Stationary blocking probability in multi-server finite queuing system with ordered entry and poisson arrivals

Analysis of performance characteristics of industry conveyor systems is a well-known research topic, which can be treated from queueing systems perspective. This paper is devoted to the analysis of the conveyor model, which is represented by markovian heterogeneous N-server queueing system with ordered entry (N ≥ 2). Servers are labelled (from 1 to N), each has a dedicated finite-capacity queue, and serve customers according to exponential distribution. Customer arrive at the system according to a Poisson flow and each customer, which finds more than one server idle, selects the queue with the lowest (server’s) number. After service completion customer leaves the system. If all the queues are full upon customer’s arrival, it is lost (no recirculation). It is shown that the stationary blocking probability can be found firstly by analyzing corresponding 2-server system, then finding inter-overflow time distributions and applying well-known results for finite-capacity GI/M/1 queue. Exact (not matrix-geometric) method for recursive computation of joint stationary probability in the 2-server system is given. © Springer International Publishing Switzerland 2016