1. ASSIGNMENT, DISTRIBUTION AND QOS PROVISIONING IN COMMUNICATION NETWORKS

2. Facility Location Theory [8]

6. Centralized Data Placement [1]  Target – Efficient distribution of internet traffic by replicating data and caching it at several locations  The problem is where to place the replicated data, in order to serve the demands with maximum performance  The problem can also be seen as a special case of the capacitated facility location problem [3]  The problem is an extension of the data placement problem mentioned in [2], described in next slide

8. Formulation  A centralized server will decide the data placement scheme. The central server will manage the routers  Access routers are connected via an undirected graph. The edges of the graph represent the links. Demand nodes are placed behind the vertices  The servers have caches installed on them. Caches have specific capacities.  Users demand data, the requests are forwarded to the access routers and if the data is found in the cache, it is served. Otherwise it is fetched from another connected access router.

9. Three types of costs are considered  1. Transmission delays  2. Time needed to process the requests on the cache serves  3. The price charged for installation and storage of data object in a cache server

10. Notation Used

11.  The Objective function is minimized with respect to the following constraints

12. Solution  The problem is NP hard, and the objective function is quadratic  Two decomposition based solutions are proposed - Lagrangian relaxation - Randomized rounding Directions for future works  Decentralized implementation of solution algorithms – in either a semi centralized or a fully decentralized way  Or to propose a decentralized algorithmic solution to the problem

13. Coded Caching [4]  To improve the performance gains of the cache networks  The coding gains are achieved at the cost of large delivery delays  Coded caching can perform better than uncoded caching  How much coded caching gain can be achieved provided a restriction on delivery delays?  The tradeoff between coded caching and delivery delay is investigated

15.  To test the ideas, a video streaming prototype is developed that uses coded caching approach

16. Resource Allocation in a Data Center[5]

19. Optimal Data Placement on Networks With Fixed Number of Clients [6]  A variant of the data placement problem  Given the set of available objects and preference for each object of each client, decide a replication scheme for the placement of data on the local caches such that the total access costs among all clients and objects are minimized  The algorithm finds optimal placement in linear time when the object lengths are uniform

20. Resource Placement in Distributed Network Topologies [7]  The objective is to place the resources in the regions to minimize the cost occurred in meeting the demands  The possible practical applications are peer supported video demand services, cloud based services  The challenge is to meet the arbitrary multidimensional demand

22.  The system is operated in two stages  1. Placement Stage: Given the demand distributions {N}, {D}, the service cost parameters {C}, area storage parameters {S}, and a matching algorithm M, optimal placement of resource that minimizes the expected costs.  This stage design depends on the assignment problem solution  2. Assignment (Matching) Stage: Given a placement L, a demand realization {N} and the service cost parameters {C}, match the resources to the demands to minimize the service cost  High complexity problems are solved by reducing complexity, the placement problem is transformed to a min-cost flow problem

23. References [1] Drwal, Maciej, Jozefczyk, Jerzy, “Decomposition algorithms for data placement problem based on Lagrangian relaxation and randomized rounding” in Annals of Operations Research, 2014 [2] Chaitanya Swamy, Rajmohan Rajaraman and Ivan Baev, “Approximation Problems for Data Placement Networks” [2008] [3] Chaitnaya Swamy and Amit Kumar, “Primal-Dual Algorithms for Connected Facility Location Problems”, 2004 [4] “Coded Caching for Delay-Sensitive Content” 2014

24. [5] Shuang Chen; Yanzhi Wang; Pedram, M., "Resource allocation optimization in a data center with energy storage devices," Industrial Electronics Society, IECON 2014 - 40th Annual Conference of the IEEE, vol., no., pp.2604,2610, Oct. 29 2014-Nov. 1 2014 [6] Angel, Eric, Bampis, Evripidis, Pollatos, Gerasimos G., Zissimopoulos, Vassilis, “Optimal data placement on networks with constant number of clients” in Theoretical Computer Science, 2013 [7] Yuval Rochman, “Resource Placement and Assignment in Distributed network topologies”, in INFOCOM 2013 [8] Facility Location – application and theory by Drezner Ziv, Hamacher, 2002, Springer