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, 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 2 3

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 Qo. S) 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 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 DEMAND ELASTICITY, In the limit, REVENUE, R = p. D if E 1 then (reduction in price revenue increases) CONSTANT ELASTICITY A is “demand potential” D A 1 p 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 innovations & cost compression OPTIMIZATION OPTIMAL PLANNING optimize NPV ECONOMICS ELASTIC DEMAND FUNCTIONS decision variables: price, investment, equipment deployment nonlinear, mixed-integer optimization BUSINESS/MARKET DECISIONS DEPLOYMENT OF NEW SYSTEMS PRICING STRATEGIES 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 (b) , capacity on link , set of admissible routes for i. e. , = r , , Route r is admissible for service s and (origin, destination) = (c) Constant demand elasticity to price D 1 P 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, Note: Dual role of price P in determining (a) demand (b) revenue

REVENUE MAXIMIZATION PROBLEM : demand constraint : link constraint : nonnegativity OBERVATIONS (a) Note (b) Justified in replacing by = in demand 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 OPTIMAL PRICES OPTIMAL ROUTING either and or and If then is “link cost”, and for any route r, “route cost” is “minimum route cost for That is, concave programming ” “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 ( 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, voice route is data route is 24

ASYMPTOTIC PROPERTIES OF OPTIMAL SOLUTION “UNIFORM CAPACITY EXPANSION”: capacities on all links scaled up uniformly i. e. OPTIMAL PRICES 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

SAMPLE NETWORK 5 2 3 4 6 1 8 Service: voice: e 1=1. 05, A 1, s=2000 data: e 2=1. 5, A 2, s=200 7 for all s Capacity: Cl=400 for all l 27

CHANGE OF TRAFFIC MIX WITH UNIFORM CAPACITY EXPANSION 28

MINIMUM-HOP ROUTING IS IMPLIED BY HIGH PRICE ELASTICITY r_A 5 4 3 2 r_B 6 R_B 1 8 7 FIXED LINK CAPACITIES FIXED VOICE ELASTICITY ROUTING OF DATA DEMAND WITH CHANGING DATA ELASTICITY R_A 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, 17 th 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 retail • differentiated services • random demand • routing policy constraints • revenue from retail, associated with risk • installed capacity • opportunity to buy capacity to serve retail and wholesale demands model • quantify revenue reward and risk; • optimize the weighted combination revenue management decisions • provisioning • routing • buying 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 providerspecific risk averseness • Make the value proposition for resource-sharing between carriers • Create tool for service providers to use for risk-

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 (V 1: 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 (V 2: set of node pairs) : wholesale price for unit bandwidth between node pair v yv (decision variable): bandwidth provisioned between node pair v for wholesale : wholesale revenue 34

The Optimization Model : W is total network revenue (random variable) where i. e. retail (mean) wholesale buying risk : provision capacity on route r is minimum bandwidth required to satisfy Go. S : link capacity constraint : non-negativity condition for traffic and bandwidth variables 35 : markets in selected links only

Example Illustrating Efficient Frontier of Revenue and the Influence of Risk Parameter (d) 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)=(s, (s 1, s 2)) Service characterization: – distinct Qo. S 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) s distinct price-demand relationship, as reflected in different values of price elasticity D A 1 P 39

Bandwidth Economics: Impact of Rapidly Descending Prices Revenue $300 K $258 K Revenue Elasticity* $200 K 1, 000 Units @ $100/each $100 K Revenue $39 K Revenue 1. 5 $100 K 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 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 OC 1) 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 44

PROBLEM FORMULATION: REVENUE, COST single UPSR ring length L I = set of city pairs N cities 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) 45

TECHNOLOGY CONSIDERATION SET MODELED Define q, technology disruptiveness, where and is the investment expense of a new system in period k, is the capacity of the new system in period k 46

PROBLEM FORMULATION: NPV, CONSTRAINTS CASH FLOW, DISCOUNT RATE, TERMINALVALUE, CONSTRAINTS PROBLEM 47

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% 48

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 49