A discrete-time batch transmission channel with random serving capacity under batch-size-dependent service:

Discrete-time queues have increasingly diverse spectrum of applications in the modern packet-basedcommunication systems. Due to the wide range of applicability of such queues, we analyze a discrete-time queue with group-arrival and batch-service, where transmission time depends on the batch-size. The arrival occurs according tothe batch Bernoulli process and service is provided according to the random serving capacity rule. First, we obtain the bivariate probability generating function of the joint distribution of queue and server content at post transmission epoch. After the determination of unknown probabilities, the complete joint distribution has been extracted. We also acquire the probability distribution at random and pre-arrival epochs. An approximation of the tail distribution is also discussed so that it will be useful to improve the cell loss ratio. Some assorted numerical examples are incorporated to validate the analytic procedure and results.