We consider a discrete-time G e o / 1 ∞ system in which customer that finishes its first essential service may opt to abandon the system, receive second optional or go at head of queue order another service. study Markov chain underlying considered queueing and ergodicity condition. Using generating function approach distribution number customers as well their respective means are given. The bu...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discreteMarkovian service process. The server terminates service whenever the system becomes empty, and recommencesservice as soon as the number of waiting customers in the queue is N. We obtain the system-length distributionsat pre-arrival and arbitrary epochs using the supplementary...