In this paper, we are interested in the description of a cross-layer architecture that supports service differentiation for real-time and best-effort traffics in Wireless Sensor Networks (WSN). We present our mathematical model that combines parameters from network and MAC layers. We aim to estimate and to enhance the throughput of multi-hop WSNs and the stability of the forwarding queues used for real-time and besteffort traffics. We suppose at the first step that we have a wireless sensor network with a single sink then we suppose that we have the same wireless sensor network with two sinks. We study the impact of transmitting real-time and best-effort traffics on the system throughput; and we also study the impact of adding a second sink on the throughput.