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Recently, many studies exploit mobile sinks to construct large-scale databases for environmental observations or weather forecasting. Mobile sinks travel in the sensing area that sensors are deployed, collect data from each sensor, and uploads them to sensor databases. By using mobile sinks, we can reduce communication traffic and maintenance cost compared with those for wireless sensor networks (WSNs). Some methods to give fairness to data collection for sensors have been proposed. However these methods give hard restrictions for sensor data collection. Therefore, the mobile sink does not always collect data from sensors even when it can collect. This causes a fewer amount of data collection. In this paper, we propose a communication protocol to increase the data amount that the mobile sink collects considering fairness of communication time. Our proposed protocol ensures fairness by giving an upper limit to the first communication time for a sensor. After that, the mobile sink collects data from the sensor again if the mobile sink cannot find any other sensors. Our simulation results demonstrated that our proposed protocol can ensure fairness of the communication time and can increase the amount of collected data.