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L12. Network optimization

L12. Network optimization. D. Moltchanov, TUT, Fall 2017. D. Moltchanov, TUT, Spring 2008. Why do we need to know more?. Analysis vs. dimensioning. Forward task Analyze system What is the delay, packet loss, throughput, given L ink rate B uffer space Routing matrix Specific protocols

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L12. Network optimization

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  1. L12. Network optimization D. Moltchanov, TUT, Fall 2017 D. Moltchanov, TUT, Spring 2008

  2. Why do we need to know more?

  3. Analysis vs. dimensioning • Forward task • Analyze system • What is the delay, packet loss, throughput, given • Link rate • Buffer space • Routing matrix • Specific protocols • Inverse task • Optimize system • What link rates, buffer space, routing weights, given • Arriving traffic • Packet loss rate • Delay

  4. Example: buffer dimensioning • We have output-queuing router • Question: how much buffer is needed at port j • We know internal routing, pij, i=1,2,..,N, j=1,2,…,M • We know arrival traffic on all the links, λi, i=1,2,…,N • We know outgoing rates, Cj, j=1,2,…,M

  5. Example: buffer dimensioning • We may consider port j in isolation • M/M/1 is a good model • Performance metric: mean delay • Mean delay for M/M/1 is given by (recalling that ρ= λ/µ) • where µ is the average service rate • where E[P] is the average packet size

  6. Example: buffer dimensioning Performance response Could analyze M/M/1/K estimating loss But… how do we know arriving traffic, link rates, routing?

  7. Example: buffer dimensioning • Let’s revisit our assumptions… • We know outgoing rates, Cj, j=1,2,…,M??? • We only know it when the network is already planned and installed • Should there be a link between two routers? • If yes, what should be its rate? • We know internal routing, pij, i=1,2,..,N, j=1,2,…,M??? • Only if someone already assigned weights to OSPF (or IS-IS) • Internal routing = generic OSPF view of the network • We know arrival traffic on all the links , λi, i=1,2,…,N??? • If traffic demands are known… • Who is going to do this for us?

  8. Generic solution • Formulate constraints • Capacity constraints • Demand constraints • Specific constraints of protocols/algorithms • Write down objective function • Maximize network throughput • Minimize network cost • Minimize network delay • Solve using optimization techniques • Classify • Solve using well-known methods

  9. Optimization problems • Depends on the nature of involved variables • Linear programming • Simplex algorithm • Interior point algorithm • Convex programming • Linearization • Method of Lagrange multipliers • Method of gradients • Integer programming • Continuitization • Branch-and-cut/branch-and-bound algorithms • Heuristic methods, e.g., genetic algorithms

  10. Problems • Dimensioning problems: minimize network cost given • Set of demands • Each can be routed over different paths • Shortest-path routing: two problems • Given link weights find shortest paths • Given a network with links find the optimal weights • Fair network problem: given greedy traffic • Allocate available resources among demands • Topological design: minimize network cost given • Set of demands • Cost of links (no links are given) • Restoration design: optimize network given • Possible failures • Multi-layer networks

  11. Very simple example

  12. Toy example • Link-demand-path-identifier-basedformalization  • Compact • Allows to list only necessary objects • Good for moderate-to-large networks • Seem strange for small networks at the first glance though… • 1. Start with demands • Enumerate from 1 to D • Only those that are non-zero • Three nodes example • Demand (1->2): demand ID 1 • Demand (1->3): demand ID 2 • Demand (2->3): demand ID 3 • We have d=1,2,3 demands • In general: d=1,2,..,D demands

  13. Toy example • 2. Continue with links • Enumerate from 1 to E • Only those that exist • Three nodes example • Link 1->2: link ID 1 • Link 1->3: link ID 2 • Link 2->3: link ID 3 • We have e=1,2,3 links • In general e=1,2,…,E links • Can perform mapping of • Demand volumes • Link capacities

  14. Toy example • 3. Continue with candidate paths for demand • There could be more than one • Enumerate from 1 to Pd for demand d • Note!paths have to be found prior to the solution of the task • Example: demand pair (1->2) ID 1 • There exist two paths, P1= 2 • These are 1-2, 1-3-2 • Path 1-2: path ID 1 • Path 1-3-2: path ID 2

  15. Toy example • Finish with path-flow variables • Demand ID: first index • Path ID for demand: second index

  16. Toy example • The allocation task now reads as • Minimize routing cost (routing over each link costs 1 unit) • subject to demands constraints • and capacity constraints • and positivity constraints

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