Order-independent (OI) queues, introduced by Berezner et al. (Queueing Syst 19(4):345–359, 1995), expanded the family of multi-class queues that are known to have a product-form stationary distribution by allowing for intricate class-dependent service rates. This paper further broadens this family by introducing pass-and-swap (P&S) queues, an extension of OI queues where, upon a service completion, the customer that completes service is not necessarily the one that leaves the system. More precisely, we supplement the OI queue model with an undirected graph on the customer classes, which we call a swapping graph, such that there is an edge between two classes if customers of these classes can be swapped with one another. When a customer completes service, it passes over customers in the remainder of the queue until it finds a customer it can swap positions with, that is, a customer whose class is a neighbor in the graph. In its turn, the customer that is ejected from its position takes the position of the next customer it can be swapped with, and so on. This is repeated until a customer can no longer find another customer to be swapped with; this customer is the one that leaves the queue. After proving that P&S queues have a product-form stationary distribution, we derive a necessary and sufficient stability condition for (open networks of) P&S queues that also applies to OI queues. We then study irreducibility properties of closed networks of P&S queues and derive the corresponding product-form stationary distribution. Lastly, we demonstrate that closed networks of P&S queues can be applied to describe the dynamics of new and existing load-distribution and scheduling protocols in clusters of machines in which jobs have assignment constraints.

Berezner等人介绍的顺序无关（OI）队列。（Queueing Syst 19（4）：345-359，1995），扩展了多类队列的族，该类通过允许复杂的类相关服务费率而具有产品形式的固定分布。本文通过引入传递和交换（P＆S）队列（一种OI队列的扩展）进一步扩展了这一家族，在OI队列中，完成一项服务后，完成服务的客户不一定是离开系统的客户。更确切地说，我们在OI队列模型上为客户类添加了无向图，我们将其称为交换图，这样，如果可以交换这些类的客户，则两个类之间会有优势彼此之间。当客户完成服务时，它将在其余队列中跳过客户，直到找到可以与之交换职位的客户，即，其类是图中的邻居的客户。反过来，从其头寸中退出的客户将成为可以与其交换的下一个客户的头寸，依此类推。重复此过程，直到一个客户不再找到要交换的其他客户为止；该客户是离开队列的客户。在证明P＆S队列具有产品形式的平稳分布之后，我们推导了P＆S队列（的开放网络）的必要和充分的稳定性条件，该条件也适用于OI队列。然后，我们研究P＆S队列的封闭网络的不可约性，并推导相应的产品形式平稳分布。最后，