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

H. T. Papadopoulos, C. Heavey, M. E.J. O'Kelly

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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 Pi distributed with Pi, 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.

Original languageEnglish
Pages (from-to)317-335
Number of pages19
JournalComputers in Industry
Issue number4
Publication statusPublished - Mar 1990


  • Block-triagonal matrices
  • Erlang type P distribution
  • Finite buffers
  • Iterative SOR method
  • Large sparse matrices
  • Multistation production lines
  • Quasi-birth-death process

ASJC Scopus subject areas

  • Computer Science(all)
  • Engineering(all)

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