Optimal order of servers in a tandem queue with general blocking

Abstract

In this paper, using the bivariate characterizations of thereversed hazard rate ordering and thestochastic ordering, and thepairwise interchange argument, we characterize the “best” strategy for allocating servers in a tandem system controlled using thegeneral blocking or theproduction authorization card (PAC) schemes. We show that when there is no buffer space between the first (resp. the last) two servers, it is “better” to allocate the “slower” server to the first (resp. the last) stage. The result extends previous results to systems where the number of buffers at the interior stages may be greater than one and the blocking mechanism may be more general. In particular, our results apply to manufacturing blocking, kanban blocking, a variation of kanban blocking, and the integral control scheme previously studied in the literature.