Analysis of a M super(X)/G(a,b)/1 queueing system with vacation interruption

In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least 'a' customers waiting for service say xi , he serves a batch of min ( xi , b) customers, where b greater than or equal to a. On the other hand, if the queue length is at the most 'a-1', the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches 'a', during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches 'a'. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.