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Performance evaluation based on transient analysis has significant importance to those systems which never reached at equilibrium. In this paper, we develop and analyze the system through controlled arrival rate using internal limits. The system is modeled with Markovian and phase-type distributions for various internal limits and queue size. The transient analysis is carried out for the systems in vector domain through matrix geometric method and Runge-kutta procedure. The comparisons ofdoaj:791a44582d5a4cbc86559a931c9442b1 fatcat:taocj5jmzzfvhe3kbrdfda5av4