1. Network Design with Constraints Chapter 10 Part 2

2. Node-Pair Constraints Traffic between certain node pairs must meet a hop constraint Two algorithms –Simply add cheapest link that meets constraints However this will also attract traffic from other nodes –Modify and use ISP algorithm in MENTOR Re-optimize network by setting new link length to minimize cost increase

3. Node-Pair Constraints If we add a new link it may end up carrying more traffic than we planned. 29 44 27 47 End 1 End 2 Cost N29N44$5045 N29N47$4727 N27N44$3975 S1 S2

4. The Simple Algorithm To reduce the hop count from End 1 to End 2 to h: 1.Compute the current route R from End 1 to End 2 2.Find all node pairs P, (p 1,p 2 ) on the route between End 1 and End 2 such that Hops(End 1,p 1 ) + Hops(End 2,p 2 ) < h 3.For each p є P, find all traffic that will flow over the (p 1,p 2 ) link if it is added with a length sp_dist[p1][p2] -1. 4.Among all candidates links in P, add the link with the smallest cost.

5. The Full Algorithm To reduce the hop count from End 1 to End 2 to h: 1.Compute the current route R from End 1 to End 2 2.Find all node pairs P, (p 1,p 2 ) on the route between End 1 and End 2 such that Hops(End 1,p 1 ) + Hops(End 2,p 2 ) < h 3.For each p є P, find all possible link lengths for (p 1,p 2 ) less than or equal to sp_dist[p1][p2] -1. We will denote these link lengths as l p,0 < l p,1 < … < l p,n = sp_dist[p1][p2] -1 4.For each link length l p,i compute C p,i (cost of the link and reduction made by moving traffic off existing links) 5.Select min C p,i. Add the link between p 1 and p 2 at length l p,i.

6. Multiple Node-Pair Constraints A-H 3-hop path required B-G 1-hop path required

7. Equipment Constraints Equipment limitations may have significant effect on network design –Degree constraints –Processing constraints Example: –Great Deal on small routers and somebody bought them. –2 slots & each slot can either have 4 64Kbps or 2 T1 circuits.

8. Degree Constraints –Say each site sends and receives 0.75 Mbps and the routers can only handle four T1s. –Clearly, each backbone node can have at most one access site attached –If we have 30 sites, 15 of them should be in the backbone in order for MENTOR to work. –We are trying to find a feasible solution

9. Degree Constraints Try to convince the organization to use different equipment or create a design!

10. Processing Constraints E.g., limitation on number of packets that can be processed per second, say pmax –Use a drop algorithm Build a complete graph Do initial loading – node terminates more than pmax/2, problem is infeasible Order links by merit = 100*utilization + (1-cost/max_cost) Choose link with lowest merit, compute alternate path If alternate path shows feasible loads, drop the link, else set merit = infinity You may end up with a very expensive network

11. Processing Constraints –Build composite nodes E.g., use two routers at each node Linked by a high speed cable Terminate half of the links on each box By doubling the node cost, we loosen the processing constraint Cap = 1000 167 333

12. Link Constraints Generally involve either forbidden or required links –Use existing link capacity –To make people feel better –Backup (disaster recovery) –Unavailability (within reasonable timeframe) –Inaccurate tariff data –Unsuitable media (e.g., satellite, high delay) –Lack of confidence in carrier

13. Modifying MENTOR for Link Constraints During tree or tour-building phase, to forbid a link, simply assign a high-enough price that the algorithm would never choose it However, direct link addition phase will add a link if u > util min –This has to be changed to add a link if u > util min and cost < “high-enough price”

14. Modifying MENTOR for Link Constraints Required links may be included –During tree/tour building E.g., by assigning a low cost to the link, and culling the designs But remember the real cost is not the artificially low cost! –During direct-link addition Can add a table specifying links to be added directly –During post-processing Easy, but may introduce significant extra cost since link is not taken account of during design phase –In AMPL we can use a binary variable to turn on or off a link.

15. Performance Constraints Evaluating performance is not easy for large network designs –Blocking for voice networks –Delay for packet-switched networks Problem Statement: Given a set of sites S and a traffic matrix Traf[i][j], find the lowest-cost design such that the average delay encountered by the traffic in transiting the network is bounded by D.

16. Evaluating Performance Simulation –You decide the granularity at which you wish to model the system –Create a model for each process E.g., Modeling a switch 1.A message arrives at the input adapter 2.The message is put into shared memory on the planar board by the direct memory access controller 3.The address of the message is added to the routing layer queue 4.… –Can be written from scratch or by Commercial network modeling packages –You run it for a long period of time –Close to the real network if the model is built skillfully

17. Evaluating Performance Analysis –Analysis relies heavily on queuing theory Average Delay on a link is: –Propagation Delay: The delay it takes for the photons or electromagnetic waves to transit the fiber, copper or atmosphere. the utilization on link L Service time for a Packet is is the average packet length

18. Total Network Delay Average delay through the node is The total network delay is All this can be calculated using Delite’s Delay Menu

19. Capacity Assignment Algorithm Aims at improving performance of an existing network Keep topology fixed, add capacity to existing links to reduce delays List node and link options with associated cost –Compute contribution to total average end-to-end delay –Compute cost per ms delay reduction compared to current network Add capacity starting with lowest cost per delay reduction

20. Capacity Assignment Example The cheapest design is NA-B1, LA-S1, NB-B1 $2400, 1100ms At least 750ms is required

21. Capacity Assignment Algorithm Algorithm may overkill on last step and add much more capacity than needed Problem is an example of the knapsack problem –Given a set of integers N = {N 1, N 2, …, N k }, find a subset that add to exactly M –2 k possible combinations …

22. Reliability Constraints Evaluating reliability not easy for large network designs –Must define failure Loss of connectivity vs. degradation of performance –Here we will discuss simple failure of connectivity –Simplest case is a tree – all nodes are connected if and only if all links and nodes are working

23. Reliability Constraints Let tree have nodes N 1, N 2, …, N n and links L 1, L 2, …Ln-1 Let failure probabilities be p i and p j * respectively Probability network is working is then If probabilities are uniform meaning all nodes have probability of failure p and all links have probability of failure p´, then Obviously tends to 0 when n is large

24. Reliability Constraints For graphs more complicated than trees, calculations can be complex Try to reduce to simpler networks –Series reduction Replace node and two edges with a single edge, probability of working = p n x p e 1 x p e 2 –Parallel reduction If two nodes have 2 parallel edges between them Replace two parallel edges with single edge, probability of working = p e 1 + p e 2 - p e 1 x p e 2

25. Reducing a Graph ABC FED 0.8 0.9 Assume nodes have reliability = 1.0

26. Reducing a Graph BC FED 0.72 0.8 0.9 Apply series reduction to A

27. Reducing a Graph B FED 0.72 0.8 0.9 Next, apply series reduction to C

28. Reducing a Graph B E 0.576 0.9 Next, apply series reduction to D and F pe1 + pe2 - pe1 x pe2

29. Reducing a Graph B E 0.982 Next, apply parallel reduction

30. Upper Bound On Network Reliability Upper bound of network reliability is

31. Reliability Continued If we have a 2-connected backbone there is no need to formally compute reliability. In Delite: there is a REL column in the equipment table for reliability for each piece of equipment. In some cases we assume that nodes are perfect (p = 0) and we only calculate link failures. (battery backup, error-correcting code, hot-pluggable line cards)