Fundamental Behaviors in Hybrid Deterministic Flow Lines With Applications

Since the mid-1960s, it has been known that regular or deterministic flow lines (DFLs) with an arbitrary arrival process possess three essential behaviors: 1) a customer exit time recursion; 2) a server reordering principle; and 3) a delay equivalence with prototype queueing systems. Even though these three fundamental behaviors were discovered decades ago, analogous results for hybrid DFLs (HDFLs)--possessing multiple servers for each stage--have not been unearthed. In this article, we prove the existence of a recursion for customer exit times in HDFLs. This result leads naturally to a server reordering principle. Furthermore, we identify specific conditions under which the total delay faced by a customer in an HDFL is equivalent to that in a G/D/c queue. Exploiting these results, we numerically determine the proportion of HDFL systems with a delay equivalent, study the computational burdens required for HDFL simulation, and assess the performance of approximations for HDFL systems. We hope these newly identified behaviors will lead to improved approximation methods and optimization models for use in modern automated manufacturing systems.