COMBINING NETWORK ECONOMICS AND ENGINEERING OVER SEVERAL SCALES*

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 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 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 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 3

My roots in networking Network Modeling model scale stochastic fluid, diffusion, large deviation models time scalecircuit-switched, packet (ATM, IP) spatial scalecore & 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 - uncertainty in traffic demand implies risk in revenue generation Objective: Maximize risk-adjusted revenue tactical, short term

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

1500 1300 1400 1100 1200 -1.40 -1.60 -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)) Elasticity of Electricity 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. Functional Form Is Constant Elasticity Demand Estimated Price Elasticity is 1.3 to 1.7 for Data Bandwidth, and 1.05 for Voice Bandwidth

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

D  A p 1 DEMAND FUNCTION DEMAND ELASTICITY, In the limit, REVENUE, R = pD if E 1 then (reduction in price  revenue increases) CONSTANT ELASTICITY Ais “demand potential”

A FRAMEWORK FOR CAPACITY PLANNING Economic Model Max NPV 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 Technology Roadmap Network Design

OPTIMAL PLANNING optimize NPV decision variables: price, investment, equipment deployment nonlinear, mixed-integer optimization ELASTIC DEMAND FUNCTIONS price-demand relations OVERVIEW OF CAPACITY PLANNING TECHNOLOGY CONTINUOUS EMERGENCE OF NEW OPTICAL SYSTEMS innovations & cost compression OPTIMIZATION BUSINESS/MARKET DECISIONS DEPLOYMENT OF NEW SYSTEMS PRICING STRATEGIES ECONOMICS

CONCLUSION CARRIER WILL MAXIMIZE NPV BY DROPPING PRICES AND GROWING NETWORK CAPACITY FREQUENTLY 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

PRICES OVER TIME LARGER ELASTICITY PRICES UNIFORMLY LOWER FOR ALL TIME PERIODS LARGER DISRUPTIVENESS  HIGHER INITIAL PRICE, LOWER PRICE IN LATER PERIODS

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. WRIGHT in Phil. Trans. R. Soc. Lond. A Vol. 358, pp. 2183-2196, 2000

BOONBusiness Optimized Optical Networks Pricing Strategy Business/economic assumptions Financials Network Architecture Capacity Expansion BOON Technology Roadmap Technology Adoption

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.

price routing revenue OVERVIEW OF THE PROBLEM Network Pricing network resources price-demand relationship demand generated carried demand 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.

MORE ON PROBLEM Route r is admissible for service s and (origin, destination) = D 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, P 1 Note:Dual role of price P in determining (a) demand and (b) revenue

REVENUE MAXIMIZATION PROBLEM : demand constraint :link constraint :nonnegativity OBERVATIONS (a) Note (b) Justified in replacing by = in demand and link constraints.

TRANSFORMED JOINT PRICING + ROUTING PROBLEM :demand satisfaction :link constraints CONCAVE OBJECTIVE FUNCTION, LINEAR CONSTRAINTS EFFECTIVE ALGORITHMS EXIST FOR CONCAVE PROGRAMMING. NOTE PATH BASED FORMULATION

LAGRANGE’S METHOD, SHADOW COSTS Lagrangian, Lagrange multipliers, shadow costs: end-to-end demand matching link capacity constraint

RESULTS FROM LAGRANGE’S METHOD OPTIMALPRICES OPTIMAL ROUTING either and or and 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

7 A B 1 1 3 D C voice route is data route is AN ILLUSTRATIVE EXAMPLE Consider traffic source A, destination B • Link costs ( ll 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,

ASYMPTOTIC PROPERTIES OF OPTIMAL SOLUTION OPTIMAL PRICES “UNIFORM CAPACITY EXPANSION”: capacities on all links scaled up uniformly i.e. Optimal prices decrease, but at a lower rate than capacity increase. OPTIMAL DEMANDS 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 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

5 4 3 2 6 1 8 7 SAMPLE NETWORK Service: voice: e1=1.05, A1,s=2000 data: e2=1.5, A2,s=200 for all s Capacity: Cl=400 for all l

CHANGE OF TRAFFIC MIX WITH UNIFORM CAPACITY EXPANSION

r_A 5 4 3 2 r_B 6 R_B 1 8 7 R_A MINIMUM-HOP ROUTING IS IMPLIED BY HIGH PRICE ELASTICITY FIXED LINK CAPACITIES FIXED VOICE ELASTICITY ROUTING OF DATA DEMAND WITH CHANGING DATA ELASTICITY

ReferencesD.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, 2001D.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)

revenue management decisions • provisioning • routing • buying • wholesale • commodity • deterministic demand • routing policy • constraints • wholesale revenue • from selling capacity • supply • installed capacity • opportunity to buy capacity to serve • retail and wholesale demands • retail • differentiated services • random demand • routing policy • constraints • revenue from retail, • associated with risk risk tolerance Risk-Aware Network Revenue Management: Overview • model • quantify revenue reward • and risk; • optimize the weighted • combination short-term tactical decisions on provisioning, routing and buying capacity - prices and installed capacity stay fixed

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

yv (decision variable): bandwidth provisioned between node pair v for wholesale : wholesale revenue network model (L: set of links) Problem Formulation 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) : 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 : retail revenue (random variable) wholesale (commodity) market (V2: set of node pairs) : wholesale price for unit bandwidth between node pair v

: provision capacity on route r is minimum bandwidth required to satisfy GoS The Optimization Model :W is total network revenue (random variable) where i.e. retail (mean) wholesale buying risk :link capacity constraint : non-negativity condition for traffic and bandwidth variables :markets in selected links only

Example Illustrating Efficient Frontier of Revenue and the Influence of Risk Parameter (d)

ReferencesD.Mitra, Q.Wang, “Stochastic Traffic Engineering, with Applications to Network Revenue Management”,to appear in Proc. INFOCOM 2003.

BACK-UP

D A P 1 MULTI-SERVICE NETWORKS • Voice & Data are examples of services • Demand formulated at aggregated level: total bandwidth for each (s,s)=(s, (s1, s2)) • 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) • distinct price-demand relationship, as reflected in different values of price elasticity = Route r is admissible for service s and (origin, destination) s r

Revenue Elasticity* $300K $258K Revenue 1,000 Units @ $100/each $100K Revenue $200K $39K Revenue 1.0 0.5 1.5 $100K $100 $15 10% Price Decline / 18 Periods Bandwidth Economics: Impact of Rapidly Descending Prices Estimated Price Elasticity for Bandwidth is 1.3 to 1.7 * Elasticity is actually expressed as a Negative

Elasticity of Electricity Demand -1.40 1400 1200 1100 1300 1500 -1.60 -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

3 Tb/s 1 Tb/s 300 Gb/s 100 Gb/s 30 Gb/s 10 Gb/s 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 Functional form is constant elasticity,i.e.,linearity

ELASTICITY THERE IS EMPIRICAL SUPPORT FOR THE CONSTANT-ELASTICITY DEMAND FUNCTIONS Memory (DRAM) 1965 – 1992 Electricity 1926 – 1970 Services voice traffic 1.05 residential voice traffic 1.337 (France Telecom, 1999) Equipment digital circuit switch 1.28 WAN ATM core switch 2.84 ATM edge switch 2.11 Optical Systems (source: Lucent Tech.) capacity doubling for same cost every 2 years traffic demand  1.5 every year  E  1.6

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 GROWTHexponentiality 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

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)

TECHNOLOGY CONSIDERATION SET MODELED 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

PROBLEM FORMULATION: NPV, CONSTRAINTS CASH FLOW, DISCOUNT RATE, TERMINALVALUE, CONSTRAINTS PROBLEM

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%

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

COMBINING NETWORK ECONOMICS AND ENGINEERING OVER SEVERAL SCALES*