In this paper, information theoretic inference methodology for system modeling is applied to estimate the probability distribution for the number of customers in a general, single server queueing system with infinite capacity utilized by an infinite customer population. Limited to knowledge of only the mean number of customers and system equilibrium, entropy maximization is used to obtain an approximation for the number of customers in the G|G|1 queue. This maximum entropy approximation is exact for the case of G = M, i.e., the M|M|l queue. Subject to both independent and dependent information, an estimate for the joint customer distribution for queueing systems in tandem is presented. Based on the simulation of two queues in tandem, numerical comparisons of the joint maximum entropy distribution is given. These results serve to establish the validity of the inference technique and as an introduction to information theoretic approximation to queueing networks.