We introduce a new scheduling problem in distributed computing that we call the DSMS problem. We are given a set of $k \geq 1$ mobile identical servers that are initially hosted by some processors of the given network. Further, we are given a set of requests that are issued by the processors possibly at any time in an online fashion, and the servers must serve them. A request must be scheduled before the request is served. The delay for scheduling a request is the time taken since the request is issued until it is scheduled. The goal is to minimize the average delay. Navigating mobile servers in a large-scale distributed system needs a scalable location service. We devise the distributed GNN protocol, a novel linked-reversal-based protocol for the DSMS problem that works on overlay trees. We prove that GNN is a starvation-free protocol that correctly integrates locating the servers and synchronizing the concurrent access to the servers despite asynchrony. Further, we analyze the GNN protocol for one-shot executions where all requests are simultaneously issued. We show that when running the GNN protocol on top of a special family of tree topologies---known as hierarchically well-separated trees (HSTs)---we obtain a randomized distributed protocol with an expected competitive ratio of $O(\log n)$ on general network topologies for the DSMS problem where $n$ is the number of processors in the given network. From a technical point of view, the main result of our paper shows that the GNN protocol optimally solves the DSMS problem on HSTs for one-shot executions. Our results hold even if communication is asynchronous.
翻译:我们在分布式计算中引入了一个新的调度问题, 我们称之为 DSMS 问题。 我们得到的是一组 $k\ geq 1$ 移动式相同服务器, 最初由给定网络的某些处理者主持。 此外, 我们得到的是处理者可能在任何时候以在线方式发出的一系列请求, 服务器必须服务这些请求。 请求在满足前必须排期。 请求的排期是发出请求的时间, 目标是尽可能减少平均延迟。 在大型分布式系统中的移动服务器导航需要一个可缩放的位置服务。 我们设计了已分发的 GNNN 协议, 这是一套新的基于链接的基于DSMS 问题的协议。 我们证明, GNNN是一个没有饥饿的协议, 正确整合服务器的位置, 并同步同时访问服务器的时间, 尽管请求被排在排期之前。 此外, 我们分析GNNN 协议, 在所有请求同时发出的一次处决中, 。 我们显示, 在以GNNW$$为主网络端端的 G- sal- weboral 协议中, 我们的S 将一个最高级网络的S 级协议显示我们最高级的S 的S- horal- seral- seral- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- salviolviolver mag- sal- sal- salg- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- masmal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal-s- sal- sal-s