Network Design with Constraints

1. Network Design with Constraints Chapter 10 Part 1 Prepared by Giray Birkan gbirkan@mail.smu.edu

2. Overview • Build a network connecting 75 stores to a HQ • Each store generates 500bps of traffic & receives about 1500bps of traffic. • An MST or CMST will be the correct solution • But you are told that each store needs 64Kbps access & 3 hops maximum. • Or the lowest cost network where the average end-to-end delay is 300 ms or less. Prepared by Giray Birkan gbirkan@mail.smu.edu

3. Designs Constraints • Cheapest design may not be acceptable for reasons of reliability, performance, … or organizational or political reasons • May have to modify algorithms or write problem-specific code to produce an acceptable design. • Manual Design? Prepared by Giray Birkan gbirkan@mail.smu.edu

4. Hop constraints Worst case Average Node-pair Equipment constraints Degree Throughput Link constraints Required or forbidden Performance constraints Worst case Average Node-pair Reliability constraints Entire network Backbone Node-pair Miscellaneous High & Low Security Nodes Types of Constraints Prepared by Giray Birkan gbirkan@mail.smu.edu

5. Over-Constrained Problem • It is possible to specify so many or so severe constraints that there is no feasible network design • War Story 10.1: each node must be of degree three, for example if n = 7. There is no solution • Suppose each site has equipment that can only terminate a LAN and two leased lines - Can only build a ring. Prepared by Giray Birkan gbirkan@mail.smu.edu

6. Over-Constrained Problem • In any network, the total amount of capacity used by all of the traffic is bounded from below by • Capacity of a leased line is C and capacity of the ring is (n-1)C. • As network grows, link capacity will be overloaded at some point Prepared by Giray Birkan gbirkan@mail.smu.edu

7. Hop-Limited Designs • Problem Statement 10.1: Given a set of traffic Trafi,j, find the lowest cost design such that if Trafi,j > 0then the path chosen by the routing algorithm through the network has less than h hops. • If h is very large, first solve the unconstrained problem maybe a cost-optimized network is sufficient. Prepared by Giray Birkan gbirkan@mail.smu.edu

8. B A C D E AMPL and Hop-Limited Design • Arc-Path Model • Set P : set of paths • Only paths with 3 hops are in the data model • A-B A-D-B A-D-E-B • A separate program can be written to find these paths Prepared by Giray Birkan gbirkan@mail.smu.edu

9. AMPL and Hop-Limited Design • Node-Arc Model • Only links and nodes no paths are given • The hop limit is 3 and each demand must be satisfied by a single path. • Giray’s Solution: Subject to HopLimit {c in N, n in {N diff {c}}: sum{e in E} (-yi[c,e,n] - xi[c,e,n]) >= 3 * rhs[c,n]; Prepared by Giray Birkan gbirkan@mail.smu.edu

10. A B C D Badly Posed Examples • MUX network : The path that a requirement takes depends on the loading sequence. Assume each link can load 2 circuits Network appears to be a 2-hop design Loading pattern 1 : { AB, AB, CB} Loading pattern 2 : { AB, CB, AB} Prepared by Giray Birkan gbirkan@mail.smu.edu

11. Badly Posed Examples • Boundary of the Network • 6 Hop Design: NY - Philadelphia - Detroit - Chicago - Denver - LA - San Diego • 6 Hops or 12 hops? BBNY – Building – 14 Floor – Workstation • Generally, we don’t cost optimize building networks Prepared by Giray Birkan gbirkan@mail.smu.edu

12. Approach I : Culling • Generate a lot of designs with varying parameters • If Mentor is used try different values for alpha, slack, nclst, seed • Throw away all that do not meet hop constraints • Select best remaining design • Brute force method may be quite acceptable if it avoids writing problem-specific code • May not work if constraints are too severe • Frequency of feasible designs may be too low to be practicable Prepared by Giray Birkan gbirkan@mail.smu.edu

13. Culling Continued • Cost Optimized design with 11 hops Prepared by Giray Birkan gbirkan@mail.smu.edu

14. Culling Continued • The best 9-hop design culled from a run • Out of 325 trial, only 28 of them had 9 hops Prepared by Giray Birkan gbirkan@mail.smu.edu

15. Culling Continued • More than 150 different networks only one of them had 7 hops Prepared by Giray Birkan gbirkan@mail.smu.edu

16. Culling Continued • If Culling fails to find 6-hop designs • Reduce the diameter of the backbone • Reduce the depth of the access trees A tree centered on N45 Prepared by Giray Birkan gbirkan@mail.smu.edu

17. Approach II : Augmentation • 5 pairs of nodes 8 hops apart, 7 hop design required Prepared by Giray Birkan gbirkan@mail.smu.edu

18. An Algorithm To Compute Hops In The Access Topology • For each backbone node b compute la(b) : max depth of the local access tree at b. • Loop until done. Compute diameter of the network: • If d > h, return fail • For each backbone site b, compute • e(b) gives the number of extra hops we can expand la(b) and still meet the h hop constraint • If any e(b) greater than 0, select a node b and increase la(b) by 1. Otherwise break loop • Return the values la(b) Prepared by Giray Birkan gbirkan@mail.smu.edu

19. Algorithm Continued h = 6 Prepared by Giray Birkan gbirkan@mail.smu.edu

20. Algorithm Continued The design with a 3 hop cluster at N45 Prepared by Giray Birkan gbirkan@mail.smu.edu

21. Average Hop Constraints • Average number of hops is a far easier constraint to meet than a constraint on the maximum number of hops • Three approaches for MENTOR • Increase alpha • Builds more star-like networks • Increase slack • Introduces more links • If slack = 1, we will build a network where there is a link between any 2 sites that have traffic • Use lower-speed links • Introduces more links – because of utilization Prepared by Giray Birkan gbirkan@mail.smu.edu

22. Average Hop Constraints • First mean tends to equalize performance among large & small sites • Second makes most people happy at the cost of a minority of users with lower grade of service Prepared by Giray Birkan gbirkan@mail.smu.edu

23. Meeting hops Constraints The cost of improving hops2 Hops & cost for various Values of slack The interesting choices for slack Prepared by Giray Birkan gbirkan@mail.smu.edu

24. Meeting hops Constraints Prepared by Giray Birkan gbirkan@mail.smu.edu

25. Homework 12 • Using node-arc model from homework 8 solve the following mesh design problem. • Use one model file • First, Minimize the number of average hops • Then, Minimize the total cost • Trunk types: • 96K bps - $50 per trunk • 128K bps - $60 per trunk • 256K bps - $105 per trunk • Each demand must be satisfied by a single path. • The utilization should be no more than 50%. Prepared by Giray Birkan gbirkan@mail.smu.edu

26. Homework 12 A F D B E C G Prepared by Giray Birkan gbirkan@mail.smu.edu

27. Homework 12 Prepared by Giray Birkan gbirkan@mail.smu.edu

28. AMPL & Multiple Objective Functions • You can define several problems in one model file • You can solve a problem then fix some variables and solve another problem #---first problem----- problem DefineBIG: # objective segmentlength, # variables X, Y, A, B, BIG, # constraints flowbalance, flowbalance2 ,linkbetweenXandA, linkbetweenYandB, linkbetweenAandB, linkbetweenBIGandX, lastAMP, firstAMP; solve DefineBIG; #---second problem----- problem ReduceAMPS: # objective amps, # variables X, Y, A, B, BIG, # constraints flowbalance, flowbalance2, linkbetweenXandA, linkbetweenYandB, linkbetweenAandB, linkbetweenBIGandX, lastAMP, firstAMP, BIGfix; solve ReduceAMPS; Prepared by Giray Birkan gbirkan@mail.smu.edu

29. GRIN • http://www.geocities.com/pechv_ru/main.html Prepared by Giray Birkan gbirkan@mail.smu.edu