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Internet routers contain buffers in order to hold packets during times of congestion. For many years, there has been a hot debate regarding the size of buffers required at core Internet routers. In recent years, studies show that the core router buffer size need only dozens of packets to meet acceptable link utilization. This means that a smooth transition is possible from electric routers to the network of all-optical routers. However, prior studies ignored whether buffer unit are structured in terms of packets or bytes. It made no much difference when only TCP traffic with the same packets size is considered in the previous studies. In this paper, we study the coexistence of real-time UDP and TCP traffic for routers with buffers of very small size. We found that the difference the buffer unit structure impacts obviously the loss performance of routers with very small buffers. When buffer unit are structured in terms of packets, the UDP packet loss rate is higher than the TCP packet loss rate. However, when buffer unit are structured in terms of bytes, the UDP packet loss rate is lower than the TCP packet loss rate.