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We analyze the latency or sojourn time L(m,n) for the last customer in abatch of n customers to exit from the m-th queue in a tandem of m queues in thesetting where the queues are in equilibrium before the batch of customersarrives at the first queue. We first characterize the distribution of L(m,n)exactly for every m and n, under the assumption that the queues have unlimitedbuffers and that each server has customer independent, exponentiallydistributed service times with an arbitrary, known rate. We then evaluate thefirst two leading order terms of the distributions in the large m and n limitand bring into sharp focus the existence of phase transitions in the systembehavior. The phase transition occurs due to the presence of either slowbottleneck servers or a high external arrival rate. We determine the criticalthresholds for the service rate and the arrival rate, respectively, about whichthis phase transition occurs; it turns out that they are the same. Thiscritical threshold depends, in a manner we make explicit, on the individualservice rates, the number of customers and the number of queues but not on theexternal arrival rate.

Batch latency analysis and phase transitions for a tandem of queues with exponentially distributed service times