Constraint-Based Routing Used in traffic engineering to compute routes for connections. Static Problems and Dynamic Problems Static Problems: known topology (network resources), known traffic pattern (Fixed), find routes for a particular optimization objective. Minimize maximum link utilization in the system Minimize network cost Minimize packet delay. Static problems can usually be formulated as a traditional optimization problem.

Dynamic Problems: Connections come and go dynamically. No knowledge about the future traffic requirement. Maximize the probability that future connection requests will not be blocked. Use short paths Use large paths Use links that will not cause other connections to be blocked.

Static problems: LP formulation Notation: Let G=(V, E) represent the physical network, where V is the set of nodes and E is the set of links. For each link (i, j) in E, let C(i, j) be the capacity of the link. Let K be the set of traffic demands. For each k in K, let d(k), s(k), t(k) be the bandwidth, source and destination respectively. For each k in K, (i, j) in E, let X(k, i, j) be the percentage of k’s demand satisfied by link (i, j). Let alpha be the maximum link utilization.

Static problems: LP formulation Objective: Minimize (alpha) Flow conservation constraint 1: Sum_{j: (i, j) in E}{X(k, i, j)} – Sum_{j:(j, i) in E}{X(k, j, i)} = 0, for all k in K, i != s(k), j != t(k). Flow conservation constraint 2a: Sum_{j: (i, j) in E}{X(k, i, j)} – Sum_{j:(j, i) in E}{X(k, j, i)} = 1, for all k in K, i == s(k) Flow conservation constraint 2b: Sum_{j: (i, j) in E}{X(k, i, j)} – Sum_{j:(j, i) in E}{X(k, j, i)} = -1, for all k in K, i == t(k) Sum{d(k)*X(k, i, j)} <= C(I, j) * alpha 0 <= X(k, i, j) <= 1 Alpha >= 0

Static problems: LP formulation Formulate the problem of finding the optimal routing solution for optimal total load in the network. Total load = the sum of the bandwidth requirement in each link The solution to the LP formulation yield the best routes for traffic demands. Traffic may be partitioned into multiple routes. How to figure out the actual route from the solution? How to make sure the solution does not partition a route with multiple paths?

Dynamic Problem: Flow are arriving dynamically. How to assign a route for each flow to maximize the system performance? Decisions must be made as the flows arrive. May not yield global optimization. Which algorithm minimizes the total bandwidth usage? What are the problems with this algorithm? Which algorithm minimizes the maximum link usage? What are the problems with this algorithm?

Dynamic Problem: A hybrid algorithm between shortest path and shortest widest path: f(i, j) be the current load, a(i, j) = (f(i, j) + d(k)) / c(i, j) + T*MAX(0, (f(i, j) + d(k)) / c(i, j) – alpha)) Minimum interference routing: Compute the maximum flow between all pairs of edge routers Links that are part of the maximum flow graph is critical (with criticality weight increased by 1). Find the path with minimum criticality.

Multipath Load sharing: Multiple paths can usually be found. Need a traffic splitter to put packets to different paths Must be fast Must produce stable traffic distribution Must maintain per-flow packet ordering Will round robin work?

Multipath Load sharing: Hashing-based traffic splitting: Direct hashing: H = distIP mod N H = s1 xor s2 xor s3 xor s4 xor d1 xor d2 xor d3 xor d4 H = CRC16(5-tuple) mod N table based hashing Have the ability to properly distributed the load.