In recent social experiments, rental motorbikes and rental bicycles have been arranged at nodes, and environments where users can ride these bikes have been improved. When people borrow bikes, they return them to nearby nodes. Some experiments have been conducted using the models of Hamachari of Yokohama, the Niigata Rental Cycle, and Bicing. However, from these experiments, the effectiveness of distributing bikes was unclear, and many models were discontinued midway. Thus, we need to consider whether these models are effectively designed to represent the distribution system. Therefore, we construct a model to arrange the nodes for distributing bikes using a queueing network. To adopt realistic values for our model, we use the Google Maps application program interface. Thus, we can easily obtain values of distance and transit time between nodes in various places in the world. Moreover, we apply the distribution of a population to a gravity model and we compute the effective transition probability for this queueing network. If the arrangement of the nodes and number of bikes at each node is known, we can precisely design the system. We illustrate our system using convenience stores as nodes and optimize the node configuration. As a result, we can optimize simultaneously the number of nodes, node places, and number of bikes for each node, and we can construct a base for a rental cycle business to use our system.

Various methods have been proposed to solve the traveling salesman problem, referred to as the TSP. In order to solve the TSP, the cost metric (e.g., the travel time and distance) between nodes is needed. As we do not always have specific criterion for the cost metric we are proposing using a new computation environment that is used all over the world-Google Maps. We think a cost metric obtained from Google maps is a good, impartial value with little room for variation, making it easier and more efficient to make map information visible. Moreover, a scalable computation environment can be prepared by using cloud computing technology. We can even expand the TSP and calculate routes taken by multiple people. The numerical results show this computation environment to be effective.