## 2 Background and Motivations  
Cloud Computing [1; 2; 3] is an emerging technology to provide users with services, which are accessible through networks including local area network (LAN), wide area network (WAN) or even Internet. More precisely, a Cloud computing platform houses 2 types of software: users' applications and system software. The users' applications are delivered as services to users, known by software as a service (SaaS) and the system software is a middleware in support of those services with a quality of service according to a Service Level Agreement [4]. Complicated applications often require a huge amount of available computing processing and network capacity, provided as an infrastructure as a service (IaaS), in support of large-scale experiments. Examples of such applications are in the domain of seismic imaging [14], aerospace [15], meteorology [16], and convolution-based applications [9]. In this work, we focus on divisible load applications, where an application load can be divided into a number of tasks that can be processed independently in parallel ([17; 18; 19]). Divisible Load Theory [17] provides a framework for mapping divisible loads to a platform of heterogeneous machines using master-worker model. The master is a processor which divides an application load into tasks and assigns each task to a separate worker. Many scientific and engineering applications can be divided using the master-worker model, such as search for a pattern, compression, join and graph coloring and generic search applications [8], multimedia and video processing ([20,21]), and image processing [22]. Divisible load applications based on the master-worker model can be easily implemented and deployed on a computational Cloud [1]. A Cloud is defined as a type of parallel and distributed system consisting of a collection of interconnected and virtualized computers that are dynamically provisioned and presented as one or more computing resources based on a Service Level Agreement. Hardware resources and software are presented to users as services. Therefore, one of the main goals of a Cloud is to deliver resources on pay-as-you-use basis. By means of virtualization and the ability of users to scale up and down their use of hardware, Cloud offers a flexible and an efficient platform for scientists and engineers [5] to run heavy-load applications. The issue of finding an optimal scheduling algorithm to schedule a divisible load application to heterogeneous distributed computing platforms have been studied thoroughly [11; 12; 13; 23]. Reference [18] describes the research in this area over the past decades, which involves the linear and continuous modeling of partitionable communication and computation loads for parallel processing. The main issue to solve was to find the optimal sizes of load partitions (tasks) that have to be distributed to a distributed computing system for application optimal execution, and the ideal number of rounds needed for optimal performance [11; 12; 13; 23]. Reference [24] discusses a scheduler efficiency based on different strategies of overlapping communication and computation on target systems. However, to our knowledge, there is no work which has studied the behavior of those applications and their blocking probabilities as a set of resources virtualized to users. The blocking probabilities are dynamically computed and provided as a feedback to a dynamic scheduler which alters resources allocations accordingly to obtain an optimal scheduling algorithm. In this work, we propose a novel model to analyze the behavior of a divisible load application implemented in a cloud system. In particular, we compute the blocking probability of running an application's tasks on a computing worker located in a Cloud computing platform. The proposed model is based on Markov chain process model.