Analysis of a tandem queue with state-dependent general blocking: A GSMP perspective

Abstract

In this paper, we study a tandem queue where there is a finite number of buffer positions at each stage. The blocking scheme is general in the sense that it can model a number of classical blocking schemes, including communication, manufacturing and kanban blockings as special cases. The system considered here differs from the conventional system in two aspects: (1) departure of jobs from the system is determined by an external arrival process of another queue lying parallel to the tandem queue; (2) the control parameters of the blocking scheme are state-dependent in that they may change values depending on the state of the system. We model this system as a generalized semi-Markov process (GSMP), we study the structural properties of its scheme, and establish monotonicity and convexity properties of event times with respect to both the clock times and the integer blocking parameters. In particular, we demonstrate that the state-dependent scheme is “better”, in certain sense, than the corresponding static scheme. Our results also recover the structural properties previously established for the classical blockings.