7/29/ 2002EMIS 8392 Maya Petkova1 Chapter 11 Network Redesign.

7/29/ 2002 EMIS 8392 Maya Petkova 1

Chapter 11Chapter 11

Network RedesignNetwork Redesign


OverviewOverview• Great success in the previous chapters : Great success in the previous chapters :

designed a network that will carry the traffic for designed a network that will carry the traffic for a real life design problem.a real life design problem.

• What if traffic changes? ( and not only traffic)What if traffic changes? ( and not only traffic) - departments grow, people move, new - departments grow, people move, new

applications come on-lineapplications come on-line - A Industries acquires B Inc. ( merge)- A Industries acquires B Inc. ( merge) - C Ltd. Spins off D Enterprises ( new networks)- C Ltd. Spins off D Enterprises ( new networks)• More work for the designers and new More work for the designers and new

approaches to solving design problems.approaches to solving design problems.


Overview – Cont’dOverview – Cont’d• Methods and algorithms in Ch. 11 cover an increasing Methods and algorithms in Ch. 11 cover an increasing

mismatch between the original network and the new mismatch between the original network and the new requirements.requirements.

• ““Network growth is like growth in the family”. Network growth is like growth in the family”. • Example:Example: designed a network that handles 500 Kbps of designed a network that handles 500 Kbps of

data traffic. Traffic grows to 600 Kbps ( fiddle with the data traffic. Traffic grows to 600 Kbps ( fiddle with the routing or might add capacity to heavily used links). routing or might add capacity to heavily used links). Next growth spurt ( new locations, new staff) and traffic Next growth spurt ( new locations, new staff) and traffic grows to 725 Kbps ( link the new locations to the existing grows to 725 Kbps ( link the new locations to the existing backbone, add capacity to a few additional links). Next a backbone, add capacity to a few additional links). Next a rival comes and we have to merge 2 separate networks - rival comes and we have to merge 2 separate networks - moment to moment to REDESIGNREDESIGN..

• PROBLEM PROBLEM : when to redesign when no single large event : when to redesign when no single large event acts as a trigger?acts as a trigger?


Calculating the Payback Calculating the Payback PeriodPeriod

• Cost of upgrading a network compared with a Cost of upgrading a network compared with a complete new design.complete new design.

• Compare the payback periods for 650 Kbps Compare the payback periods for 650 Kbps traffic and 1.25 Mbps traffic.traffic and 1.25 Mbps traffic.


Calculating the Payback Calculating the Payback Period - Period - Cont’dCont’dQ.Q. What info do the network designers need to What info do the network designers need to

know in order to be able to carry out the know in order to be able to carry out the business analysis in the Table on slide 4?business analysis in the Table on slide 4?

A.A. They need the traffic and the costs. They need the traffic and the costs.• Optimal cost can be calculated by a variant of Optimal cost can be calculated by a variant of

Mentor. Mentor. • Incremental cost can not be calculated by the Incremental cost can not be calculated by the

algorithms we already have at hand.algorithms we already have at hand.• Need new class of algorithms that takes the Need new class of algorithms that takes the

existing network topology as an input not just existing network topology as an input not just the traffic and the link costs. the traffic and the link costs.


Incremental Design ProblemIncremental Design Problem (( ) ) • Produce the minimal-cost change to the network Produce the minimal-cost change to the network

that will bring it back to an operating point where that will bring it back to an operating point where we feel comfortable.we feel comfortable.

• Capacity assignment problem is one way of solvingCapacity assignment problem is one way of solving

• Drawback – CAP tries to provide a better fit if the Drawback – CAP tries to provide a better fit if the initial network is close to what is needed. It does initial network is close to what is needed. It does not do a good job if the network and the traffic are not do a good job if the network and the traffic are out of kilter. out of kilter.


A Tutorial Introduction to theA Tutorial Introduction to the Three basic approaches to incremental Three basic approaches to incremental

design:design:

1.1. Routing changes. Routing changes. 2.2. Link resizing.Link resizing.3.3. Link addition.Link addition.

Above is the order in which they should be Above is the order in which they should be considered.considered.


Routing ChangesRouting Changes• Main advantage – no additional cost ( no circuits to Main advantage – no additional cost ( no circuits to

order, no equipment to acquire).order, no equipment to acquire).• No delay in implementing them.No delay in implementing them.• Main disadvantage – only work with certain routing Main disadvantage – only work with certain routing

algorithms and with relatively small changes in algorithms and with relatively small changes in traffic.traffic.

• With larger changes in traffic rerouting attempts With larger changes in traffic rerouting attempts will fail. ( if we use min. hop routing no point in will fail. ( if we use min. hop routing no point in even considering routing changes).even considering routing changes).

• The more the network is able to control the flow, The more the network is able to control the flow, the more we want to consider rerouting before the more we want to consider rerouting before redesign.redesign.


Example - Routing Example - Routing Changes Changes

Each link has capacity 4. We can split or bifurcate Each link has capacity 4. We can split or bifurcate requirements.requirements.

Traffic AH = 2 .Traffic between adjacent nodes is 1.Traffic AH = 2 .Traffic between adjacent nodes is 1. Initial routing - split the AH traffic so half flows along the Initial routing - split the AH traffic so half flows along the

top of the network and half flows along the bottom.top of the network and half flows along the bottom.

A B C D

E F G H


Example –Routing Changes - Example –Routing Changes - Cont’dCont’d

Traffic grows with BC = 3, AH = 3. Initial routing not Traffic grows with BC = 3, AH = 3. Initial routing not

feasible - BC will be saturated by 4.5 units of flow. feasible - BC will be saturated by 4.5 units of flow. We have 7 units of flow across (BC, FG) cut which has We have 7 units of flow across (BC, FG) cut which has

capacity of 8. We want a routing that carries a flow of 3.5 capacity of 8. We want a routing that carries a flow of 3.5 on both BC and FG.on both BC and FG.

A B C D

E F G H


Example - Link Resizing Example - Link Resizing

Traffic grows with BC = 3, AH = 3, AC = 2. Traffic grows with BC = 3, AH = 3, AC = 2. We have saturated the (BC, FG) cut. No clever routing We have saturated the (BC, FG) cut. No clever routing

can fix this problem. Need to add capacity.can fix this problem. Need to add capacity. The cheapest solution double the capacity of the BC link. The cheapest solution double the capacity of the BC link.

A B C D

E F G H


Example - Link AdditionExample - Link Addition

Traffic grows with BC = 3, AH = 6, AC = 3, FG = 2. We have Traffic grows with BC = 3, AH = 6, AC = 3, FG = 2. We have

saturated the (BC, FG) cut again. We choose to add a new link saturated the (BC, FG) cut again. We choose to add a new link AH of capacity 4. Therefore new cut (BC, FG, AH) of capacity 16. AH of capacity 4. Therefore new cut (BC, FG, AH) of capacity 16.

Add 3 units of flow on AH link – the remaining flow can be Add 3 units of flow on AH link – the remaining flow can be distributed as before.distributed as before.

A B C D

E F G H


Network Cost as a Function of Network Cost as a Function of

the Total Traffic the Total Traffic

Traffic ( Mbps )Traffic ( Mbps )


Design Principle 11.1Design Principle 11.1 The fundamental thing to understand about any network is The fundamental thing to understand about any network is

how much traffic it can carry before it breaks. This process how much traffic it can carry before it breaks. This process is called sensitivity analysis.is called sensitivity analysis.

• ““Break” Break” - unacceptable blockage or delay, depending on - unacceptable blockage or delay, depending on the network type. the network type.

• Cost deferral rather than cost avoidance –different Cost deferral rather than cost avoidance –different prospective of network optimization.prospective of network optimization.

• If we build a network for a stable user base with fixed If we build a network for a stable user base with fixed usage – build the cheapest.usage – build the cheapest.

• If we build for a rapidly changing concern we may If we build for a rapidly changing concern we may overbuild initially to defer the upgrade costs.overbuild initially to defer the upgrade costs.


The Rerouting AlgorithmThe Rerouting Algorithm There are 2 principal purposes for rerouting There are 2 principal purposes for rerouting

algorithms.algorithms. 1.1.The actual traffic on a network is different The actual traffic on a network is different

than what was plannedthan what was planned 2.2.The network traffic is growing and we want to The network traffic is growing and we want to

eke out few more months before redesign.eke out few more months before redesign. What can be done depends critically on the What can be done depends critically on the

network layer of the network we are using.network layer of the network we are using.


The Rerouting Algorithm - The Rerouting Algorithm - Cont’dCont’d

• RIP routing – nothing can be doneRIP routing – nothing can be done• FSMH routing – the network will try to deal with FSMH routing – the network will try to deal with

congestion by finding alternate routes (we congestion by finding alternate routes (we could help by putting traffic in another order, could help by putting traffic in another order, still beyond control)still beyond control)

• If network allows arbitrary bifurcation there If network allows arbitrary bifurcation there exists elegant math approach developed by exists elegant math approach developed by Bertsekas and Gallager. Produces optimal Bertsekas and Gallager. Produces optimal routing for the traffic, but is beyond the ability routing for the traffic, but is beyond the ability of most commercial switches and routers.of most commercial switches and routers.


The Rerouting Algorithm - Cont’dThe Rerouting Algorithm - Cont’d• Focus on minimum distance routing since it is one Focus on minimum distance routing since it is one

of the most widely used routing schemes. of the most widely used routing schemes. • Suppose we designed a network with link Suppose we designed a network with link

utilization below 50%. If 2 months after going on-utilization below 50%. If 2 months after going on-line a link reaches 52% utilization we do not want line a link reaches 52% utilization we do not want to go back to a full-scale redesign. to go back to a full-scale redesign.

• ““Newton’s first low of networks”:Newton’s first low of networks”: A network that is A network that is working tends to continue working; a network that working tends to continue working; a network that is not working tends to continue not to work. is not working tends to continue not to work.

• A stable slightly congested network is always A stable slightly congested network is always preferable to an unstable, uncongested network. preferable to an unstable, uncongested network.


When to RedesignWhen to Redesign• The policy issues involving redesign are quite The policy issues involving redesign are quite

interesting but impossible to quantify. interesting but impossible to quantify. • The network passes the threshold between The network passes the threshold between

slightly congested and significantly congested slightly congested and significantly congested at some point. Network users, mangers and at some point. Network users, mangers and owners decide where that transition occurs.owners decide where that transition occurs.

• Generally: we design a network with a Generally: we design a network with a maximum utilization maximum utilization u u ( or a blocking level ( or a blocking level b b ). ). We don’t undertake any redesign until the We don’t undertake any redesign until the utilization reaches level utilization reaches level u’u’ (or (or b’ b’ ))


The Balancing AlgorithmThe Balancing Algorithm• Assume some link has reached level Assume some link has reached level u’u’. Examining . Examining

the network we find that there are n links with the network we find that there are n links with utilization over utilization over uu. Should we insist that the . Should we insist that the network be returned to a max utilization of network be returned to a max utilization of uu??

• The balancing algorithmThe balancing algorithm starts with a network at starts with a network at one level of utilization and produces a new one level of utilization and produces a new network at another, lower level of utilization. It will network at another, lower level of utilization. It will try to reduce congestion by rerouting. If it is not try to reduce congestion by rerouting. If it is not possible it will fail and leave it to another possible it will fail and leave it to another algorithm like capacity assignment to upgrade the algorithm like capacity assignment to upgrade the links. The goal is to reduce the utilization on all links. The goal is to reduce the utilization on all links belowlinks below


The Balancing Algorithm – The Balancing Algorithm – Cont’dCont’d

• Uses ISP ( incremental shortest-path ) Uses ISP ( incremental shortest-path ) algorithm used in MENTOR II to decide whether algorithm used in MENTOR II to decide whether or not to add a direct link. or not to add a direct link.

• ISP : ISP : – – is there an a length we can give a direct link is there an a length we can give a direct link

with which it will attract an amount of traffic with which it will attract an amount of traffic that will justify the linkthat will justify the link

- goal is to identify all the pairs that could use - goal is to identify all the pairs that could use a link in place of the current path. a link in place of the current path.


The Balancing Algorithm – The Balancing Algorithm – Cont’dCont’d

• Denote the initial network N. N is a directed graph, Denote the initial network N. N is a directed graph, each link is represented by 2 directed edges, 1 in each link is represented by 2 directed edges, 1 in each direction.each direction.

• After loading the traffic a link can be in 1 of 3 After loading the traffic a link can be in 1 of 3 stages :stages :

- uncongested in both directions- uncongested in both directions - congested in 1 direction, but not in the other- congested in 1 direction, but not in the other - congested in both directions- congested in both directions• The goal is to remove the congestion by changing The goal is to remove the congestion by changing

the link lengths and not by adding capacity.the link lengths and not by adding capacity.


The Balancing Algorithm – StepsThe Balancing Algorithm – Steps1.1. Divide the links into mesh links and tree links.Divide the links into mesh links and tree links.

Links AB, YZ, QR, RS, ST are called tree links. There is no Links AB, YZ, QR, RS, ST are called tree links. There is no

alternate route between the endpoints. The rest of the links alternate route between the endpoints. The rest of the links are mesh links.are mesh links.

ZC

BA Q R S

T


The Balancing Algorithm – Steps The Balancing Algorithm – Steps -- Cont’d Cont’d

If Any of the tree links has a utilization of greater than If Any of the tree links has a utilization of greater than then the algorithm returns FAIL. then the algorithm returns FAIL.

2. Consider only the subgraph of mesh links N’ N. 2. Consider only the subgraph of mesh links N’ N. N’ = N \ { A, R, S, T, Z }. Such a network is called N’ = N \ { A, R, S, T, Z }. Such a network is called

reduced reduced network.network.3. Collapse the traffic onto the reduced subnetwork.3. Collapse the traffic onto the reduced subnetwork. If we had traffic form A to T in the original network it If we had traffic form A to T in the original network it

becomes traffic from B to Q in N’. If we had traffic becomes traffic from B to Q in N’. If we had traffic form Q to T it does not enter the subnetwork. form Q to T it does not enter the subnetwork.

Let , n = |O|. If n= 0, return.Let , n = |O|. If n= 0, return...


The Balancing Algorithm – Steps The Balancing Algorithm – Steps -- Cont’d Cont’d4. Divide the directed links into 3 categories:4. Divide the directed links into 3 categories: - overutilized : utilization > = - overutilized : utilization > = - underutilized: utilization < = , - underutilized: utilization < = ,

wherewhere is a parameter passed to the algorithmis a parameter passed to the algorithm - the rest of the links have utilization - the rest of the links have utilization uu:: < < u u < < 5. Try to reduce the number of links with utilization 5. Try to reduce the number of links with utilization

greater than by changing the lengths of greater than by changing the lengths of overutilized and underutilized links. overutilized and underutilized links.


The Balancing Algorithm – Steps The Balancing Algorithm – Steps -- Cont’d Cont’dLet n is the number of overutilized links. Let n is the number of overutilized links. • Sort the overutilized links in decreasing order Sort the overutilized links in decreasing order

of utilizationof utilization• Loop over the overutilized links.Loop over the overutilized links. - A link - A link LL initially has length initially has length lenlen. Use ISP to . Use ISP to

compute candidate lengths forcompute candidate lengths for L L : : At each new length the link will move some of At each new length the link will move some of

its traffic to an alternate route not using its traffic to an alternate route not using L.L.



• Loop over the candidate lengths.Loop over the candidate lengths. - Set len(- Set len(LL) to each to each candidate length ) to each to each candidate length

- Compute : , let n’ =|O’|.- Compute : , let n’ =|O’|. - If n’ < n then set len(- If n’ < n then set len(LL) = , n = n’ and ) = , n = n’ and

break from the inner loop.break from the inner loop.• If n = 0 return SUCCESS.If n = 0 return SUCCESS.• Sort the underutilized links in increasing order Sort the underutilized links in increasing order

of utilization.of utilization.• Loop over the underutilized links.Loop over the underutilized links.


The Balancing Algorithm – Steps The Balancing Algorithm – Steps -- Cont’d Cont’d - A link - A link LL initially has length initially has length lenlen. Use ISP to . Use ISP to

compute candidate lengths forcompute candidate lengths for L L : :

- At each length the link will attract some traffic - At each length the link will attract some traffic from another route not using from another route not using L.L.

• Loop over the candidate lengths.Loop over the candidate lengths. - Set len(- Set len(LL) to each to each candidate length ) to each to each candidate length

- Compute : , let n’ =|O’|.- Compute : , let n’ =|O’|. - If n’ < n then set len(- If n’ < n then set len(LL) = , n = n’ and ) = , n = n’ and

break from the inner loop.break from the inner loop.



• If n = 0, return SUCCESS. If n is lower than the If n = 0, return SUCCESS. If n is lower than the previous round loop through the links again.previous round loop through the links again.

6. At this point we have been unable to reduce 6. At this point we have been unable to reduce the number of links with utilization of greater the number of links with utilization of greater thanthan

to 0, return FAILURE.to 0, return FAILURE.


The Effectiveness of the The Effectiveness of the Balancing Algorithm Balancing Algorithm

• Hard to measure ( interested in the behavior of Hard to measure ( interested in the behavior of the algorithm on a network that has been the algorithm on a network that has been carefully optimized to meet the previous traffic).carefully optimized to meet the previous traffic).

• To test : take an optimized mesh network of n To test : take an optimized mesh network of n nodes and grow the traffic. Can see the nodes and grow the traffic. Can see the maximum congestion on links using the default maximum congestion on links using the default loading and then using the link lengths provided loading and then using the link lengths provided by the balancing algorithm.by the balancing algorithm.

• To grow the traffic: several ways implemented To grow the traffic: several ways implemented as as randreq3.crandreq3.c. Can be viewed as incremental . Can be viewed as incremental traffic generators traffic generators


The Effectiveness of the The Effectiveness of the Balancing Algorithm – Cont’d Balancing Algorithm – Cont’d

• UniformUniform traffic growth, each existing piece of traffic growth, each existing piece of traffic Traf[i][j] becomestraffic Traf[i][j] becomes

• Node-basedNode-based growth. Each site is given a growth growth. Each site is given a growth

rate. Increase the traffic between site rate. Increase the traffic between site i i and siteand site j j by by • Average Average growth. Each existing piece of traffic is growth. Each existing piece of traffic is

multiplied by multiplied by where rand() is a pseudorandom number where rand() is a pseudorandom number

generator uniformly distributed in [0,1]. generator uniformly distributed in [0,1].


The Effectiveness of the The Effectiveness of the Balancing Algorithm – Cont’d Balancing Algorithm – Cont’d

• CenteredCentered growth. We generate additional growth. We generate additional traffic form a given site to and from all other traffic form a given site to and from all other sites.sites.

• ScatteredScattered growth generates new traffic that is growth generates new traffic that is independent of the previous traffic on the independent of the previous traffic on the network. Use the population to select the city network. Use the population to select the city pairs and then allocate traffic in the rangepairs and then allocate traffic in the range

• All generally useful in doing sensitivity All generally useful in doing sensitivity analysis and capacity planning. analysis and capacity planning.


The Effectiveness of the The Effectiveness of the Balancing Algorithm – Balancing Algorithm – ExampleExample

• Variant of the 50 sites problem with 10-node Variant of the 50 sites problem with 10-node backbone. Built 2 designs backbone. Built 2 designs

- costing $95,251/month – N507-95k.net( mixed - costing $95,251/month – N507-95k.net( mixed backbone with 56K and 256K links) backbone with 56K and 256K links)

- costing 96,906/month – N507-96k.net ( only - costing 96,906/month – N507-96k.net ( only 256K links)256K links)

• Suppose the initial traffic estimates Traf[i][j] Suppose the initial traffic estimates Traf[i][j] were wrong and the observed traffic was Traf’[i]were wrong and the observed traffic was Traf’[i][j]. Assume is uniformly [j]. Assume is uniformly

distributed in the range [0.9,1.25]distributed in the range [0.9,1.25]


The Effectiveness of the The Effectiveness of the BalancingBalancing Algorithm – Example - Cont’d Algorithm – Example - Cont’d

• If we load the more expensive design with the If we load the more expensive design with the new traffic – no problemnew traffic – no problem

• If we load N507-95 design link form N50 to N48 If we load N507-95 design link form N50 to N48 is loaded 50.9%.is loaded 50.9%.

• We we have a hard constraint of 50 % We we have a hard constraint of 50 % utilization,utilization,

• Collapse the the traffic into the backbone. Collapse the the traffic into the backbone. There are 5 requirements that use the link N50 There are 5 requirements that use the link N50 to N48. to N48.



• Pair (N42, N48) has alternate length 669.Pair (N42, N48) has alternate length 669.• Pair (N43, N48) has alternate length 669.Pair (N43, N48) has alternate length 669.• Pair (N46, N48) has alternate length 669.Pair (N46, N48) has alternate length 669.• Pair (N50, N48) has alternate length 1169.Pair (N50, N48) has alternate length 1169.• Pair (N50, N49) has alternate length 71.Pair (N50, N49) has alternate length 71.• The initial length on N50 to N48 in 348. If we The initial length on N50 to N48 in 348. If we

lengthen it to 348+71+1 = 420 then the traffic lengthen it to 348+71+1 = 420 then the traffic between N50 and N49 will take the 3-hop path between N50 and N49 will take the 3-hop path via N46 and N45 rather than the 2-hop path via via N46 and N45 rather than the 2-hop path via N48.N48.



• The size of the range is quite important – if traffic The size of the range is quite important – if traffic estimates are uniformly distributed in the range of estimates are uniformly distributed in the range of [0.7, 1.45] we will have different behavior.[0.7, 1.45] we will have different behavior.

• In general - the balancing algorithm can not do In general - the balancing algorithm can not do miracles.miracles.

• If the congested links are sparse it could do a good job If the congested links are sparse it could do a good job provided that the quantum of traffic is not too large. provided that the quantum of traffic is not too large.

• If the smallest amount of traffic that moves when we If the smallest amount of traffic that moves when we change the routing length of a link is 2% or 5%, we change the routing length of a link is 2% or 5%, we can probably reduce traffic in small steps to the can probably reduce traffic in small steps to the desired level.desired level.

..


Redesigning for New Redesigning for New TrafficTraffic

• Large change in the traffic - the balancing Large change in the traffic - the balancing algorithm will notalgorithm will not be able to restore the network be able to restore the network to an acceptable operating point.to an acceptable operating point.

• Either alter the network or live with a degraded Either alter the network or live with a degraded level of service.level of service.

• Capacity assignment is one approach to altering Capacity assignment is one approach to altering the network.the network.

• The difference between capacity assignment(CA) The difference between capacity assignment(CA) to reach a performance constraint and capacity to reach a performance constraint and capacity assignment for redesign is change in the stopping assignment for redesign is change in the stopping condition rather than changing the method of condition rather than changing the method of selecting which links to upgrade.selecting which links to upgrade.


Redesigning for New Traffic Redesigning for New Traffic - - Cont’d Cont’d

• CA with performance constraint stopped adding CA with performance constraint stopped adding capacity when we reached a preset average capacity when we reached a preset average packet delay. Paid no attention to the total cost.packet delay. Paid no attention to the total cost.

• Redesigning the network we may or may not have Redesigning the network we may or may not have a performance constraint. We are interested in a performance constraint. We are interested in the cost. the cost.

• Modify the algorithm to stop when we have either Modify the algorithm to stop when we have either reached the performance constraint, say, 100 ms reached the performance constraint, say, 100 ms average delay or reached the budget limit, say, $ average delay or reached the budget limit, say, $ 50, 000/month. May also wish to stop when we 50, 000/month. May also wish to stop when we changed certain number of links. changed certain number of links.


Redesigning for New Traffic - Redesigning for New Traffic - Cont’d Cont’d

• CA gives more flexibility than balancing but does CA gives more flexibility than balancing but does not allow the network to grow naturally. Suppose not allow the network to grow naturally. Suppose we design a series of network for total traffic we design a series of network for total traffic levels: levels:

• At each stage designed the best network At each stage designed the best network available with the algorithms in hand. How does available with the algorithms in hand. How does the network grow?the network grow?

- sparse with low-speed links – as traffic grows it - sparse with low-speed links – as traffic grows it adds a few direct links – more growth, more adds a few direct links – more growth, more direct links – sparse design with higher-speed direct links – sparse design with higher-speed links links


Redesigning for New Traffic - Redesigning for New Traffic - Example Example

Linear networkLinear networkLinear tariff:Linear tariff:A+ B x dist forA+ B x dist for 64 Kbps links64 Kbps links2A + 2B x dist for2A + 2B x dist for256 Kbps links. 256 Kbps links. Traffic between all node Traffic between all node pairs is exactly 1Kbps.pairs is exactly 1Kbps.

N1

N2

N10



• Initial design – string of 64 Kbps links.Initial design – string of 64 Kbps links.• If there are n nodes on one end of the link and If there are n nodes on one end of the link and

(10-n) nodes on the other end the total traffic (10-n) nodes on the other end the total traffic over the link in each direction is n x (10-n).over the link in each direction is n x (10-n).



• Assume traffic between the node pairs grows to 1.5 Kbps.Assume traffic between the node pairs grows to 1.5 Kbps.• Assume traffic doubles – at least 3 links are over 75% Assume traffic doubles – at least 3 links are over 75%

utilized.utilized.• Difficulty using CA is alone is that there are so many links Difficulty using CA is alone is that there are so many links

that are congested.that are congested.• If we want 50 % utilization - upgrade 5 links, if 66% - If we want 50 % utilization - upgrade 5 links, if 66% -

upgrade 3 links with more expensive ones.upgrade 3 links with more expensive ones.• For the 3 links update what is the cost?For the 3 links update what is the cost?• Delay will be low but what if A is large compared toDelay will be low but what if A is large compared to B x dist( Ni, Nj)?B x dist( Ni, Nj)?• Better approach – enrich the topology.Better approach – enrich the topology.



• Suppose we add a single link for N3 to N8 and use it to Suppose we add a single link for N3 to N8 and use it to route all the traffic between (N1, N2, N3) and route all the traffic between (N1, N2, N3) and (N8,N9,N10). (N8,N9,N10).

• Flow in each direction will be 9x2Kbps = 18 Kbps.Flow in each direction will be 9x2Kbps = 18 Kbps.• Utilization will be 28 % ( alternative was to add 3 Utilization will be 28 % ( alternative was to add 3

separate links).separate links).• If we add the link from N3 to N8 we have reduced the If we add the link from N3 to N8 we have reduced the

traffic on most heavily used links, brought back the traffic on most heavily used links, brought back the utilization at max 50% , reduced the max number of utilization at max 50% , reduced the max number of hops from 9 to 5. hops from 9 to 5.

• Perfect example of adding link, saving money, adding Perfect example of adding link, saving money, adding reliability and decreasing the maximum hops.reliability and decreasing the maximum hops.


Homework # 15Homework # 15 Show that when we add link from N3 to N8 to Show that when we add link from N3 to N8 to

the chain network from slide 40, we reduce the the chain network from slide 40, we reduce the maximum number of hops to 5 if we give the maximum number of hops to 5 if we give the link an appropriate length. If the length of each link an appropriate length. If the length of each chain link is 100, what range of lengths can we chain link is 100, what range of lengths can we give the N3 to N8 link to achieve the 5 hop give the N3 to N8 link to achieve the 5 hop limit using shortest-path routing?limit using shortest-path routing?

7/29/ 2002EMIS 8392 Maya Petkova1 Chapter 11 Network Redesign.

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Transcript of 7/29/ 2002EMIS 8392 Maya Petkova1 Chapter 11 Network Redesign.