Recursive solution to a quorum queueing system

In this paper, a single-channel bulk service queueing system is considered. Given an accumulation level r, the server stops processing new customers whenever the queue falls below r and resumes service when the queue reaches level r. We have developed a recursive numerical procedure to find the steady-state system size probabilities. We assess accuracy and efficacy of the recursive procedure by comparing it to the exact solution procedure. Effectiveness and computation time of the recursive procedure are further assessed through comparison with other approximate solution procedures on a sample of 323 experimental problems.