A parallel priority queueing system with finite buffers

In this paper we pose and analyze a novel model of a priority queueing system that represents a conveyor model. What is novel in this model is that priority is designed to minimize the idleness of the system. Thus, we discussed a general parallel finite buffer multi-server priority queueing system with balking and reneging and analyze a two-station case of it. An algorithmic solution for the general two-station case and closed-form solutions for special cases of this model are given. We use block-matrix method to find distribution of the queue length, probability of the system idleness, probability of loss to the system, probability of stations being busy, and the first two moments. Numerical examples are given for comparison with Disney's model [R.L. Disney, Some multichannel queueing problems with order entry, J. Ind. Engng. 13 (1962) 46–48; R.L. Disney, D. Kögin, Queuing networks: a survey of their random processes, SIAM Rev. 27 (3) (1958) 335–400] and discussion of properties of the model.