combining network economics and engineering over several scales* debasis mitra mathematical sciences...
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COMBINING NETWORK ECONOMICS AND ENGINEERING
OVER SEVERAL SCALES*
Debasis MitraMathematical Sciences Research Center
Bell Labs, Lucent TechnologiesMurray Hill, NJ 07974
*JOINT WORK WITH QIONG WANG, STEVEN LANNING, RAM RAMAKRISHNAN and MARGARET WRIGHT
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BELL LABS MATH CENTER COMPOSITION
FUNDAMENTAL MATH
Non-linear Analysis- Special focus on Wave PropagationCombinatorics, Probability and Theory of Computing- Applications to Algorithms and OptimizationAlgebra and Number Theory- Applications to Coding Theory and Cryptography
MATH OF NETWORKS & SYSTEMS
Networking Fundamentals- Scheduling, statistical multiplexing, resource allocation- Asymptotics and Limit Laws- Large Deviations, Diffusions, Fluid LimitsData Networking- Traffic Engineering, IETFOptical Networking- Design, Optimization, ToolsWireless Networking:- Air-interface Scheduling, Traffic Engineering,ToolsSupply Chain Networks- Modeling, Optimization
STATISTICS
Statistical Computing Environments-Analysis of RDBMSData traffic measurements, models and analysis-Packet header capture and analysisOnline analysis of data streams-Fraud detectionData visualizationStatistics in Manufacturing
MATH OF COMMUNICATIONS
Information TheoryWireless: Multiple Antenna CommunicationsCoding: Fundamental Theory Applications - Optical, Data, WirelessSignal Processing: Source CodingSpectral Estimation
BUSINESS PLANNING & ECONOMICS RESEARCH
Economics/Business Planning Fundamentals- Models for Competition, Game Theory, Price-Demand RelationshipsNetwork Economics- Optimization of Investments, Technology Selections, Net Present ValueStrategic Bidding
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My roots in networkingNetwork Modeling
model scale stochastic fluid, diffusion, large deviation modelstime scale circuit-switched, packet (ATM, IP)
spatial scale core & access, wireless & wireline ( optical, data) Network (and QoS) Control closed loop congestion control, designing for delay-bandwidth productopen loop leaky-bucket regulation, traffic shaping, prioritieseffective bandwidth burstiness measure, admission control
Network Resource Managementscheduling generalized processor sharing + statistical multiplexingresource sharing trunk reservation, virtual partitioningservice level agreements structure & management
Network Design & Optimizationmulti-service loss network framework connection-oriented network designtraffic engineering deterministic, stochastic, nonlinearsoftware packages PANACEA, TALISMAN, D’ARTAGNAN, VPN DESIGNER
Network Economics and Externalitiesnew services diffusion, pricing and investment strategies
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A Modelling Approach Combining Economics, Business Planning and Network Engineering
CAPACITY PLANNING
given price-demand relationships and unit cost trends, determine optimal capacity growth path
COMBINED ECONOMICS & TRAFFIC ENGINEERING
- joint optimization of multiservice pricing and provisioning
- services have characteristic price elasticity of demand and routing constraints
Objective: Maximize Revenue wrt prices and routing
RISK-AWARE NETWORK REVENUE MANAGEMENT
- revenue from carrying traffic and bandwidth wholesale/acquisition
- uncertainty in traffic demand implies risk in revenue generation
Objective: Maximize risk-adjusted revenue
network capacity fixed
prices and expected demand fixed
strategic, long term
tactical, short term
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AGENDA
CAPACITY PLANNING
- long time scale, strategic
COMBINED ECONOMICS & TRAFFIC ENGINEERING
- intermediate time scale, strategic/tactical
RISK-AWARE NETWORK REVENUE MANAGEMENT
-short time scale, tactical
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Functional Form Is Constant Elasticity Demand
Source: Shawn O’Donnell from Historical Statistics of the Electric Utility Industry: Through 1970, New York: Edison Electric Institute, 1973, Tables 7 and 33.
-1.40
-1.60
-1.80
-2.00
-2.20
-2.40
-2.60
-2.80
-3.00
1100 1200 1300 1400 1500
In (Electricity Generated (M k Wh))
Elasticity = 2.2 1926-1970
= 2.2 1962-1970 with very close fit
Elasticity of Electricity Demand
Estimated Price Elasticity is 1.3 to 1.7 for Data Bandwidth,and 1.05 for Voice Bandwidth
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PRICE vs. DEMAND (log scales)(a) DRAM (b) Electricity
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DEMAND FUNCTION
DEMAND ELASTICITY,
In the limit,
REVENUE, R = pD
pp
DD
E
pp
DD
E
p
pE
R
R)1(
if E 1 then (reduction in price revenue increases)
CONSTANT ELASTICITY
Ep
AD
A is “demand potential”
D
A
p1
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A FRAMEWORK FOR CAPACITY PLANNING
Economic Model:
High price elasticity of demand for bandwidth
Technology Roadmap:
High rate of innovations in optical networking
Exponential decrease in time of unit cost
Network Design
Algorithms to optimize network design for various technologies
Economic Model
Max NPV
Technology Roadmap Network Design
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OVERVIEW OF CAPACITY PLANNING
CONTINUOUS EMERGENCE
OF NEW OPTICAL SYSTEMS
innovations & cost compressionOPTIMAL PLANNING
optimize NPV
decision variables:
price, investment,
equipment deployment
nonlinear, mixed-integer optimization
TECHNOLOGY
ECONOMICS
OPTIMIZATION BUSINESS/MARKETDECISIONS
ELASTIC DEMAND
FUNCTIONS
price-demand relations
DEPLOYMENT OF
NEW SYSTEMS
PRICING STRATEGIES
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A SPECIFIC MODEL (Phil. Trans. Royal Soc. 2000)
OPTIMIZE NET PRESENT VALUE (NPV) OVER TIMEcarrier’s long-haul transport network
PARAMETRIC MODEL OF PROJECTED INNOVATIONS IN DWDMcapacity growth & cost compressionexponentiality
MODEL PRICE-DEMAND RELATIONSHIP constant elasticity model
JOINT OPTIMIZATION OF PRICES & INVESTMENTSmultiple time periodsnonlinear objective function, nonlinear constraints, integer variables
EXAMPLE: 5 CITY, SINGLE RINGsensitivity analysis
CONCLUSION
CARRIER WILL MAXIMIZE NPV BY DROPPING PRICES AND
GROWING NETWORK CAPACITY FREQUENTLY
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PRICES OVER TIME
LARGER ELASTICITY PRICES UNIFORMLY LOWER FOR ALL TIME PERIODS
LARGER DISRUPTIVENESS HIGHER INITIAL PRICE, LOWER PRICE IN LATER PERIODS
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CAPACITY (ON A LOG SCALE) OVER TIME
EXPONENTIAL GROWTH IN CAPACITY
LARGER ELASTICITY LARGER CAPACITY IN ALL PERIODS
LARGER DISRUPTIVENESS LOWER INITIAL CAPACITY, GROWS MORE RAPIDLY IN LATER PERIODS
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“OPTIMAL PLANNING FOR OPTICAL TRANSPORT NETWORKS”
S. LANNING, D. MITRA, Q. WANG, M.H. WRIGHTin
Phil. Trans. R. Soc. Lond. AVol. 358, pp. 2183-2196, 2000
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BOONBusiness Optimized Optical Networks
BOON
Business/economic assumptions
Network Architecture
Technology Roadmap
Financials
Pricing Strategy
Technology Adoption
Capacity Expansion
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AGENDA
CAPACITY PLANNING
- long time scale, strategic
COMBINED ECONOMICS & TRAFFIC ENGINEERING
- intermediate time scale, strategic/tactical
RISK-AWARE NETWORK REVENUE MANAGEMENT
-short time scale, tactical
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JOINT OPTIMIZATION OF PRICING & ROUTING IN MULTI-SERVICE NETWORKS
• Intermediate time scale i.e. network link capacities are fixed, prices for services are decision variables
• Voice & Data are examples of services• Services have distinct demand elasticity to price• Services have distinct traffic engineering/routing
requirements e.g. voice needs to be routed over fewer hops than data
SERVICE PROVIDER’S PROBLEM:
Set prices, which generate demands, and route demands over network to maximize network revenue.
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price
price-demandrelationship routing
network resources
demandgenerated
carrieddemand
revenue
Traffic EngineeringTraffic Engineering
Network PricingNetwork Pricing
Fixed network capacity, Price is adjustable
Traffic Engineering: Mapping generated demand to network resources
Dual role of price: (a) determines demand (b) determines revenue
SERVICE PROVIDER’S JOINT OPTIMIZATION PROBLEM:Set prices, which generate demands, and route demands over network to maximize network revenue.
OVERVIEW OF THE PROBLEM
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MORE ON PROBLEM
GIVEN: (a) Network and , capacity on link ,
(b) , set of admissible routes for ,
i.e., = r
(c) Constant demand elasticity to price
D.. is demand, P.. is price, A.. is demand potential
Assume: elasticity
is carried bandwidth (flow) of service type s on route r
NETWORK REVENUE,
C
,s ,s
,s Route r is admissible for service sRoute r is admissible for service sand (origin, destination) = and (origin, destination) =
D
1
),,(, srX sr
,, srsrs
sXPW
Note:Dual role of price P in determining (a) demand and (b) revenue
2,1
P
1 s
1 s
s
s
ss
P
AD
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REVENUE MAXIMIZATION PROBLEM
: demand constraint
:link constraint
0sP 0srX :nonnegativity
OBERVATIONS
(a) Note
(b) Justified in replacing by = in demand and link constraints. sss DPP
srsr
ss
XPXPW
srs ),(,,
max
),(
,
sDXst ssrsr
CX srrsrs :,.
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TRANSFORMED JOINT PRICING + ROUTING PROBLEM
CONCAVE OBJECTIVE FUNCTION, LINEAR CONSTRAINTS EFFECTIVE ALGORITHMS EXIST FOR CONCAVE PROGRAMMING.
NOTE PATH BASED FORMULATION
:demand satisfaction
:link constraints
0,0 srs XD
,
11
,max
sss
XD
sss
srs
DAW
,),(
sDXst ssrsr
CX srs rsr , :,
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LAGRANGE’S METHOD, SHADOW COSTS
s
Lagrangian,
Lagrange multipliers, shadow costs:
end-to-end demand matching
link capacity constraint
,
)1(1),,,(s
sssss DAXDL
s
srsr
ss DX
,,
, :,s rsrsrXC
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RESULTS FROM LAGRANGE’S METHODRESULTS FROM LAGRANGE’S METHOD
OPTIMALOPTIMAL PRICESPRICES
OPTIMAL ROUTINGOPTIMAL ROUTING
either and
or and
0srX
If is “link cost”, and for any route r, “route cost”
then is “minimum route cost for ”
That is, concave programming “minimum cost routing” policy is optimal
NOTE UNIFICATION OF OPTIMAL PRICING & ROUTING MECHANISMS
s ),( s
sr
sr
,
r
ss
s
s
ss
s
D
AP
1
1
0srX
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AN ILLUSTRATIVE EXAMPLE
A
D
B
C
7
3
1 1
Consider traffic source A, destination B– Link costs ( l from optimization) shown in figure
– Min-hop route cost = 7– Least cost of route = 5– Voice required to take min-hop route(s)– Data allowed to take up to 5 hops
In example,
data route is )( BCDA voice route is )( BA
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ASYMPTOTIC PROPERTIES OF OPTIMAL SOLUTION
“UNIFORM CAPACITY EXPANSION”: capacities on all links scaled up uniformly
i.e.
OPTIMAL PRICESOPTIMAL PRICES
max
1
smOD
mD
s
s
Optimal prices decrease, but at a lower rate than capacity increase.
OPTIMAL DEMANDSOPTIMAL DEMANDS
max1
11
mO
PmP
s
s
Demand for most elastic service grows linearly with capacity.
Demands for all other services grow at sub-linear rates.
mmCC ,0,
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ASYMPTOTIC PROPERTIES OF OPTIMAL ASYMPTOTIC PROPERTIES OF OPTIMAL ROUTINGROUTING
Uniform Capacity Expansion
1. does not necessarily result in minimum-hop routing,
2. provided capacities are sufficiently high, i.e.
high price elasticity of one service
minimum-hop routing for all services
m
,])1
[(),(
min
ss
s
s AC s
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SAMPLE NETWORK
1
2 3 4
5
6
78
Service:voice: 1=1.05, A1,=2000data: 2=1.5, A2,=200 for all
Capacity:Cl=400 for all l
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CHANGE OF TRAFFIC MIX WITH UNIFORM CAPACITY EXPANSION
20%
40%
60%
80%
100 10000
voice
data
Traffic Mix
Capacity
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MINIMUM-HOP ROUTING IS IMPLIED BY HIGH PRICE ELASTICITY
1
2 3 4
5
6
78
r_B
R_A
R_B
r_A
r_A(4 hops)
R_A (3 hops)
r_B(3 hops)
R_B(2 hops)
=1.1 100% 0% 100% 0%=1.2 100% 0% 28% 72%=1.3 62.7% 37.3% 0% 100%=1.4 9.5% 90.5% 0% 100%=1.5 0% 100% 0% 100%
FIXED LINK CAPACITIES
FIXED VOICE ELASTICITY
ROUTING OFDATA DEMAND WITH CHANGING DATA ELASTICITY
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References
D.Mitra, K.G.Ramakrishnan, Q.Wang, “Combined Economic Modeling and Traffic Engineering: Joint Optimization of
Pricing and Routing in Multi-Service Networks”,Proc, 17th International Teletraffic Congress, 2001
D.Mitra, Q.Wang, “Generalized Network Engineering:Optimal Pricing and Routing for Multi=Service Networks”,
Proc. SPIE, 2002
(on my website: http://cm.bell-labs.com/~mitra)
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AGENDA
CAPACITY PLANNING
- long time scale, strategic
COMBINED ECONOMICS & TRAFFIC ENGINEERING
- intermediate time scale, strategic/tactical
RISK-AWARE NETWORK REVENUE MANAGEMENT
-short time scale, tactical
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Risk-Aware Network Revenue Management: OverviewRisk-Aware Network Revenue Management: Overview
wholesale• commodity• deterministic demand• routing policy constraints• wholesale revenue from selling capacity
retail• differentiated services• random demand• routing policy constraints• revenue from retail, associated with risk
supply• installed capacity• opportunity to buy capacity to serve retail and wholesale demands
model• quantify revenue reward and risk; • optimize the weighted combination
risk tolerance
short-term tactical decisions on provisioning, routing and buying capacity - prices and installed capacity stay fixed
revenue management decisions
• provisioning• routing• buying
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Objectives
•Understand the implications of (uncertain) demand variability on network management, i.e., on provisioning, routing,
resource utilization, revenue and risk
• Understand the implications of service provider-specific risk averseness
•Make the value proposition for resource-sharing between carriers
•Create tool for service providers to use for risk-aware network revenue management
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Problem Formulationnetwork model network model ((LL: set of links): set of links)
wholesale wholesale ((commoditycommodity)) market market ((VV22:: set of node pairs set of node pairs))
cl : installed capacity on link l , pl : unit price for short-term capacity incrementbl (decision variable): amount of capacity to buy on link lcl + bl: total capacity on link lNote: we allow cl =0, in which case l is considered a virtual link
: wholesale price for unit bandwidth between node pair v)( 2Vvev
2Vv
vv ye
yv (decision variable): bandwidth provisioned between node pair v for wholesale
: wholesale revenue
retail retail ((serviceservice)) market market ((V1:: set of node pairs set of node pairs))
)( 1Vvv : unit retail price for node pair v,
dv (decision variable): bandwidth provisioned between node pair v for serving retail demand, which is random
1
)()(Vv
vvr dwdW
Fv(x) : CDF of retail demand
: retail revenue (random variable)
11
0 )()()]([Vv
dvv
Vvvvr
v dxxFdmdWE
11
)]()(2[)()]([ 20
222
Vvvv
dvv
Vvvvvr dmdxxFxddWVar v
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The Optimization ModelThe Optimization Model
),,,,(max byd
)(
)(0
2)(
1)(
2
1
Vvy
Vvdd
vvRr
r
vvRr
rv
lbvy lv certainfor,certainfor 00
)(0
):)((0
):)((0
22
11
Llb
VvvRr
VvvRr
l
r
r
)(:)(:)( 21
Llbc llrlvRrr
rlvRrr
: link capacity constraint
: markets in selected links only
: non-negativity condition for traffic and bandwidth variables
: provision capacity on route r is minimum bandwidth required to satisfy GoS
vd
121
22)(Vv
vvLl
llVv
vvVv
vvv bpyedm
)()(),,,,( WWEbyd
where
i.e.
: W is total network revenue (random variable)
retail (mean)
wholesale buying risk
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2500
2700
2900
3100
3300
3500
75000 76000 77000 78000 79000
expected value
standard deviation
infeasible
inefficient
Example Illustrating Efficient Frontier of Revenue and the Example Illustrating Efficient Frontier of Revenue and the Influence of Risk Parameter Influence of Risk Parameter (())
0%
25%
50%
75%
100%
0 0.5 1 1.5 2 2.5
% increase in provisioned bandwidth for wholesale
% decrease in expenseof buying bandwidth
% of total capacity to serve retail demand
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References
D.Mitra, Q.Wang, “Stochastic Traffic Engineering, with Applications to Network Revenue Management”,
to appear in Proc. INFOCOM 2003.
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BACK-UP
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39
• Voice & Data are examples of services
• Demand formulated at aggregated level: total bandwidth for each (s,)=(s, ((1, 2))
• Service characterization:– distinct QoS routing restrictions (e.g.. voice needs to be routed over fewer hops than data)
set of admissible routes for (s,)
– distinct price-demand relationship, as reflected in different values of price elasticity
Route r is admissible for service sRoute r is admissible for service s
and (origin, destination) and (origin, destination) ,s = rr
ss
ss
P
AD
ss
sss PdP
DdD
/
/
MULTI-SERVICE NETWORKS
D
1
A
P
1 s
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40
$100K
$200K
$300K
Revenue
10% Price Decline / 18 Periods
$100 $15
1,000 Units@ $100/each
Bandwidth Economics: Impact of Rapidly Descending Prices Bandwidth Economics: Impact of Rapidly Descending Prices
* Elasticity is actually expressed as a Negative
0.5
1.5
Elasticity*
1.0
$39KRevenue
$258KRevenue
$100KRevenue
Estimated Price Elasticity for Bandwidth is 1.3 to 1.7
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Elasticity of Electricity Demand
-1.40
-1.60
-1.80
-2.00
-2.20
-2.40
-2.60
-2.80
-3.00
1100 1200 1300 1400 1500
In (Electricity Generated (M k Wh))
Functional Form Is Constant Elasticity Demand
Source: Shawn O’Donnell from Historical Statistics of the Electric Utility Industry: Through 1970, New York: Edison Electric Institute,1973, Tables 7 and 33.
Elasticity = 2.2 1926-1970
= 2.2 1962-1970 with very close fit
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42
Bandwidth
• Bandwidth market is characterized by:– High elasticity---our updated estimate is 1.3-1.7
– rapidly decreasing unit capital costs
Elasticity = 2.2 1926 -1970 = 2.2 1962 -1970 with very close fit
Elasticity of Electricity Demand
-3.00
-2.80
-2.60
-2.40
-2.20
-2.00
-1.80
-1.60
-1.4011.00 12.00 13.00 14.00 15.00
ln(Electricity Generated (M kWh) )
3 Tb/s1 Tb/s
300 Gb/s
100 Gb/s
30 Gb/s10 Gb/s
WDM Capacity doubling every generation (2 years)
Functional form is constant elasticity,i.e.,linearity
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ELASTICITY
THERE IS EMPIRICAL SUPPORT FOR THE CONSTANT-ELASTICITY DEMAND FUNCTIONS
Memory (DRAM) 1965 – 1992
Electricity 1926 – 1970
Servicesvoice traffic 1.05residential voice traffic 1.337 (France Telecom, 1999)
Equipmentdigital circuit switch 1.28WAN ATM core switch 2.84ATM edge switch 2.11
Optical Systems (source: Lucent Tech.)capacity doubling for same cost every 2 yearstraffic demand 1.5 every year E 1.6
)//log()/log( / 2112 ppDDEpAD E
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MODEL FOR TECHNOLOGY
K = set of WDM technologies
k = time period that tech. k is introduced
k = max capacity (in OC1) of tech. k
CAPACITY GROWTH exponentiality
COST
Ikt = acquisition cost of a WDM system of tech. k at time period t
exponentiality in per-unit investment costs
d = “disruptiveness”
COST COMPRESSION
)1( 1 kk
1
,1 1)1(
k
k
k
k kkI
dI
ktktk tII ,1,
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PROBLEM FORMULATION: REVENUE, COST
single UPSR ring length L N cities
I = set of city pairs time periods 1, 2, . . . , T
REVENUE
COST
conduits, laying fiber are sunk costs, not modelled investment cost for OTU,
terminals, regen. & amplifiers: (Ikt)
maintenance cost per fiber per mile: mkt
bkt = # (WDM systems of tech. k bought in period t)
ukt = # (WDM systems of tech. k used in period t)kt
kktkt
kktt u m 2Lb I N Expense
I
I
ji,ijtijtt
Eijtijtijt
D p R
ji, pAD / )(
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TECHNOLOGY CONSIDERATION SET MODELED
Period Transmission Speed Wavelengths
1 OC48 40
2 OC192 20
3 OC192 40
4 OC192 80
5 OC768 40
6 OC768 80
. . . . . . . . .
Define q, technology disruptiveness,
where is the investment expense of a new system in period k,
and is the capacity of the new system in period k
1
1 1)1(
k
k
k
k kkI
qI
kkI
k
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PROBLEM FORMULATION: NPV, CONSTRAINTS
CASH FLOW,
DISCOUNT RATE,
TERMINALVALUE,
TV NPV1
t
T
t
tC
ktb
tk, ubu
tuD
kkt
tk,ktkt
ji, kkktijt
0(iii)
(ii)
(i)
1
)(
I
PROBLEM
itynonnegativsconstraint st
}{ },{ },{
NPVmax
ktktjti, bup
CONSTRAINTS
ttt RC Expense
T
fC
1
1TV
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RESULTS: PARAMETERS
5 city 20 city pair L = 2500 mile T= 10
CAPACITY GROWTH
= 2
INVESTMENT COST
per system cost for tech. 1 in period 1,
d = 0.2, 0.3, 0.4
e.g. d = 0.3 30% reduction per-unit cost with each new technology
= 0.9
per-period reduction in investment cost of already introduced tech. is 10%
1-OC per $ 105.2$ 108.4 3611 I
d, , ,11II kt
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TECHNOLOGY ACQUISITIONS OVER TIME
LARGER ELASTICITY NEW TECHNOLOGIES ACQUIRED SOONER, IN LARGER NUMBERS, MORE FREQUENTLY
LARGER DISRUPTIVENESS LESS ACQUISITIONS IN EARLY TIME PERIODS, MORE IN LATER PERIODS