Cloud computing has revolutionized the information technology era. It offers high-speed computing, storage, and ICT resources on demand. One of the significant challenges in cloud computing is the impact of impatient users or request (task) reneging. When a request has been compromised, missed its execution deadline, or depends on other rejected ones, it must be removed from the queue without being processed. The reneging or removal of tasks from queues may trigger the reneging or removal of other tasks that depend of them. We refer to this reneging of requests from the load balancing or computing queues as correlated reneging. We presented the performance analysis of a network of queues that constitute a queueing model of a simplified cloud computing infrastructure. We show the relationship between the load, delay, and probability of buffer saturation (blocking probability). It is seen that at about 80% utilization, a small increase in utilization (due to a small increase in the arrival rate Δλ for a fixed service rate μ) results in a sharp increase in the delay experienced by the tasks, and on the probability of task rejection or blocking.