We consider a discrete-time system comprising a first-come-first-served queue, a non-preemptive server, and a scheduler that governs the assignment of tasks in the queue to the server. The server has an availability state that indicates, at each instant, whether the server is busy working on a task or is available. In the latter case, if the queue is nonempty, then a task-assignment control policy implemented by the scheduler either assigns a new task to the server or allows it to rest. The server also has an integer-valued activity state that is non-increasing during rest periods, and is non-decreasing otherwise. An instantaneous service rate function ascribes to each possible value of the activity state a probability that the server can complete a task in one time step. For a typical instantaneous service rate function, the completion probability decreases (server performance worsens) as the activity state increases. The scheduler policy has access to the queue size and the entire state of the server. In this article, we study the problem of designing scheduler policies that stabilize the queue. We show that stability, whenever viable, can be achieved by a simple policy that bases its decisions on the availability state, a threshold applied to the activity state, and a flag that indicates when the queue is empty. The supremum of the service rates achievable by stabilizing policies can be determined by a finite search. Our results remain valid even when the instantaneous service rate function is not monotonic.
翻译:我们考虑的是一个离散时间系统, 由先到先到先到的队列、 非先发制人服务器, 以及管理向服务器的队列中任务指派的排程器组成。 服务器有一个可用状态, 显示服务器是否每时忙于执行某项任务或可用。 在后一种情况下, 如果排队不是空的, 则由调度员执行的任务分配控制政策, 或者向服务器指派新的任务或者允许它休息。 服务器还有一个整数值的活动状态, 它在休息期间没有增加, 并且没有停止。 即时服务率函数对活动的每一种可能值进行记录, 显示服务器在每时都有可能完成一项任务的可能性。 对于典型的即时速服务率功能, 完成概率会随着活动状态的上升而降低( 服务器性能恶化 ) 。 排队列政策可以访问到服务器的排队列大小和整个服务器状态。 在此篇文章中, 我们研究设计固定排队列的排队政策的问题。 我们显示, 只要可行, 只要可以应用一个简单的标准, 就可以通过一个简单的政策标准, 就可以通过一个可以实现一个稳定的服务率值, 标准,, 当一个可以显示, 当一个可稳定到一个稳定的服务级别政策在一条状态上, 当一个稳定的状态上, 当一个稳定的状态中, 当一个稳定的状态中, 当一个可以决定时, 当一个固定到一个固定到一个固定到一个固定的状态的状态, 当一个稳定的状态, 。