4.5 Statistical Evaluation
4.5.2 Independent Replications Method
Normally in simulations the data gathered for the statistical evaluation are corre- lated with each other. Thus, the confidence interval calculation method explained earlier cannot be used directly. In literature, a number of solutions exist to solve the correlated data problem: e.g., replications method, estimation of autocorrela- tion function, batch means and regenerative method. Within this subsection, the independent replications method is explained which is also used to evaluate the confidence interval for this thesis.
The independent replication method [Per09], as the name suggests, relies on replicating several independent simulation runs. For example, N number of repli- cations are done each with M number of data elements:
Replication 1: x11,x12,x13...x1M Replication 2: x21,x22,x23...x2M Replication 3: x31,x32,x33...x3M . . . Replication n: xN1,xN2,xN3...xNM
The sample mean of each replication i can be evaluated as:
xi = 1 M M
∑
j=1 xi j (4.8)This will lead to having N approximately independent sample means[x1,x2,...xN],
the sample mean and variance of them will be:
x= 1 N N
∑
i=1 xi (4.9) δ2 = 1 N− 1 N∑
i=1 xi− x 2 (4.10) Now, using this variance the confidence interval can be calculated as explained before. Although the independent replications method is easy and simple two issues still need to be determined: first, how long each independent replication should be run (i.e., choosing M which should be a large number), and the seed used for each independent run must be chosen very carefully in order to have the replications independent. The independence between the replications can be checked by calculating the autocorrelation between them.This chapter presents the concepts of network virtualization, focusing specifically on wireless virtualization of the LTE mobile communication system. A novel wireless virtualization framework is proposed and developed by this thesis, which allows mobile network operators to share the wireless spectrum as well as the in- frastructure (i.e., hardware equipments). The work presented in this chapter targets proving the concept of using virtualization in wireless systems and highlighting its potential gain. The chapter is structured in the following manner: in section 5.1 the virtualization history and concepts are discussed. Section 5.2.1 describes the 4WARD European project and its virtualization architecture, the work was done by the author as part of the 4WARD project. In section 5.3 the novel LTE virtualiza- tion framework is proposed, explaining the technical details behind the framework. Proof of concept evaluations are discussed in section 5.4, where three different sce- narios are presented each showing a different potential gain area within the LTE virtualization. Finally section 5.5 summarizes and concludes this chapter. The proposed LTE virtualization framework, results/achievements and other related virtualization work are published in [ZZGTG10a], [ZZGTG10b], [ZZGTG11], [ZKZG11], [KZ11], [ZLZ+11], [LZZ+12] and [UZZ+10].
5.1 Virtualization
Virtualization is the process of creating virtual versions of physical resources that emulate the same physical characteristics. It is often used in the Information Tech- nology (IT) context to partition a physical resource into several virtual ones, for example, virtual memory, hard disk partition and virtual machine. The virtual- ization concept [Sin04] was first introduced at the beginning of the 1960s, when Christopher Strachey published a paper entitled “Time Sharing in Large Fast Com- puters” that focused on multi-programming. Then came the IBM M44/44X Project in the mid 1960s, where the term Virtual Machine (VM) was introduced for the first time. The creation and maintenance of such virtual machines is what is known to- day as “Server Virtualization”. The idea at that time was to create several virtual machines out of one mainframe computer to enable multi-tasking, i.e., running
simultaneous applications and processes in one computer, since such computers were very expensive at the time. The virtualization concept can be applied in dif- ferent areas. But from what can be seen in today’s IT interest three main areas emerge that adopt the use of virtualization, and these are:
• Storage Virtualization: according to IBM [IBM03], “it is considered as an
intelligent “layer” or abstraction that pools storage from multiple storage devices into a common storage pool. Often part of a Storage Area Network (SAN) virtualized storage appears as one device to the server-operating sys- tems and can be centrally managed and provisioned from a single view”.
• Server Virtualization: is the process of hiding the resources of the physical server and dividing the server into a number of virtual servers that share the physical resources and appear to the operating system running on top as an actual hardware. Server virtualization is used to minimize the IT cost in enterprises, as well as utilizing the full potentials of the physical servers. • Network Virtualization: is the process of aggregating the created virtual re-
sources into forming a Virtual Network (VNet). It enables multiple virtual networks to coexist on a common infrastructure in an isolated way. Each virtual network is operating similar to a normal network and does not nec- essarily have the awareness of the underlying virtualization process.