Resources Allocation with QoS Provisioning for M2M services over Long Term Evolution
ASSIGNMENT, DISTRIBUTION AND QOS PROVISIONING IN COMMUNICATION NETWORKS.
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Transcript of ASSIGNMENT, DISTRIBUTION AND QOS PROVISIONING IN COMMUNICATION NETWORKS.
ASSIGNMENT, DISTRIBUTION AND QOS PROVISIONING IN COMMUNICATION NETWORKS
Facility Location Theory [8]
Underlying model in the analysis of many of the combinatorial optimization network problems, also known as Location analysis
In general, given a collection of potential facility (source) sites where the facility can be opened, and a set of demand points that must be serviced, the problem is to find the subset of , to minimize a user defined metric.
Several costs and constraints can be associated with the model for e.g. the cost of opening the facilities, the cost due to delays incurred in service, the capacities of facilities, the capacities of the links etc.
The problem is NP Hard to solve optimally, therefore has to be reduced
Various variants of the problem have been investigated
Uncapacitated Facility Location Problem
Given
a distance function d :
a cost function f
Find a subset of , that minimizes
No Constraints on capacities of the facilities and the links between demand and supply are assumed
The Metric Uncapacitated Facility Location Model
In this version, the clients and the facilities are located in a metric space, and satisfy the triangle inequality
Connected Facility Location Problem [3]
Given a graph , some potential facility nodes and some client nodes
The additional constraint is that the open facilities must be connected through a Steiner Tree
The solution opens some facilities from , assigns each client to an open facilityand connects the facilities by a tree T , minimizing
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
Data Placement Problem mentioned in [2]
Given
a set of caches , a set of clients and a universe of data objects
Each cache has a capacity , each user a demand for a particular data object
Each user has to be assigned a cache, taking into account the storage and access cost
The goals is to find the placement of data objects to caches respecting the capacities of caches and minimizing the costs incurred
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.
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
Notation Used
The Objective function
is minimized with respect to the following constraints
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
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
Formulation
An origin server is connected to a network of k edge caches. The server stores a collection of video, split into a number of symbols
To each edge caches are connected a number of users , and each user can connect to only one cache
Each cache prefetches every symbol independently with probability p , such that the memory constraints are satisfied
The server knows which symbols are stored in which caches. The users attached to the caches issue a sequence of requests for one content symbol
The server responds to these request by sending multicast packets to all k edge caches associated with it
The cached symbols can be used to create coded multicast opportunities, where a single coded packet is beneficial to more than one demand
To test the ideas, a video streaming prototype is developed that uses coded caching approach
Resource Allocation in a Data Center[5]
Formulation
Consider a data center with a set of heterogeneous servers
The incoming service requests are distributed to the server with probability
‘Time of use’ pricing policy is assumed in power distribution to the servers
Time of the day is divided in slots, indexed by , with duration , and appropriate pricing is assumed for each slot duration
Request arrival follows a poisson process, with rate in the time slot
Provided the request arrival rate, the energy pricing function, specifications of the battery array and data center, a request allocation scheme for the servers and a charging discharging scheme for the batteries is proposed
Pose the problem as a convex optimization problem and solve for the required parameters
Notations used: share of resources allocated by the server in the time
period, the probability that a service request is dispatched to server in the time slot
denotes the average processing rate of the server, is the indicator whether server is turned on ( = 1) or off in
the time slot
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
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
Formulation
The system consists of k areas numbered by 1,2,3…k.
In every one can place multiple resources of different types numbered 1..m
Assume that area is associated with placement . The placement L is feasible only if storage constraints are met
Consider a stochastic demand reflecting the demand at peak hours. Let represent the number of requests for type resource in area
The statistics are calculated by an external data base
If a request is made is an area , and is assigned a resource in the placement L, then it is satisfied with cost If it assigned to a remote source, then the cost incurred is If it is not served at all, the cost is
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
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
[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