COMBINING NETWORK ECONOMICS
AND ENGINEERING
OVER SEVERAL SCALES*
Debasis Mitra
Mathematical Sciences Research Center
Bell Labs, Lucent Technologies
Murray Hill, NJ 07974
mitra@lucent.com
*JOINT WORK WITH QIONG WANG, STEVEN LANNING,
RAM RAMAKRISHNAN and MARGARET WRIGHT
BELL LABS MATH CENTER COMPOSITION
FUNDAMENTAL MATH
Non-linear Analysis
- Special focus on Wave Propagation
Combinatorics, Probability and Theory of Computing
- Applications to Algorithms and Optimization
Algebra and Number Theory
- Applications to Coding Theory and Cryptography
STATISTICS
Statistical Computing Environments
-Analysis of RDBMS
Data traffic measurements, models and analysis
-Packet header capture and analysis
Online analysis of data streams
-Fraud detection
Data visualization
Statistics in Manufacturing
MATH OF NETWORKS & SYSTEMS
Networking Fundamentals
- Scheduling, statistical multiplexing, resource
allocation
- Asymptotics and Limit Laws
- Large Deviations, Diffusions, Fluid Limits
Data Networking
- Traffic Engineering, IETF
Optical Networking
- Design, Optimization, Tools
Wireless Networking:
- Air-interface Scheduling, Traffic Engineering,Tools
Supply Chain Networks
- Modeling, Optimization
MATH OF COMMUNICATIONS
Information Theory
Wireless: Multiple Antenna Communications
Coding: Fundamental Theory
Applications - Optical, Data, Wireless
Signal Processing: Source Coding
Spectral Estimation
BUSINESS PLANNING & ECONOMICS RESEARCH
Economics/Business Planning Fundamentals
- Models for Competition, Game Theory, Price-Demand Relationships
Network Economics
- Optimization of Investments, Technology Selections, Net Present Value
Strategic Bidding
23
My roots in networking
Network Modeling
model scale
time scale
stochastic fluid, diffusion, large deviation models
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 product
open loop
leaky-bucket regulation, traffic shaping, priorities
effective bandwidth burstiness measure, admission control
Network Resource Management
scheduling
generalized processor sharing + statistical multiplexing
resource sharing
trunk reservation, virtual partitioning
service level agreements structure & management
Network Design & Optimization
multi-service loss network framework connection-oriented network design
traffic engineering deterministic, stochastic, nonlinear
software packages PANACEA, TALISMAN, D’ARTAGNAN, VPN DESIGNER
Network Economics and Externalities
new services diffusion, pricing and investment strategies
A Modelling Approach Combining Economics,
Business Planning and Network Engineering
strategic,
long term
CAPACITY PLANNING
given price-demand relationships and unit cost trends, determine
optimal capacity growth path
network capacity fixed
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
prices and expected demand fixed
RISK-AWARE NETWORK REVENUE MANAGEMENT
- revenue from carrying traffic and bandwidth wholesale/acquisition
tactical,
short term
- uncertainty in traffic demand implies risk in revenue generation
Objective: Maximize risk-adjusted revenue
4
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
5
Elasticity of Electricity Demand
-1.40
1100
1200
1300
1400
1500
-1.60
-1.80
-2.00
Elasticity = 2.2 1926-1970
= 2.2 1962-1970 with very close fit
-2.20
-2.40
-2.60
-2.80
-3.00
In (Electricity Generated (M k Wh))
Source: Shawn O’Donnell from Historical Statistics of the Electric Utility Industry: Through 1970, New
York: Edison Electric Institute, 1973, Tables 7 and 33.
Functional Form Is Constant Elasticity Demand
Estimated Price Elasticity is 1.3 to 1.7 for Data Bandwidth,
and 1.05 for Voice Bandwidth
6
PRICE vs. DEMAND (log scales)
(a) DRAM (b) Electricity
7
DEMAND FUNCTION
D   p 
  
D

  p 
p 

p 
DEMAND ELASTICITY, E   
 D 
E   
D
In the limit,
REVENUE,
R = pD



 p 
R
 ( E  1) 
R
 p
if E  1 then (reduction in price  revenue increases)
D
CONSTANT ELASTICITY
D
A
A

pE
A is “demand potential”
p
1
8
A FRAMEWORK FOR CAPACITY PLANNING
Economic Model
Max NPV
Technology Roadmap
Network Design
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
9
OVERVIEW OF CAPACITY PLANNING
TECHNOLOGY
CONTINUOUS EMERGENCE
OF NEW OPTICAL SYSTEMS
OPTIMIZATION
innovations & cost compression
OPTIMAL PLANNING
optimize NPV
ECONOMICS
ELASTIC DEMAND
FUNCTIONS
decision variables:
price, investment,
equipment deployment
BUSINESS/MARKET
DECISIONS
DEPLOYMENT OF
NEW SYSTEMS
PRICING
STRATEGIES
nonlinear, mixed-integer
optimization
price-demand
relations
10
A SPECIFIC MODEL (Phil. Trans. Royal Soc. 2000)
OPTIMIZE NET PRESENT VALUE (NPV) OVER TIME
carrier’s long-haul transport network
PARAMETRIC MODEL OF PROJECTED INNOVATIONS IN DWDM
capacity growth & cost compression
exponentiality
MODEL PRICE-DEMAND RELATIONSHIP
constant elasticity model
JOINT OPTIMIZATION OF PRICES & INVESTMENTS
multiple time periods
nonlinear objective function, nonlinear constraints, integer variables
EXAMPLE: 5 CITY, SINGLE RING
sensitivity analysis
CONCLUSION
CARRIER WILL MAXIMIZE NPV BY DROPPING PRICES AND
GROWING NETWORK CAPACITY FREQUENTLY
11
PRICES OVER TIME
LARGER ELASTICITY PRICES UNIFORMLY LOWER FOR ALL
TIME PERIODS
LARGER DISRUPTIVENESS  HIGHER INITIAL PRICE, LOWER
PRICE IN LATER PERIODS
12
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
13
“OPTIMAL PLANNING FOR OPTICAL TRANSPORT
NETWORKS”
S. LANNING, D. MITRA, Q. WANG, M.H. WRIGHT
in
Phil. Trans. R. Soc. Lond. A
Vol. 358, pp. 2183-2196, 2000
BOON
Business Optimized Optical Networks
Pricing Strategy
Business/economic
assumptions
Financials
Network Architecture
Capacity Expansion
BOON
Technology Roadmap
Technology Adoption
15
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
16
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.
17
OVERVIEW OF THE PROBLEM
price
Network Pricing
network
resources
price-demand
relationship
demand
generated
routing
carried
demand
revenue
Traffic Engineering
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.
18
MORE ON PROBLEM
GIVEN: (a) Network and C , capacity on link  ,
(b)
s,  , set of admissible routes for s,  ,
i.e.,
s,  
=
r
Route r is admissible for service s
and (origin, destination) =  1, 2  

(c) Constant demand elasticity to price
D s


D
 s  1
A
 s
Pss
1
P
D.. is demand, P.. is price, A.. is demand potential
Assume: elasticity
X sr , r  ( s,  ),
 s  1
is carried bandwidth (flow) of service type s on route r
NETWORK REVENUE, W   Ps  X sr
s ,
r s , 
Note:Dual role of price P in determining (a) demand and (b) revenue
REVENUE MAXIMIZATION PROBLEM
max
W 
Ps ,X sr 
st
r s ,
s.
Ps
s,
X

 

 


sr

r ( s ,
X sr
)
 Ds ( s,  )

 
r s ,
:r
Ps  0
X sr  C  
X sr  0
: demand
constraint
:link
constraint
:nonnegativity
OBERVATIONS
(a) Note Ps  Ps Ds
(b) Justified in replacing


by = in demand and link constraints.
TRANSFORMED JOINT PRICING + ROUTING PROBLEM
max
W  
Ds 
, X sr 
st
s ,

r ( s ,

s,
1  s
As
 s 1  s
Ds
X sr  Ds s,  
)

 
r s ,
:r
X sr  C  
:demand
satisfaction
:link
constraints
Ds  0, X sr  0
CONCAVE OBJECTIVE FUNCTION, LINEAR CONSTRAINTS EFFECTIVE
ALGORITHMS EXIST FOR CONCAVE PROGRAMMING.
NOTE PATH BASED FORMULATION
LAGRANGE’S METHOD, SHADOW COSTS
Lagrangian,
 s 1)
L( D, X ,  ,  )   As1 s Ds(
 s
s ,

   s   X sr  Ds
s ,
 r s , 



    C  
X sr 


s , r s , :r  

Lagrange multipliers, shadow costs:
 s 
end-to-end demand matching
 
link capacity constraint




RESULTS FROM LAGRANGE’S METHOD
OPTIMAL PRICES
 As
Ps  
D
 s
1  s





 s
 s  1
 s
OPTIMAL ROUTING
either
or
X sr  0
and
X sr  0
and


r
r
   s
   s
If  is “link cost”, and for any route r, “route cost” 
then
 s
is “minimum route cost for ( s,  )”
That is, concave programming

r
 ,
“minimum cost routing” policy is optimal
NOTE UNIFICATION OF OPTIMAL PRICING & ROUTING MECHANISMS
AN ILLUSTRATIVE EXAMPLE
A
7
1
D
B
1
3
C
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,
voice route is ( A  B)
data route is ( A  D  C  B)
24
ASYMPTOTIC PROPERTIES OF OPTIMAL SOLUTION
“UNIFORM CAPACITY EXPANSION”: capacities on all links scaled up uniformly
i.e.
C  mC,0, m  
OPTIMAL PRICES
Ps m 
1


 O 1 

max
Ps 1
m


Optimal prices decrease, but at a lower rate than capacity increase.
OPTIMAL DEMANDS
Ds m 
 O m s
D s 1

 max

Demand for most elastic service grows linearly with capacity.
Demands for all other services grow at sub-linear rates.
ASYMPTOTIC PROPERTIES OF OPTIMAL ROUTING
Uniform Capacity Expansion
m  
1. does not necessarily result in minimum-hop routing,
2. provided capacities are sufficiently high, i.e.


 s  1 s
) As ] ,
 Cmin   [(
s
( s , )


high price elasticity of one service
 minimum-hop routing for all services
SAMPLE NETWORK
5
2
3
4
6
1
8
Service:
voice: 1=1.05, A1,=2000
data: 2=1.5, A2,=200
7
for all 
Capacity:
Cl=400 for all l
27
CHANGE OF TRAFFIC MIX WITH
UNIFORM CAPACITY EXPANSION
Traffic Mix
80%
data
60%
40%
voice
Capacity
20%
100
10000
28
MINIMUM-HOP ROUTING IS IMPLIED BY
HIGH PRICE ELASTICITY
r_A
5
3
2
4
FIXED VOICE
ELASTICITY
6
ROUTING OF
DATA DEMAND
WITH CHANGING
DATA ELASTICITY
r_B
R_B
1
8
FIXED LINK
CAPACITIES
7
R_A
=1.1
=1.2
=1.3
=1.4
=1.5
r_A
(4 hops)
100%
100%
62.7%
9.5%
0%
R_A
(3 hops)
0%
0%
37.3%
90.5%
100%
r_B
(3 hops)
100%
28%
0%
0%
0%
R_B
(2 hops)
0%
72%
100%
100%
100%
29
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)
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
31
Risk-Aware Network Revenue Management: Overview
supply
wholesale
•
•
•
commodity
deterministic demand
routing policy
constraints
• wholesale revenue
from selling capacity
• installed capacity
• opportunity to buy capacity to serve
retail and wholesale demands
model
• quantify revenue reward
and risk;
• optimize the weighted
combination
retail
revenue management
decisions
• provisioning
• routing
• buying
•
•
•
differentiated services
random demand
routing policy
constraints
• revenue from retail,
associated with risk
risk tolerance
short-term tactical decisions on provisioning, routing and buying capacity
- prices and installed capacity stay fixed
32
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
Problem Formulation
network model (L: set of links)
cl : installed capacity on link l , pl : unit price for short-term capacity increment
bl (decision variable): amount of capacity to buy on link l
cl + bl: total capacity on link l
Note: we allow cl =0, in which case l is considered a virtual link
retail (service) market (V1: set of node pairs)
 v ( v  V1 ) : unit retail price for node pair v,
Fv(x) : CDF of retail demand
dv (decision variable): bandwidth provisioned between node pair v for
serving retail demand, which is random

Wr (d )   wv (d v ): retail revenue (random variable)
vV1

E[Wr ( d )]   mv ( d v )    v 0dv Fv ( x )dx
vV1
vV1

Var[Wr ( d )]    v2 v2 ( dv )    v2[ 0dv 2 xFv ( x )dx  mv2 ( dv )]
vV1
vV1
wholesale (commodity) market (V2: set of node pairs)
ev (v  V2 ) : wholesale price for unit bandwidth between node pair v
yv (decision variable): bandwidth provisioned between node pair v for wholesale
e
vV2
v
yv : wholesale revenue
34
The Optimization Model
    
max ( d , y, b ,  ,  )
where
    
 ( d , y, b ,  ,  )  E (W )   (W )
i.e.
    v mv ( d v )   ev yv   pl bl  
vV1
vV2
retail (mean)
0  dv 

wholesale
lL
buying
: W is total network revenue
(random variable)
 v  v
2
2
vV1
risk
( v  V1 )  : provision capacity on route r
 d is minimum bandwidth
rR1 ( v )
v



y
(
v

V
)
 r
required to satisfy GoS
v
2 
rR2 ( v )

  r    r  cl  bl ( l  L) : link capacity constraint
rR1 ( v ):lr
0  r
0  r
0  bl
r
 dv
rR2 ( v ):lr
( r  R1 ( v ) : v  V1 )  : non-negativity condition

( r  R2 ( v ) : v  V2 ) for traffic and bandwidth
variables
( l  L) 

yv  0 for certain v,
bl  0 for certain l
35
: markets in selected links only
Example Illustrating Efficient Frontier of Revenue and the
Influence of Risk Parameter ()
standard de viation
3500
3300
inefficient
3100
2900
infeasible
2700
e xpe cte d value
2500
75000
76000
77000
78000
79000
% increase in provisioned
bandwidth for wholesale
100%
75%
% of total capacity to serve
retail demand
50%
% decrease in expense
of buying bandwidth
25%

0%
0
0.5
1
1.5
2
2.5
36
References
D.Mitra, Q.Wang, “Stochastic Traffic Engineering, with
Applications to Network Revenue Management”,
to appear in Proc. INFOCOM 2003.
BACK-UP
MULTI-SERVICE NETWORKS
•
•
•
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,)
s,  =
–
r
Route r is admissible for service s
and (origin, destination) 
distinct price-demand relationship, as reflected in different values of price elasticity
 s
dDs / Ds

dPs / Ps
Ds 
As
Pss
D
A
1
 s  1
P
39
Bandwidth Economics: Impact
of Rapidly Descending Prices
Revenue
$300K
$258K
Revenue
Elasticity*
$200K
1,000 Units
@ $100/each
$100K
Revenue
$39K
Revenue
1.5
$100K
1.0
0.5
$100
$15
10% Price Decline / 18 Periods
Estimated Price Elasticity for
* Elasticity is actually expressed as a Negative
40
Elasticity of Electricity Demand
-1.40
1100
-1.60
1200
1300
1400
1500
-1.80
Elasticity = 2.2 1926-1970
= 2.2 1962-1970 with very close fit
-2.00
-2.20
-2.40
-2.60
-2.80
-3.00
In (Electricity Generated (M k Wh))
Source: Shawn O’Donnell from Historical Statistics of the Electric Utility Industry: Through 1970, New York: Edison Electric Institute,
1973, Tables 7 and 33.
Functional Form Is Constant Elasticity Demand
41
Bandwidth
• Bandwidth market is characterized by:
– High elasticity---our updated estimate is 1.3-1.7
– rapidly decreasing unit capital costs
WDM Capacity doubling
every generation (2 years)
Elasticity = 2.2 1926 -1970
= 2.2 1962 -1970 with very close fit
3 Tb/s
1 Tb/s
300 Gb/s
100 Gb/s
30 Gb/s
10 Gb/s
Functional form is constant elasticity,i.e.,linearity
42
ELASTICITY
THERE IS EMPIRICAL SUPPORT FOR THE CONSTANTELASTICITY DEMAND FUNCTIONS
D  A/ pE
E  log( D2 / D1 ) /log( p1 / p2 )
Memory (DRAM)
1965 – 1992
Electricity
1926 – 1970
Services
voice traffic
residential voice traffic
(France Telecom, 1999)
Equipment
digital circuit switch
WAN ATM core switch
ATM edge switch
1.05
1.337
1.28
2.84
2.11
Optical Systems (source: Lucent Tech.)
capacity doubling for same cost every 2 years
traffic demand  1.5 every year
 E  1.6
43
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
 k    k 1
exponentiality
(   1)
COST
Ikt = acquisition cost of a WDM system of tech. k at time period t
exponentiality in per-unit investment costs
I k k
k
 (1  d )
I k 1,  k 1
 k 1
d = “disruptiveness”
COST COMPRESSION
I k , t 1   I k , t
t k
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PROBLEM FORMULATION: REVENUE, COST
single UPSR ring
length L
I = set of city pairs
REVENUE
time periods 1, 2, . . . , T
E
Dijt  Aijt /pijt
Rt 
N cities

i, jI
(i, j )  I
pijt Dijt
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)
Expense t  N
 I kt bkt  2L  mkt ukt
k
k
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TECHNOLOGY CONSIDERATION SET MODELED
Period
Transmission Speed
Wavelengths 
1
2
3
4
5
6
...
OC48
OC192
OC192
OC192
OC768
OC768
...
40
20
40
80
40
80
...
Define q, technology disruptiveness,
I k k
k
 (1  q)
I k 1 k 1
 k 1
where I k k is the investment expense of a new system in period k,
and  k is the capacity of the new system in period k
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PROBLEM FORMULATION: NPV, CONSTRAINTS
CASH FLOW,
Ct  Rt  Expense t

DISCOUNT RATE,
TERMINALVALUE,
1  f
TV 
 CT
1 
NPV 
T
  t Ct
 TV
t 1
CONSTRAINTS
(i)

(i, j )I
(ii)
(iii)
Dijt 
 ukt k
t
k
ukt  bkt  uk,t 1
bkt  0
t  k
k ,t
k
PROBLEM
max
NPV
{ pi, jt }, {ukt }, {bkt }
st constraints  nonnegativ ity
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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,
I11  4.8  10 6
$  2.5  103 $ per OC - 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%
I kt  I11, , d, 
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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
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