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The unsatisfactory performance of TCP in high speed wide area networks has led to several versions of TCP- like H-TCP, Fast TCP, Scalable TCP, Compound or CUBIC, all aimed at speeding up the window update algorithm. In this paper we focus on Scalable TCP (STCP), a TCP version which belongs to the class of Multiplicative Increase Multiplicative Decrease (MIMD) congestion protocols. We present a new stochastic model for the evolution of the instantaneous throughput of a single STCP flow in the Congestion Avoidance phase, under the assumption of a constant per-packet loss probability. This model allows one to derive several closed-form expressions for the key stationary distributions associated with this protocol: we characterize the throughput obtained by the flow, the time separating Multiplicative Decrease events, the number of bits transmitted over certain time intervals and the size of rate decrease. Several applications leveraging these closed form expressions are considered with a particular emphasis on QoS guarantees in the context of dimensioning. A set of ns2 simulations highlights the model accuracy.