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A primary design objective for user-facing services for cloud and edge computing is to maximize query throughput, while meeting query tail latency Service Level Objectives (SLOs) for individual queries. Unfortunately, the existing solutions fall short of achieving this design objective, which we argue, is largely attributed to the fact that they fail to take the query fanout explicitly into account. In this paper, we propose TailGuard based on a Tail-latency-SLO-and-Fanout-aware Earliest-Deadline-First Queuing policy (TF-EDFQ) for task queuing at individual task servers the query tasks are fanned out to. With the task pre-dequeuing time deadline for each task being derived based on both query tail latency SLO and query fanout, TailGuard takes an important first step towards achieving the design objective. A query admission control scheme is also developed to provide tail latency SLO guarantee in the presence of resource shortages. TailGuard is evaluated against First-In-First-Out (FIFO) task queuing, task PRIority Queuing (PRIQ) and Tail-latency-SLO-aware EDFQ (T-EDFQ) policies by both simulation and testing in the Amazon EC2 cloud. It is driven by three types of applications in the Tailbench benchmark suite, featuring web search, in-memory key-value store, and transactional database applications. The results demonstrate that TailGuard can significantly improve resource utilization (e.g., up to 80% compared to FIFO), while also meeting the targeted tail latency SLOs, as compared with the other three policies. TailGuard is also implemented and tested in a highly heterogeneous Sensing-as-a-Service testbed for a data sensing service, demonstrating performance gains of up to 33% . These results are consistent with both the simulation and Amazon EC2 results.