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 of results of transient analysis for Markovian and phase-type controlled arrival rate systems are also done.