A Queuing Model to Analyze Data Center Performances in a Cloud Computing Environment

In the last decades cloud computing has been the focus of a lot of research in both academic and industrial
fields, however, implementation-related issues have been developed and have received more attention than
performance analysis which is an important aspect of cloud computing and it is of crucial interest for both cloud
providers and cloud users. Successful development of cloud computing paradigm necessitates accurate
performance evaluation of cloud data centers. Because of the nature of cloud centers and the diversity of user
requests, an exact modeling of cloud centers is not practicable; in this work we report an approximate analytical
model based on an approximate Markov chain model for performance evaluation of a cloud computing center.
Due to the nature of the cloud environment, we considered, based on queuing theory, a MMPP task arrivals, a
general service time for requests as well as large number of physical servers and a finite capacity. This makes
our model more flexible in terms of scalability and diversity of service time. We used this model in order to
evaluate the performance analysis of cloud server farms and we solved it to obtain accurate estimation of the
complete probability distribution of the request response time and other important performance indicators such
as: the Mean number of Tasks in the System, the distribution of Waiting Time, the Probability of Immediate
Service, the Blocking Probability and Buffer Size