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This paper designs and measures the performance of a message scheduling scheme for the mobile sensor network employing two sinks. For the purpose of enhancing the successful delivery ratio for time-sensitive sensor messages and also avoiding congestion around the sinks, the proposed scheme keeps their loads different, and makes each sensor node send the urgent message to the low-load sink. For a neutral node, the urgency of a message is estimated by comparing the slack value of the message and slack distribution of overall messages observed at the node. With this information, each node decides the destination of each message. The simulation performed via ns-2 reveals that the proposed scheme, called chop partition, can improve the deadline meet ratio of real-time messages by up to 7.2% for AODV case and 8.2% for DSDV case, compared with the random selection scheme, or even partition, for the given experiment parameters.