The paper considers a discrete-time queueing system and its application to related models. The model is defined by XnÅ+1=Xn+An-DnÅ+1 with discrete states, where Xn is the queue-length at the nth time epoch, An is the number of arrivals at the start of the nth slot and DnÅ+1 is the number of outputs at the end of the nth slot. In this model, the arrival process {An} is described as a sequence of independently and identically distributed random variables. The departure DnÅ+1 depends only on the system size Xn+An at the beginning of the time slot. The paper studies the reversibility for the model. The departure discipline in which the system has quasi-reversibility is determined. Models with special arrival processes were studied by Walrand and nOsawa. This paper generalizes their results. Moreover, it considers discrete-time queueing networks with some reversible nodes. The paper then obtains the product-form solution for these networks.
