in a market.

78

Simulation Marginal Cost FunctionSimulation Marginal Cost FunctionSimulation Marginal Cost FunctionSimulation Marginal Cost Function

* * *, 1 , 1 ,

, 1 , 1 ,

* * *, 1 , 1 ,

, 1

* *, 1 ,* *

, , , , ,

ˆ ˆ ˆ

ˆ ˆ ˆ

( )

ˆ ˆˆ ˆ( ) ( )

( )

n t n t n t

n t n t n t

n t n t n t

n t OD DO

n t n tn s t n t s n t n t n

OD DO

M M M

Y Y Y

M M M

Y b b

M MM Y M

b bω δ θ

+ +

+ +

+ +

+

+

∂ −≈

∂ −

∂ −≈

∂ +

−= + +

+

79

Profit FunctionsProfit FunctionsProfit FunctionsProfit Functions

*

*, , , , , , , ,

* * * *

* *

( ) ( )

; 2

(.) (.)

bid bidMarket s t A s t A t B s t B t

A B

A B

p p Y p Y

Y Y Y Y

u u

= =

= = ∆ =

=

*

* * *

*

* *

* * * * * *, , ,

* * *, , , , , , , ,

* * * * * * * * * *, , , , , , , , , , , , , , ,

2

(.) (.)

2 3 4, ,

9 9 9( ) ( )

2 3 4(.) ( )( ) ( )( ) ( )( )

9 9 9

A B

A B

n b n n g n n r n

Market s t A s t A t B s t B t

n n b t n b t n t n g t n g t n t n r t n r t n t

Y Y Y

Y

u u

Y Y Y Y Y Y

p p Y p Y

u p Y p Y p Yω ω ω

= =

∆ ==

= = =

= =

= − + − + −

Homogeneous Service Market

Heterogeneous Service Market

80

Select an ODij PairU~[0,1]

Set-UPCRD + b < MRD ?

NO

Send RFP To NSP A, NSP B (s, b, )

NSP AProduction: YA 0Traffic: [XA] [0]

Constrained Minimization of Mean Num. of Packets in Network

(M/M/1 Queuing System)Non-Linear Program(Gradient Projection

and Golden Section Line search)




ZA YA + b[WA ][XA] + botd

A =D(ZA)

ZB YB + b[WB] [XB]+ botd

B =D(ZB)

*A

AA

MY

ε ∂=∂

*B

BB

MY

ε ∂=∂

A=f(ZA, A,A,s)

,K,MRD,Tnext_call

B=f(ZB, B,B,s)

Game Theory:F(p) = G(,A, A, )

START

Read sessionDatabase for

the NSP, OD pair,

Class,OD & DO route

indicesof the

session

Tear-Down

Select the Least Cost Route, botd

Delete both the OD & DO legsof the session

ClockInterval =1 secMax duration=

1e6 sec CRD: Current Regional DemandMRD: Maximum Regional Demand

12

3

4a

5a

4b4c

4d

4e

4f

4g

4h

4i

5b

4j

ForAll fourRegions

NSP BProduction: YB 0Traffic: [XB] [0]

NSP A: CAC

Game Theory:F(p) = G(,B, B, )

NSP B: CAC


Tnow = Tnext_call

Tnow = Ttear_down

Tnext_call=Tnow+ EXP(1/)

81







ZA YA + b[WA ][XA] + botd

A =D(ZA)

ZB YB + b[WB] [XB]+ botd

B =D(ZB)

*A

AA

MY

ε ∂=∂

*B

BB

MY

ε ∂=∂

A=f(ZA, A,A,s) B=f(ZB, B,B,s)

Game Theory:F(p) = G(,A, A, )

PA= H(F(p)) PB= H(F(p))

CustomerInitiates

Session withSmaller bid

NSP

YA ZA[XA] [WA]

Ttear_down = Tnow+ EXP(L)

YB ZB[XB] [WB]

Ttear_down= Tnow + EXP(L)

PA < PB PA > PB

the NSP, OD pair,

Class,OD & DO route

indicesof the

session


Delete both the OD & DO legsof the session

YA YA - b

[XA] [XA] - botd

YB YB - b

[XB] [XB] -botd

NSP_Index == A NSP_Index == B

4e

4f

4g

4h

4i

5b

4j

5c

NSP A: CAC

Game Theory:F(p) = G(,B, B, )

NSP B: CAC


4kAdd both OD and DO legs Add both OD and DO legs

optimizing providers’ profit in peer networks …...optimizing providers’ profit in peer...

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