COMBINING NETWORK ECONOMICS AND ENGINEERING

OVER SEVERAL SCALES*

Debasis MitraMathematical Sciences Research Center

Bell Labs, Lucent TechnologiesMurray Hill, NJ 07974

mitra@lucent.com

*JOINT WORK WITH QIONG WANG, STEVEN LANNING, RAM RAMAKRISHNAN and MARGARET WRIGHT

23

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

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

4

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

5

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

6

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

7

PRICE vs. DEMAND (log scales)(a) DRAM (b) Electricity

8

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

9

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

10

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

11

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

12

PRICES OVER TIME

LARGER ELASTICITY PRICES UNIFORMLY LOWER FOR ALL TIME PERIODS

LARGER DISRUPTIVENESS HIGHER INITIAL PRICE, LOWER PRICE IN LATER PERIODS

13

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

“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

15

BOONBusiness Optimized Optical Networks

BOON

Business/economic assumptions

Network Architecture

Technology Roadmap

Financials

Pricing Strategy

Technology Adoption

Capacity Expansion

16

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

17

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.

18

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

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

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 :,.

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 , :,

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

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

24

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

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,

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

27

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

28

CHANGE OF TRAFFIC MIX WITH UNIFORM CAPACITY EXPANSION

20%

40%

60%

80%

100 10000

voice

data

Traffic Mix

Capacity

29

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

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)

31

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

32

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

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

34

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

35

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

36

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

References

D.Mitra, Q.Wang, “Stochastic Traffic Engineering, with Applications to Network Revenue Management”,

to appear in Proc. INFOCOM 2003.

BACK-UP

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

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

41

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

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

43

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

44

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,

45

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 / )(

46

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

47

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

48

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

49

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