Markovian analysis of production lines with Coxian-2 service times

This paper is concerned with the analysis of reliable production lines. The service times at each station of the line are assumed to follow the Coxian-2 distribution. Raw material arrives at the first station of the line which is assumed that is never empty. 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, for any number of stations K. This method allows one to obtain the exact solution of a sparse linear system by the use of the Gauss–Seidel method. From the solution of these systems the throughput rate of the production lines is calculated. However, this algorithm is not computationally efficient as it is restricted by the size of the problem. The main contribution of this paper is the study of the transition matrices of production lines with Coxian service times.