1. Network Resource Design - Overview ECE/CSC 570: Fall, 2010, Sections 001, 601

2. Positioning Networks must be designed (resource provisioned) Design should proceed on the basis of – What use the network is likely to be put to – What behavior is expected or desired from network Different answers to above questions – Will result in different approach to design Copyright Rudra Dutta, NCSU, Fall, 2010

3. Network Traffic Ultimately, networks exist to serve traffic (enable traffic to be carried) What is traffic? – That which occupies / is carried by links Traffic is offered to the network by/at network nodes – Network is made of end nodes, intermediate nodes, and links – All traffic ultimately originated by end-nodes – However, for hierarchical networks, aggregation may occur In some network paradigms, E2E traffic is recognizable at all “places” in network In others, components within aggregated traffic not recognizable inside network

4. Copyright Rudra Dutta, NCSU, Fall, 2010 Traffic Characterization Traffic - “Demand” for networking services: b/w and switching Magnitude (bandwidth) – Could vary with time, if “reasonably long” life Lifetime – How long it is resident in the network Arrival and departure patterns – Call (like telephony) arrival and departure – Increment and decrement – Periodic (scheduled) – Static (long-term) Requirement of performance – Hard or statistical

5. Copyright Rudra Dutta, NCSU, Fall, 2010 Network Design Various aspects of the network must be determined/chosen/configured Network resources - nodes and links Nodes – Circuit (physical connection) interface – Buffers, scheduling, routing/forwarding, protocol Links – Circuit enablement, bandwidth (bitrate capacity), protocol Goals are in terms of network performance (experienced by traffic) – Basic goal: Connectivity – Basic design methodology: Routing – Others: b/w (if possible), buffer, resource management e.g. link scheduling – Topology, transmission power, battery allocation, …

6. Copyright Rudra Dutta, NCSU, Fall, 2010 Issue of Traffic Engineering Connectivity-only routing (traditional shortest path) ignores all traffic metrics But traffic exists – Consider flows 1  4, 1  6, 2  4, 2  6 3 4 5 6 4 4 3 10 1 2 1 5 1 6

7. Copyright Rudra Dutta, NCSU, Fall, 2010 Network Performance Ultimately, measured in quantities the end-user cares about – Assuming we have connectivity, now what? Delay, throughput – Other metrics derived from these More sophisticated metrics – Predictability of above metrics – Predictability of connectivity: Reliability / Survivability – Predictability of delay or throughput Guarantees - Quality of Service contracts – Other emergent characteristics: e.g. Security

8. Copyright Rudra Dutta, NCSU, Fall, 2010 Designing in Traffic Networks Controversial proposition: – “If delay is not important, capacity is not important” – “If delay is important, capacity must be large OR aggregation must be slotted OR both” Consider the position of router R below R 1 3 2 4 Q

9. Copyright Rudra Dutta, NCSU, Fall, 2010 Statistical TDM Performance Bursty traffic, statistical TDM Usual M/M/1 assumptions – In reality, traffic process is heavier-tailed D( ,  ) = 1 / (  -  ) Delay is lower on average: “Statistical Multiplexing Gain” – But unpredictable for individual packet - prediction is statistical Link utilization  /  Average Delay (ms) R 1 3 2 4 Q

10. Copyright Rudra Dutta, NCSU, Fall, 2010 M/M/1 Queue 0123456 p 2  + p 4  = p 3 (  +  ) p 1 = p 0 -   λλλλλλλ μμμμμμμ

11. Network of Routers Copyright Rudra Dutta, NCSU, Fall, 2010

12. Blocking in Telephony Delay - very small and constant, operative quantity is blocking ratio Average call rate  Average holding time  Offered traffic load or intensity a =  a c / c! B(a,c) = -------------------  k=0 a k / k! c X Q

13. Telephone Network Copyright Rudra Dutta, NCSU, Fall, 2010

14. Static Traffic Performance Given “matrix” of traffic demand components – Static, “always-on” – Usually aggregate – Measured or estimated Delay - fairly constant for each demand, small Blocking - none; loss - none – Except in unusual circumstances Performance is measured globally – Various objectives – Delay or throughput (global, across all components) – Revenue, fairness, protection, …

15. Copyright Rudra Dutta, NCSU, Fall, 2010 Transport, Demand, Capacity Traffic Networks and Transport Networks Traffic networks: where stochastic demand picture is operative – Short term switching/routing Transport networks: where traffic demands of static magnitude are seen to be operative – (Semi-) Permanent – QoS considerations paramount – Demands seen to be injected at transport network nodes, lower level networks not visible Links must have capacity to carry traffic – But routing can be designed on basis of traffic

16. Copyright Rudra Dutta, NCSU, Fall, 2010 Flow Routing and Global Routing Most general view of routing – Any part of any flow can be routed along some path from source to destination Requires the ability to “mark” every part that has to be routed in a distinct manner – Using labels, or timeslots 3 4 5 6 4 4 3 10 1 2 1 5 1 6

17. Copyright Rudra Dutta, NCSU, Fall, 2010 Mathematical Programming Problems A steel company must decide how to allocate production time on a rolling mill. The mill takes unfinished slabs of steel as input and can produce either of two products: bands and coils. Bands roll off the mill at 200 Tons/hr, generate $25/Ton profit, and at most 6000 Tons per week can be produced. The same figures for coils are 140 Tons/hr, $30/Ton profit, 4000 Tons/wk. If 40 hours of production time are available, what should be produced to maximize profit? Example adapted from “AMPL”, by Kernighan et al, 1993 Maximize:total profit Subject to:total number of production hours  40 tons of bands produced  6,000 tons of coils produced  4,000 Verbal model – Put the objective and constraints into words – For constraints, use the form {a verbal description of the LHS} {a relationship} {an RHS constant} Define the Decision Variables – X B number of tons of bands produced. – X C number of tons of coils produced. Construct the Symbolic Model Maximize: Subject to:

18. Copyright Rudra Dutta, NCSU, Fall, 2010 Solving LP Problems Bands 0 02000400060008000 Coils 2000 4000 6000 Constraints Feasible region 0 02000400060008000 Bands Coils 2000 4000 6000 220K 192K 120K Profit Optimal solution Hours Graphical Solution Method

19. Copyright Rudra Dutta, NCSU, Fall, 2010 Solving LP Problems Unique Optimal SolutionAlternate Optimal Solutions No Feasible Solution Unbounded Optimal Solution 4 Possible Outcomes

20. Copyright Rudra Dutta, NCSU, Fall, 2010 Solving LP Problems Simplex method – Efficient algorithm to solve LP problems by performing matrix operations on the LP Tableau – Developed by George Dantzig (1947) – Can be used to solve small LP problems by hand AMPL and CPLEX – AMPL: modeling language (and software) for designing large and complex LP/IP problems (now use OPL) – CPLEX: software package (“solver”) to solve large and complex LP/IP problems Sub-Optimal Algorithms (Heuristics) – Simulated annealing – Genetic algorithms – Tabu search – Many others, often very specific to the type of problem.

21. Copyright Rudra Dutta, NCSU, Fall, 2010 Integer Programming Maximize: Subject to: integer Convert Example to Integer Program – Assume that orders for bands and coils are placed (and filled) in 1,000s of pounds only. – Although feasible region is greatly reduced, problem becomes much more difficult. New Symbolic Model – Let the new decision variables be the number of 1000 pound “units” or orders of bands and coils.

22. Copyright Rudra Dutta, NCSU, Fall, 2010 Integer Programming 0 0 246 8 2 4 6 Feasible integer solutions Bands Coils $185K Optimal integer solution ($185K) Graphical Solution Method

23. Copyright Rudra Dutta, NCSU, Fall, 2010 Multi-Commodity Flow Formulation Parameters – n : number of nodes – A : set of all links ( i, j ) – u ij : bitrate of link – c ij : cost per bit on link – b kl : traffic demand from node k to node l Variables – x kl ij : traffic from k to l using link from i to j Goal: minimize total cost Source: Bertsimas and Tsitsilkis j l i k

24. Copyright Rudra Dutta, NCSU, Fall, 2010 Multi-Commodity Flow Formulation i

25. Copyright Rudra Dutta, NCSU, Fall, 2010 Management Cycle and Design Near Real-Time Capacity Mgmt, Netw Engg. Network Planning Reactive Protocol Design Algorithm Design Resource Design

26. Copyright Rudra Dutta, NCSU, Fall, 2010 Summation In low level networks, traffic is bursty, unpredictable, and in general low – A traffic network – Impractical to design for peak traffic, other notions not very meaningful – Design for connectivity, with roughly correct capacities L3-switched/routed traffic can be thought of as static at a high level of network – A transport view of network is appropriate, using slotted TDM – This approach is indispensable when strong guarantees must be made w.r.t. delay, variability of delay, and bandwidth – Capacity of links becomes important in meeting such guarantees – Capacity, routing, and other variables can be thought of as “control knobs” in the ensuing design problem For circuits, can reflect physical resource occupations to obtain quantitative idea – May also be useful for “logical” circuits at L3 (or not)