Analysis of a two-level queueing production system with finite dedicated buffers

This paper analyzes a two-level queueing production system with finite dedicated buffers under exponential assumptions. We consider n types of arriving jobs which upon completion of service at the first-level workstation proceed to the second level and join their dedicated workstations that are laid out in parallel. Blocking occurs when the flow of job i through the first-level queue is momentarily stopped owing to the capacity limitation of its second-level dedicated queue having been reached. Approximate results are derived for the blocking probabilities and the mean effective service time in the first-level workstation.