In this study an attempt was made to compare the performance of three widely accepted Markovian models of urban growth based on Cellular Automata (CA_MC), Multi-Layer Perceptron (MLP_MC), and Logistic Regression (LR_MC) in the Kolkata Metropolitan Area. The long-term Landsat images (from 1975 to 2020) were used to study the urban growth. A set of performance metrics, i.e., Kappa, Probability of Detection, False Alarm Ratio, Critical Success Index, and Accuracy Score, were employed to assess the accuracy of the model outputs. Different factors and constraints, were considered to observe their impacts on urban growth. The results indicate that while AHP-based CA_MC performs better overall, relying on any one performance metric alone may provide a misleading conclusion. It was observed that the CA_MC with the AHP performed the best and used for future simulation of the urban land-use/cover maps was generated from 2025 to 2070 at regular intervals. Much of that happens at the expense of the agricultural lands and vegetation cover, which are predicted to decrease by 18% and 5.3%, respectively. The distance-directional growth analysis showed that the areas closer to the central locations are expected to reach saturation, and the fringe areas are expected to register higher urban growth.