Reliability Analysis Based on a Jump Diffusion Model with Two Wiener Processes for Cloud Computing with Big Data

Abstract

At present, many cloud services are managed by using open source software, such as OpenStack and Eucalyptus, because of the unification management of data, cost reduction, quick delivery and work savings. The operation phase of cloud computing has a unique feature, such as the provisioning processes, the network-based operation and the diversity of data, because the operation phase of cloud computing changes depending on many external factors. We propose a jump diffusion model with two-dimensional Wiener processes in order to consider the interesting aspects of the network traffic and big data on cloud computing. In particular, we assess the stability of cloud software by using the sample paths obtained from the jump diffusion model with two-dimensional Wiener processes. Moreover, we discuss the optimal maintenance problem based on the proposed jump diffusion model. Furthermore, we analyze actual data to show numerical examples of dependability optimization based on the software maintenance cost considering big data on cloud computing.

Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1

“…It is clear that for n = 2, the trace function defined in (4) is a one-homogeneous function because we have tr 2 1 (xy) = ytr 2 1 (x) for y ∈ F q and x ∈ F q 2 . Therefore, from a q-ary m-sequence of period q 2 − 1, we can construct a cyclic RDS with parameters (q + 1, q − 1, q, 1).…”

“…[29]. By using a lexicographic order, we can similarly obtain the following incidence matrix for a (16, 4, 4) FR code as: (4,2), (4,3), (1, 4)}, which corresponds to the first row of the proposed incidence matrix when we use a lexicographic order. The remaining rows can be obtained by adding all elements in G = Z 5 ⊕ Z 5 just as in the previous examples.…”

“…Equation (2) says that M(k) can be strictly larger than the MBR capacity if some pairs of rows have no collision and the other pairs have one collision. The incidence matrices of the proposed FR codes satisfy the above condition for a given k, and thus, M(k) of the proposed FR codes is larger than or equal to the MBR capacity.…”

“…As users of social media services and cloud services frequently upload large data files such as images and videos, huge storage space is required, which is implemented in the form of distributed storage systems (DSSs) [1,2]. DSSs manage a tremendous amount of storage nodes and a large number of failed nodes occur every day.…”

Construction of Fractional Repetition Codes with Variable Parameters for Distributed Storage Systems

“…As users produce a tremendous amount of data everyday and these big data need to be stored in cloud storage [1,2], the efficiency and reliability of distributed storage systems (DSSs) become more crucial. Rather than using a random protocol, we need to adopt some mathematical structures in storing big data to minimize the overall cost of DSSs.…”