Bounding aggregations on phase-type arrivals for performance analysis of clouds

We evaluate the performance of a cloud system using ahysteresis queueing system with phase-type and batch arrivals. To represent the dynamic allocation of the resources, the hysteresis queueactivates and deactivates the virtual machines according to the threshold values of the queue length. We suppose a variable traffic intensity as the client requests (or jobs) arrive by batches, and follow a phase-type process. This system is represented by a complex Markov chain which is difficult to analyze, especially when the size of the state space increases and the length of batch arrival distribution is large. So, to solve this problem, we propose to use stochastic bounds and define bounding systems less complex. We give some results for the performance measures and compare the proposed bounding models with the exact one. The relevance of our methodology is to offer a trade-off betweencomputational complexity and accuracy of the results and provide very interesting solutions for network dimensioning.