Analyzing state-dependent arrival in GI/BMSP/1/∞ queues

We consider an infinite-buffer single-server queue with renewal input. The service to the queueing system is provided in batches of random size, according to a batch Markovian service process (BMSP). The queue length distribution of the number of customers in the system at pre-arrival and arbitrary epochs has been obtained along with some important performance measures, such as the mean number of customers in the system and the mean system sojourn time of a customer. Secondly, we study a similar queueing system with queue-length-dependent inter-arrival times and obtain the above-mentioned state probabilities and performance measures. These queueing models have potential applications in the areas of computer networks, telecommunication systems, manufacturing systems, etc.