A Common Model for the Approximate Analysis of Tandem Queueing Systems With Blocking

This work proposes a common model that unifies several approximate methods for the analysis of tandem queueing systems with blocking. Two abstract functions are introduced to characterize the relationship between starvation and blockage in neighboring machines. Using the functions, the equilibrium equations are determined, and a general procedure is developed to solve them. The sufficient conditions for the existence and uniqueness of a solution are obtained. More generally, the proposed model leads to the concept of a bidirectional cascade system, in which each subsystem has both forward and backward inputs and forward and backward outputs. Finally, the theory of the common model is applied to specific systems to demonstrate its applicability.