Pass-and-swap queues

Order-independent (OI) queues, introduced by Berezner, Kriel, and Krzesinski in 1995, expanded the family of multi-class queues that are known to have a product-form stationary distribution allowing for intricate class-dependent service rates. This paper further broadens this introducing pass-and-swap (P&S) an extension OI where, upon completion, customer completes is not necessarily one leaves system. More precisely, we supplement queue model with undirected graph on classes, which call swapping graph, such there edge between two classes if customers these can be swapped another. When service, it passes over remainder until finds swap positions with, is, whose class neighbor graph. In its turn, ejected from position takes next so on. repeated no longer find another with; queue. After proving P&S distribution, derive necessary sufficient stability condition (open networks of) also applies queues. We then study irreducibility properties closed corresponding distribution. Lastly, demonstrate applied describe dynamics new existing load-distribution scheduling protocols clusters machines jobs assignment constraints.