Throughput rate of multistation reliable production lines with inter station buffers (II) Erlang case

This paper is concerned with reliable multistation series production lines. Items arrive at the first station according to a Poisson distribution with an operation performed on each item by the single machine at each station. The processing times at each station i is Erlang type P_i distributed with P_i, the number of phases, allowed to vary for each station. Buffers of non-identical capacities are allowed between successive stations. The structure of the transition matrices of these specific type of production lines is examined and a recursive algorithm is developed for generating them. The transition matrices are block-structured and very sparse and by applying the proposed algorithm, one can create the transition matrix of a K-station line for any K. This process allows one to obtain the exact solution of the large sparse linear systems via the use of the Successive Overrelaxation (SOR) method with a dynamically adjusted factor. Referring to the throughput rate of the production lines, new numerical results are given.