Line Reversibility of Tandem Queues with General Blocking

We extend the "line reversibility" property to a serial production system controlled using the "general blocking" scheme. The control mechanism is characterized by three vectors of integer parameters (a, b, k) which are, respectively, control parameters for the number of raw jobs, finished jobs, and buffer positions at each stage. We establish conditions under which the time to process a given set of jobs in a system does not change when the control parameters are in the reversed order. For cases where reversibility does not hold, we introduce a more restrictive from reversibility---referred to as "semi-reversibility"---and establish conditions under which the property holds. Our results imply reversibility of the kanban system and provide an alternative proof for previous results established for the communication and the manufacturing blockings. Our approach is simple and readily extends to closed systems where the number of jobs in the system is kept constant. Finally, we show, via an example, that in general reversibility does not prevail for this blocking mechanism.