This article covers a batch arrival finite Markovian queueing system with multi-server support in phase-wise service and consumer impatience. We considered two types of customers with different arrival rates in terms of batches and state-dependent service. Poisson and Exponential distributions are assumed for arrival and departure times under FCFS mode. We model the system as a Markovian process and generated transition probabilities for different number of customers based on Runge-Kutta of order four. We also determined system’s performance indices. We have demonstrated the sensitivity analysis results and examined the effect of various input parameters on the system's constants.