On Investigating Energy Stability for Cellular Automata Based PageRank Validation Model in Green Cloud

Introduction

At present, the widely spread presence of Cloud Computing may be sensed in most of our daily life activities. Cloud computing may be referred to as the uses of networked remote servers located over the Internet, which enables the efficient storage, management, and processing of data (Delvenne, 2005; Richardson et al., 2006; and Chung, 2010). The web servers (resources) in today’s world may be considered as Clouds. Search Engine performs a significant role in the information retrieval process over Internet. Search Engines provides a list of indexed Clouds (web resources) in view of the content relevancy. PageRank (Page et al., 1999; Baeza-Yates, 2004; and Duhan et al., 2009) refers to the index number of a Cloud assigned by a Search Engine. Thus, PageRank plays an important role towards online information retrieval process. By convention, a low valued PageRank signifies high rank for that Cloud. Different static PageRank (Richardson et al., 2006) and dynamic PageRank algorithms (Baeza-Yates et al., 2001; Sullivan et al., 2005) were presented by researchers to enhance the PageRank computation process. PageRank algorithm is not only used towards the indexing of Clouds but may be used to maximize the influence in social network (Zhang et al., 2015), and may also be used to enhance the security against “Cross-Site Scripting (XSS) attacks” (Chaudhary et al., 2016, 2018; Gupta et al., 2018; and Zhang et al., 2019). Several researches are available on static and dynamic modelling of PageRank. Among others, studies on PageRank using Cellular Automata (CA) were presented in (Kundu et al., 2006 and 2007). It is found in (Kundu et al., 2006 and 2007) that web traffic, in-links, and out-links are important towards the computation of PageRanks. Though several researches are available on static and dynamic modelling of PageRank, unfortunately we have found a very little efforts towards the validation of computed PageRank. PageRank validation model in CA was presented in (Mitra et al., 2015 and 2017). In our studies, we further explored that following significant parameters were additionally considered in PageRank validation model (Mitra et al., 2015, 2017):

• 1.

  Number of visitors;

• 2.

  Average value for web pages accessed by an individual visitor;

• 3.

  Average session (period of the visiting time);

• 4.

  Average value for web pages accessed within a time slot;

• 5.

  Busy times;

• 6.

  In-links, etc.

CA based models are quite popularly investigated by researchers towards modelling of dynamic and complex problems as inherent supports towards parallel computing, and easy and cost-effective physical implementation capabilities are found with CA models. For the same reason, we find different CA based models in view of several Engineering, and Scientific applications (Chaudhuri et al., 1997; Mazoyer et al., 1999; and Kundu et al., 2007). CA based PageRank validation is also investigated in this research. Hence, a brief discussion on CA is presented next.

Several CA cells are arranged together in the form of a lattice, which advance over discrete space, and time. CA growth may be observed in multi-dimensions. The simplest CA arrangement is of one-dimensional in 3-neighborhood (left-cell, self-cell, and right-cell) at periodic boundary or, null boundary scenario, which is referred to as the ECA (elementary CA). ECA evolve, based on the binary values (zero, and one) of the concerned cells and transition functions (also referred to as Wolfram CA rules, total 256 rules). Next state (transition function) of a cell in ECA scenario may be determined with Equation 1 (Chaudhuri et al., 1997):