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Federated learning (FL) over mobile devices has fostered numerous intriguing applications/services, many of which are delay-sensitive. In this paper, we propose a service delay efficient FL (SDEFL) scheme over mobile devices. Unlike traditional communication efficient FL, which regards wireless communications as the bottleneck, we find that under many situations, the local computing delay is comparable to the communication delay during the FL training process, given the development of high-speed wireless transmission techniques. Thus, the service delay in FL should be computing delay + communication delay over training rounds. To minimize the service delay of FL, simply reducing local computing/communication delay independently is not enough. The delay trade-off between local computing and wireless communications must be considered. Besides, we empirically study the impacts of local computing control and compression strategies (i.e., the number of local updates, weight quantization, and gradient quantization) on computing, communication and service delays. Based on those trade-off observation and empirical studies, we develop an optimization scheme to minimize the service delay of FL over heterogeneous devices. We establish testbeds and conduct extensive emulations/experiments to verify our theoretical analysis. The results show that SDEFL reduces notable service delay with a small accuracy drop compared to peer designs.