Locating network monitors: complexity, heuristics, and coverage

1. Locating network monitors: complexity, heuristics, and coverage Kyoungwon Suh Yang Guo Jim Kurose Don Towsley

2. Motivation • Need to understand the performance of the network infrastructure. • A monitor can achieve this goal. • A monitor is placed inside a router • A monitor can be deployed as a standalone measure box that taps into a communication link • A monitor may capture or sample packets carried by this link • In order to capture large fraction of the traffic, we may place multiple monitors on different links.

3. Several things we need to consider when deploying the monitors. • Placing a monitor on a link incurs a deployment cost: • Hardware/software cost • Space cost • Maintenance cost • Each operation by the monitor also incurs some cost. • Per-packet operating cost • Placing the monitors on different position may have different benefits. • The general goal will be maximizing the benefit while minimizing the cost.

4. Problem setting • A flow: a collection of packets going through the same route on the network. • D: a set of all flows. • Si : the set of all flows carried by link i. • yi: whether a monitor is deployed at link i. • yi = 1: deployed. • yi = 0: not deployed.

5. Deployment cost: deployment cost may be different from link to link. • fi: the cost of deploying a monitor on link i. • The total deployment cost is: • Operating cost: • Depend on the link speed, specific to the link, • ci: the cost per-packet at link i. • Depend on the volume of flows the monitor is monitoring • j: the number of packets sent by flow j. • mij: the fraction of flows sampled by the monitor on link i. • The total operating cost:

6. Monitoring reward: • The reward depends on which flow is monitored. • The reward depends on what fraction of each flow is monitored • If the monitor can capture every packet traversing the link, • If the monitor only sample a fraction of each flow

7. Monitoring problems without sampling • Each monitor collects all the packets of monitored flows, • mij = 1 or 0 for all i, j. • Budget Constrained Maximum Coverage problem (BCMCP) • Total deployment cost is constrained. • Maximize benefit • Operating cost is ignored • Minimum deployment cost problem (MDCP) • A certain amount of monitoring reward should be guaranteed • Minimize the deployment cost • Operating cost is ignored • Minimum deployment and operating cost problem (MDOCP) • Minimize the sum of deployment and operating cost

8. Budget Constrained Maximum Coverage problem (BCMCP) • Problem formulation • The problem is NP-Complete, which can be shown by a reduction from a known NP-Complete problem, budgeted maximum coverage problem(MCP).

9. Budgeted maximum coverage problem (MCP) • Definition: • A collection of sets S = { S1, S2, …, Sm} with associated costs {c1, c2, …, cm} over a a domain of elements X = {x1, x2, …, xn}with associated weights {w1, w2, …, wn} • Goal: find sets S’S such that total cost of elements in S’ does not exceed a given budget L and the total weight of elements covered by S’ is maximized. • This problem is known to be NP-Complete • Find some approximation algorithm • Performance of an approximation algorithm A. • A is said to achieve approximation ratio  if the weight generated by A is at least ( * optimal)