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Timeout control is a simple mechanism used when direct feedback is either impossible, unreliable, or too costly, as is often the case in distributed systems. Its effectiveness is determined by a timeout threshold parameter and our goal is to quantify the effect of this parameter on the system behavior. In this paper, we extend previous results to the case where there are N transmitting nodes making use of a common communication link bandwidth. After deriving the stochastic hybrid model for this problem, we apply Infinitesimal Perturbation Analysis to find the derivative estimates of aggregate average goodput of the system. We also derive the derivative estimate of the goodput of a transmitter with respect to its own timeout threshold which can be used for local and hence, distributed optimization.