Optimal placement of Charging stations (CSs) and infrastructure planning are one of the most critical challenges that face the Electric Vehicles (EV) industry nowadays. A variety of approaches have been proposed to address the problem of demand uncertainty versus the optimal number of CSs required to build the EV infrastructure. In this paper, a Markov-chain network model is designed to study the estimated demand on a CS by using the birth and death process model. An investigation on the desired number of electric sockets in each CS and the average number of electric vehicles in both queue and waiting times is presented. Furthermore, a CS allocation algorithm based on the Markov-chain model is proposed. Grey Wolf Optimization (GWO) algorithm is used to select the best CS locations with the objective of maximizing the net profit under both budget and routing constraints. Additionally, the model was applied to Washington D.C. transportation network. Experimental results have shown that to achieve the highest net profit, Level 2 chargers need to be installed in low demand areas of infrastructure implementation. On the other hand, Level 3 chargers attain higher net profit when the number of EVs increases in the transportation network or/and in locations with high charging demands.