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We study a linear-increase multiplicative-decrease flow control mechanism. We consider congestion signals that arrive in batches according to a Poisson process. We focus on the case when the transmission rate cannot exceed a certain maximum value. The distribution of the transmission rate in steady state as well as its moments are determined. Our model is particularly useful to study the behavior of TCP (Transmission Control Protocol) the congestion control mechanism in the Internet. Burstiness of packet losses is captured by allowing congestion signals to arrive in batches. By a simple transformation, the problem can be reformulated in terms of an equivalent M/G/1 queue, where the transmission rate in the original model corresponds to the workload in the `dual' queue. The service times in the queueing model are not i.i.d., and they depend on the workload in the system.