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In applied queueing theory, it is often important to deal with transient system behavior. Performance evaluation of congestioncontrol mechanisms in a packet-switching network is an excellent example in which there is frequently a strong need to deal with the intrinsic dynamic character of congestion. In that case, the queueing models have to be analyzed for a transient environment. In this paper, we show that such problems can be treated in a uniform way, when the system of coupled differential equations describing the system-state or flow process is solved numerically. For this, the fourth-order RungeKutta procedure allows a good balance between memory requirements, computing time, and accuracy. To illustrate the explanatory power of this kind of transient queueing analysis, three models will be considered: the common-store queueing system showing the priority deadlock, the foreground-background congestion-control mechanism, and a two-level global congestion-control mechanism.