Matrix-analytic solutions in production lines without buffers

•Exact matrix-analytic method for multistation production lines without buffer.•Service periods have non-identical matrix-based phase-type distributions.•Generate distribution functions of holding, idle, blocking periods at each station.•Formula for distribution function of interdeparture period of finished products.•Accommodate multi products and certain station's ‘breakdown-repair’ mechanism. An exact analysis of multistation production lines in which the service periods at all stations follow a matrix-based continuous phase-type (PH) distribution is proposed. The approach uses a holding period model for production lines without buffers, and it is shown that the PH distribution satisfies closure properties in this model. Accordingly, due to the production line mechanism, the model contains random variables, such as the holding, blocking, and starving/idle periods at each station, which also follow PH distributions. Utilizing these properties, an algorithm for generating the distribution functions of these random variables, instead of only calculating the mean values, is derived, and it includes the distribution function of the production cycle. Numerical results for several numbers of stations and service period distributions are presented.