A recursive algorithm for generating the transition matrices of multistation series production lines

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

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

This paper is concerned with reliable multistation series production lines, where an operation is performed on each job by the single machine at each station and jobs for the first station arrive according to a Poisson distribution. The processing times of all the stations are exponentially distributed and no buffers are allowed between successive stations. The structure of the transition matrices of these specific types of production lines is examined and a one-stage recursive algorithm is provided for generating them. The transition matrices are block-structured and sparse and by applying the proposed algorithm, one can create the transition matrix of a K-station line from the (K-1)-station transition matrix. This process avoids the necessity of writing down explicitly all the feasible states and transitions of the model, which is tedious and time-consuming especially for long production lines (i.e. for K=12 stations, the number of states is 46, 368.

Original languageEnglish
Pages (from-to)227-240
Number of pages14
JournalComputers in Industry
Volume12
Issue number3
DOIs
Publication statusPublished - Jul 1989

Keywords

  • Block-triagonal matrices
  • Blocking phenomenon
  • Finite buffers
  • Matrix geometric form
  • Multistation production lines
  • Open queueing networks
  • Quasi-Birth-Death process
  • large sparse matrices

ASJC Scopus subject areas

  • Computer Science(all)
  • Engineering(all)

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