ABSTRACTThis paper is an analysis of the optimal reneging decision of a customer who joins a G/M/1 queue, having imperfect information about the queue. It is assumed that a customer receives a constant, known reward upon completion of service and incurs a cost proportional to the time spent in the queueing system. It is also assumed that a customer revises his estimated remaining waiting time in the system based on his initial estimate and observations of service time. Thus, a customer will renege when his estimated cost of remaining in the system exceeds his reward. The probability of a customer reneging during any given service is determined. Finally, it is shown how this probability varies with the parameters of the customer.