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A novel mathematical model is presented to analyse the performance of cloud computing centers using non-Markovian queuing model M/G/c/c+r/PR with priority as a queue discipline.Task arrivals are categorized as higher-priority (Hpriority) task queue and low-priority (Lpriority) task queue.This model allows cloud providers to determine the performance metrics of the task queue such as average number of tasks, probability of congestion, and probability of no waiting time with respect to server and buffer size. Two feasible conditions, namely non-preemptive and preemptive task priorities are discussed in this work. This approach is validated using discrete-event simulator and Maplesoft for the above mentioned parameters and the analysis has been done based on the arrived results.

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