The analysis of a discrete-time queuing system with batch arrival

The paper considered the discrete-time queueing system with batch arrival on the basis of the classical queueing system. On the assumption that a single server provides service to the customers in the system, and the batch arrival of the customers submits to the geometrical distribution, the number of the customers in a batch arrival is random variable and has the generalized distribute function, and the service time also depends on the geometrical distribution; using the method of embedded Markov chain, the distribution functions of the queue length and the waiting queue length were described. Then, the waiting time of the queueing system was characterized and the distribution of the busy time was obtained. These conclusions are similar to that of the classical queueing system.