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In this study, a distributed traffic-aware routing scheme is proposed for a wireless sensor network with multiple sinks. In multi-sink networks, traffic moving towards one sink may congest that moving towards others. The algorithm proposed here considers the traffic of surrounding neighbours before jumping to any sink. This is accomplished by building for each single sink, a gradient field and using gradient-based search for routing. The gradient index of one node contains two parts. (i) The first represents the distance-cost to travel, based on routing over lossy link) proposed by an IETF working group. (ii) The second contains the implicit traffic delay carried by the current holding node. Gradient field is built in distributed way and proven to free from loops. In a simulation, the authors show that this method of building gradient field routes balances the shortest path and possible congestion made by sinks, especially in heavy traffic networks, thereby reducing the overall end-to-end delay.