We consider a system with several job types and two parallel server pools. Within the pools the servers are homogeneous, but across pools possibly not in the sense that the service speed of a job may depend on its type as well as the server pool. Immediately upon arrival, jobs are assigned to a server pool. This could be based on (partial) knowledge of their type, but such knowledge might not be available. Information about the job type can however be obtained while the job is in service; as the service progresses, the likelihood that the service speed of this job type is low increases, creating an incentive to execute the job on different, possibly faster, server(s). Two policies are considered: reroute the job to the other server pool, or replicate it there. We determine the effective load per server under both the rerouting and replication policy for completely unknown as well as partly known job types. We also examine the impact of these policies on the stability bound, and find that the uncertainty in job types may significantly degrade the performance. For (highly) unbalanced service speeds full replication achieves the largest stability bound while for (nearly) balanced service speeds no replication maximizes the stability bound. Finally, we discuss how the use of threshold-based policies can help improve the expected latency for completely or partly unknown job types.

中文翻译：

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基于阈值的重新路由和复制，用于解决作业-服务器关联关系

我们考虑一个具有多种作业类型和两个并行服务器池的系统。在池中，服务器是同构的，但跨池可能不是因为作业的服务速度可能取决于其类型以及服务器池。到达后，作业会立即分配到服务器池。这可能基于其类型的（部分）知识，但此类知识可能不可用。但是，可以在作业服务期间获取有关作业类型的信息；随着服务的进展，这种作业类型的服务速度较低的可能性会增加，从而鼓励在不同的、可能更快的服务器上执行作业。考虑了两种策略：将作业重新路由到另一个服务器池，或者在那里复制它。对于完全未知和部分已知的作业类型，我们在重新路由和复制策略下确定每台服务器的有效负载。我们还检查了这些政策对稳定性界限的影响，并发现工作类型的不确定性可能会显着降低性能。对于（高度）不平衡的服务速度，完整复制实现了最大的稳定性界限，而对于（几乎）平衡的服务速度，没有复制可以最大化稳定性界限。最后，我们讨论了使用基于阈值的策略如何帮助改善完全或部分未知作业类型的预期延迟。对于（高度）不平衡的服务速度，完全复制实现了最大的稳定性界限，而对于（几乎）平衡的服务速度，没有复制可以最大化稳定性界限。最后，我们讨论了使用基于阈值的策略如何帮助改善完全或部分未知作业类型的预期延迟。对于（高度）不平衡的服务速度，完全复制实现了最大的稳定性界限，而对于（几乎）平衡的服务速度，没有复制可以最大化稳定性界限。最后，我们讨论了使用基于阈值的策略如何帮助改善完全或部分未知作业类型的预期延迟。