Performance analysis of a versatile bulk-service queue with group-arrival, batch-size-dependent service time and queue-length-dependent vacation

Queueing systems with bulk-service and vacation policy have become one of the pivotal interest for the researchers due to their widespread application in food processing technology, manufacturing systems, power consumption in small cell base stations etc. This article analyzes a single server versatile bulk-service queueing system wherein the customers arrive according to a compound Poisson process and the service time is dependent on the batch size of undergoing service. Moreover, single and multiple vacation policies have been incorporated along with queue-length-dependent vacation. After providing the steady-state system equations, the bivariate probability generating function of queue and server content distribution together has been derived at departure epoch. After the evaluation of the unknown probabilities, complete joint distributions have been extracted in terms of roots of the denominator of the bivariate probability generating function. The discussed procedure and the reported results have been depicted through some numerical examples for different service and vacation time distributions. Some significant observation about the model has been sketched graphically.