The taxi sector is being revolutionized worldwide due to innovative companies, such as Uber, Lyft and more, that are trying to acquire a share of the market. In the same context, contemporary businesses in Greece have started to expand their activities. This present research is subsumed into the concept of innovation in the conventional taxi sector in Greece and attempts to implement pioneering ideas, to offer better services for taxi customers and profitable financial circumstances for taxi owners and drivers. The main data source regarding the taxi trips are the Hellenic Institute of Transport and Taxiway, the largest taxi fleet management company that operates in Thessaloniki. The given data consisted of 170 taxi trips originating from a taxi stand in the city center, 1981 routes which began from the area around the taxi stand and 1832 trips of taxis that passed through the examined area near the stand. These data, in accordance with a financial analysis of taxis' operational costs, have been processed to produce statistical results, such as the mean waiting time in each stand or possible spots for a taxi to pick up a customer. The research relies on these data, for the sake of building an application in which taxi drivers would be advised on their dilemma of choosing between waiting in taxi stands or hailing in the surrounding area to find a customer. With the utilization of such a website, drivers can compare the predicted benefit values for hailing or standing alternatives aiming to optimize the taxi downtime. The analysis concluded that the system can potentially increase the average expected profit per trip, even by 50% in a comparison to a different decision taken by the taxi driver.