Abstract
Cloud computing is known as a new trend for computing resource provision. The process of entering into the cloud is formed as queue, so that each user has to wait until the current user is being served. In this model, the web applications are modeled as queues and the virtual machines are modeled as service centers. M/M/K model is used for multiple priority and multiple server systems with preemptive priorities. To achieve that it distinguish two groups of priority classes that each classes includes multiple items, each having their own arrival and service rate. It derives an approximate method to estimate the steady state probabilities. Based on these probabilities, it can derives approximations for a wide range of relevant performance characteristics, such as the expected postponement time for each item class and the first and second moment of the number of items of a certain type in the system.
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