Two-stage paced transfer line with buffer: geometric failures and repairs

A two-stage transfer line with a deterministic cycle time and a finite buffer is considered. Both stations have geometric distributed operation-dependent failures and repairs. This two-stage transfer line is the building block of the decomposition of longer lines as proposed by Gershwin. The system is described with a discrete Markov chain.

Two versions are available: in the complete version the transition probabilities are computed exactly (e.g. (1-a)(1-b)). In the simplified version the probabilities are computed based on the assumption that the product a·b may be neglected resulting in (1-a)(1-b) => (1-a-b). For more information, see table 3.1 in Askin/Standridge (1993).

The transition matrix is constructed and the stationary state probabilities are computed with the help of a general algorithm for the solution of systems of linear equations. Note that for this two-stage transfer line explicit solutions are also available.

Literature:

- Papadopoulos/Heavey/Browne (1993), Chapter 5.3.1
- Buzacott/Shanthikumar (1993), chapter 6.6
- Askin/Standridge (1993), chapter 3.3.1