The Quality of Service (QoS) offered to telecommunication applications is related to the transient behavior of network elements in the case of congestion. In this paper, we analyze the variations of the bit rate process $\\Lambda_t\$ created on an ATM link transmitting data bursts in an open-loop statistical multiplexing scheme. This process is modeled by means of an M/M/\infty$ queuing system. The performance of statistical multiplexing is then characterized by transient QoS parameters, namely the duration $\theta$ of a congestion where the process $\\Lambda_t\$ remains above the link transmission capacity $C$, the area $V$ swept by that process and the number $N$ of bursts arriving over this congestion period. The respective distributions of random variables $\theta$, $V$ and $N$ are computed by means of a uniformization technique. The corresponding numerical algorithms are described in full detail. This approach allows us, in particular, to provide a simple proof for the so-called local approximation of process $\\Lambda_t\$, which has been previously introduced in the literature as a heuristic.