Models for Internet Cache Location

1. Models for Internet Cache Location Adam Wierzbicki Institute of Telecommunications Warsaw University of Technology adamw@icm.edu.pl

2. Introduction - 1 • Replica Location Problem (RLP) • Cache Location Problem (CLP) • Previous work on CLP • oriented on complexity: heuristics, special-case optimal solutions • black-box approach to decision problem

3. Introduction - 2 • Aim of this work: • design a Decision Support System (DSS) for cache location that allows the Decision Maker (DM) to find solutions that match his preferences • secondary goal: evaluate the practical complexity of using Mixed Integer Linear Programming for the CLP

4. Modules of a DSS • Information module could be integrated with other network management tools

5. The Decision Maker (DM) of the CLP • Who is the DM? • manager of a Content Delivery Network (CDN) • manager of a public caching infrastructure • What other parties can influence DM preferences? • content providers • clients of content providers • DM preferences • can change over time • are not known to the DM in advance

6. The information module - 1 Summary of input information

7. location variables • assignment variables Multicriteria models of the CLP - 1 • (Binary) Decision variables • Constraints • assignments must be a function • assignment to a node implies location of cache at that node • can constrain number of new caches or moved caches

8. compute "best" values , estimate "worst" values Multicriteria models of the CLP - 2 • cost of new cache location • Criteria • cost of movement of old caches • delay • average delay of fetching a unit of data by a client • average delay of sending a unit of data from a server • network resource cost • Find a common scale for all criteria • define a scaling function

9. weighted sum (WS) • preferences expressed using weights • reference point (RP) • preferences expressed using aspiration levels (to achieve) and reservation levels (to avoid) • objective function contains a minimum of scaled criteria Supporting the decision process - 1 • Objective functions that allow the DM to express his preferences

10. Supporting the decision process - 2 • Both the WS and RP methods always find a Pareto-optimal solution • The new models allow the DM to: • change his preferences during a session with the DSS • interactively explore the available optimal solutions by changing his preferences • The DSS should graphically display solution quality with respect to each criterion

11. Hit rates (equal): • Servers • Potential cache locations Comparison of WS and RP methods - 1 • Locate cache in small example topology to minimize server delays

12. "Best" values • "Worst" values Comparison of WS and RP methods - 2 Delays of the two servers: • Pareto-optimal solutions • Korhonen paradox

13. Comparison of WS and RP methods - 3 • RP method is more precise in searching for solutions that best match DM preferences • regardless of type of criteria • regardless of type of DM preferences (fair, not fair) • Expressing preferences using aspiration and reservation levels allows the DM to consider criteria separately (one at a time)

14. Solving models of the CLP using MILP • CLP of up to 100 nodes, 500 demands solvable by MILP solvers (cplex) • Complexity depends on number of demands and number of potential cache locations • MILP solvers can produce approximate solutions with controlled quality • Practical limitation of MILP: size of linear program

15. Solving models of the CLP by heuristics • Example: greedy heuristic • Modification for multiple criteria: use objective function of RP method • Greedy heuristic has similar drawback as WS method, but is suitable as a solver for the DSS • Future work - test other heuristics (l-greedy)

16. Conclusions • Supporting DM preferences and the decision process requires different (multicriteria) models of the CLP • Most model variants can be expressed using Mixed Integer Linear Programming • Heuristics can be adapted to models that support DM preferences Questions?