The throughput rate of multistation unreliable production lines

This paper is concerned with unreliable multistation series production lines. The first station is never starved and the last station is never blocked. 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 nonidentical capacities are allowed between successive stations. A station maybe reliable or unreliable. Time to failure is exponentially distributed and repair times are Erlang type R_i distributed with R_i allowed to vary, at each station. In this paper a methodology for generating the associated set of linear equations is presented. These set of linear equations are solved via the use of the Successive Over-Relaxation (SOR) method with a dynamically adjusted relaxation factor as used by Seelen [25]. Referring to the throughput rate of the production lines, many numerical cases are solved and documented. These exact results are of use for comparison purposes against approximate results which exist in the literature. Although many new results are obtained, the size of the system which can be solved is inherently limited by the technique being used. This is due to the curse of dimensionality.