传递和交换交换密钥
Pass-and-Swap Queues
摘要：
由Berezner、Kriel和Krzesinski在1995年引入的顺序无关（OI）队列，通过允许复杂的类相关服务率，扩展了已知具有乘积形式平稳分布的多类队列家族。本文进一步扩大了这个家庭通过引入通行证和交换（P&S）队列，扩展OI队列，在服务完成后，完成服务的客户不一定是一个离开系统。更准确地说，我们补充OI队列模型与无向图的客户类，我们称之为交换图，这样，有两个类之间的边缘，如果这些类的客户可以相互交换。当客户完成服务时，它会越过队列中剩余的客户，直到它找到一个可以交换位置的客户，也就是说，其类是图中邻居的客户。然后，被逐出的顾客会换到下一个顾客的位置，以此类推，直到一个顾客再也找不到另一个顾客来交换，这个顾客就离开了队列。在证明了P&S队列具有乘积形式的平稳分布后，我们得到了P&S队列（开放网络）稳定的充要条件，该条件也适用于OI队列。然后，我们研究了P&S排队闭网络的不可约性，并导出了相应的乘积型平稳分布。最后，我们证明了P&S队列的封闭网络可以应用于描述新的和现有的负载分配和调度协议的机器集群中的工作分配约束的动态。
英文摘要：
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 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.
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