We investigate the problem of estimating the transmission time of fragmented messages over multiple disrupted links. We build a system model for the case where a single message is sent over a chain of links and the disruptions in these links are identically and independently distributed. For this case, we derive approximation formulas for the mean transmission time, based on number of links, length of fragments and distributions of disruptions. The formulas are verified against simulation experiments in the cases of uniform and exponential distributions for disruptions. (C) 2014 Elsevier B.V. All rights reserved.