Post on 28-Jun-2020
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
A_user@Dallas.Enterprise.com
NewYork.Enterprise.com
Atlanta.Enterprise.com
SIP User Agents (UA)
SIP Phone
PCSIP Mobile
SIP User Agents (UA)
SIP Phone
PCSIP Mobile
B_user@NewYork.Enterprise.com
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
Chicago.Enterprise.com
A_user@Dallas.Enterprise.com
NewYork.Enterprise.com
Atlanta.Enterprise.com
SIP User Agents (UA)
SIP Phone
PCSIP Mobile
SIP User Agents (UA)
SIP Phone
PCSIP Mobile
B_user@NewYork.Enterprise.com
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
Session Control Function (e.g. SIP proxy)
Bearer Function (e.g. IP Router)
Security Function (e.g. Firewall)
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;
I am willing to Pay ?
(1)I Want a Price of a Session
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;
I am willing to Pay ?
(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; 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
by proposedGame of Oligopoly
(2)Compute Price P3
by proposedGame of Oligopoly
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: Alice@Wildcat.com
(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: Alice@Wildcat.com
(7) 200 OK
(8) INVITESIP: Alice@Z.com
(9) 200 OK(10) INVITESIP: Alice@Wildcat.com
(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
Chicago.Enterprise.com
A_user@Dallas.Enterprise.com
NewYork.Enterprise.com
Atlanta.Enterprise.com
SIP User Agents (UA)
SIP Phone
PCSIP Mobile
SIP User Agents (UA)
SIP Phone
PCSIP Mobile
B_user@NewYork.Enterprise.com
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
Session Control Function (e.g. SIP proxy)
Bearer Function (e.g. IP Router)
Security Function (e.g. Firewall)
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
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
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
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
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
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 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 x x C
x x x x x x x x x 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 x x x C
x x x x x x x x x 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 x x x x C
x x x x x x x x 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)
CustomerRegion#4(Atlanta)
300300
CustomerRegion#1(Chicago)
CustomerRegion#1(Chicago)
CustomerRegion#3(Dallas)
CustomerRegion#3(Dallas)
CustomerRegion#2
(NY)
100
100
100 100
100
100
300
CustomerRegion#4(Atlanta)
EnterpriseRegion#4(Atlanta)
300300
CustomerRegion#1(Chicago)
EnterpriseRegion#1(Chicago)
CustomerRegion#3(Dallas)
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
CustomerRegion#4(Atlanta)
CustomerRegion#4(Atlanta)
300300
CustomerRegion#1(Chicago)
CustomerRegion#1(Chicago)
CustomerRegion#3(Dallas)
CustomerRegion#3(Dallas)
CustomerRegion#2
(NY)
100
100
100 100
100
100
300
CustomerRegion#4(Atlanta)
EnterpriseRegion#4(Atlanta)
300300
CustomerRegion#1(Chicago)
EnterpriseRegion#1(Chicago)
CustomerRegion#3(Dallas)
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
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
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
Mixed Strategy Profile of A
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
n s t n s t n s t n s tp F p prob p p γ= ≤ = =
Very High Rejection , , , , , , , ,: ( ) ( ) 0.95bid bid bid
n s t n s t n s t n s tp F p prob p p γ= ≤ = =
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
Network Load (ρNetw ork)
Mar
gina
l Cos
t ($)
Plot 3: Marginal Cost
0.4 0.6 0.8 10
2
4
6x 10
4
Network Load (ρNetw ork)
Uni
t Pro
fit ($
)
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
Network Load (ρNetw ork)
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90
50
100
Network Load (ρNetw ork)
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
Network Load (ρNetw ork)
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
Network Load (ρNetw ork)
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90
50
100
Network Load (ρNetw ork)
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
Network Load (ρNetw ork)
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
Market Load (ρMarket)
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 Load (ρMarket)
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
Market Load (ρMarket)
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
Market Load (ρMarket)
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
($)
Market Load (ρMarket)
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 %
Market Load (ρMarket)
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
Market Load (ρMarket)
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#1(Chicago)
CustomerRegion#1(Chicago)
CustomerRegion#3
(Dallas)
CustomerRegion#3
(Dallas)
yDallas
CustomerRegion#2(NewYork)
CustomerRegion#2(NewYork)
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)
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
Select the Least Cost Route, botd
Tnow = Tnext_call
Tnow = Ttear_down
Tnext_call=Tnow+ EXP(1/)
81
Constrained Minimization of Mean Num. of Packets in Network
(M/M/1 Queuing System)Non-Linear Program(Gradient Projection
and Golden Section Line search)
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) 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
Select the Least Cost Route, botd
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
Select the Least Cost Route, botd
4kAdd both OD and DO legs Add both OD and DO legs