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In multi-server systems, selecting to which server to dispatch an arriving job is a key factor influencing system response time. One of the most widely studied policies is Join-the-Shortest-Queue (JSQ), which is known to minimize mean response time in certain settings [7]. Many variants on JSQ have been proposed, including JSQ-d, under which a job is dispatched to the shortest queue among d servers selected uniformly at random [3, 5]; Join-Idle-Queue (JIQ), under which the dispatcher knows which servers are idle but not the queue lengths of non-idle servers [2]; and others.
The vast majority of work analyzing JSQ and related policies makes a key assumption: that the system is homogeneous, meaning that all servers have the same speed. This assumption is inaccurate in most modern computer systems. Server heterogeneity can arise, e.g., when a server farm consists of several generations of hardware, or when many virtual machines contend for resources on the same physical machine. Unfortunately, the wealth of results about how best to dispatch in homogeneous systems does not translate well to heterogeneous systems. Policies like JSQ-d and JIQ, which can achieve near-optimal performance in homogeneous systems, can lead to unacceptably high response times and even instability in heterogeneous systems [4, 8].
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