The fog/edge computing paradigm is increasingly being adopted to support a range of latency-sensitive IoT services due to its ability to assure the latency requirements of these services while supporting the elastic properties of cloud computing. IoT services that cater to user mobility, however, face a number of challenges in this context. First, since user mobility can incur wireless connectivity issues, executing these services entirely on edge resources, such as smartphones, will result in a rapid drain in the battery charge. In contrast, executing these services entirely on fog resources, such as cloudlets or micro data centers, will incur higher communication costs and increased latencies in the face of fluctuating wireless connectivity and signal strength. Second, a high degree of multi-tenancy on fog resources involving different IoT services can lead to performance interference issues due to resource contention. In order to address these challenges, this paper describes URMILA, which makes dynamic resource management decisions to achieve effective trade-offs between using the fog and edge resources yet ensuring that the latency requirements of the IoT services are met. We evaluate URMILAtextquoterights capabilities in the context of a real-world use case on an emulated but realistic IoT testbed.