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Serious traffic congestion and emission by excessive usage of private cars are crucial issues in our modern society. As one solution for these, a concept of Park-and-Ride (PnR) where people stop their private cars (i.e. single-occupancy vehicles) at stations and ride on public vehicles (i.e. mass transportation) are receiving wide attention recently. In this paper, we propose a comprehensive mathematical model which can evaluate waiting times and traveling times of customers, and the total emission of vehicles for various usage ratio of PnR and operation policies of public transportation. Using a system of queues integrated with an emissions model we perform a case-study of Tsukuba city, in Japan. We indicate an intriguing trade-off between the waiting time of customers for the PnR and the long traveling time due to the traffic congestion (leading to high emissions) caused by private cars depending on the usage ratio through some numerical experiments. Moreover, we study the total cost to society caused by total trip times and pollution, in which the decision variables are the capacities and frequencies of the public transportation for the PnR system. Our numerical results showed a significant reduction in the total social cost under the optimal transit policy for the current high usage rate of single-occupancy vehicles. Furthermore, we show that further reduction in the total social cost can be revealed by considering the reduction on the use of private cars compared to the current state implying the social importance of promoting car-free movement., Comment: 52 pages, 35 figures