We present a framework to analyse the latency budget in wireless systems with Mobile Edge Computing (MEC). Our focus is on teleoperation and telerobotics, as use cases that are representative of mission-critical uplink-intensive IoT systems with requirements on low latency and high reliability. The study is motivated by a general question: What is the optimal compression strategy in reliability and latency constrained systems? We address this question by studying the latency of an uplink connection from a multi-sensor IoT device to the base station. This is a critical link tasked with a timely and reliable transfer of potentially significant amount of data from the multitude of sensors. We introduce a comprehensive model for the latency budget, incorporating data compression and data transmission. The uplink latency is a random variable whose distribution depends on the computational capabilities of the device and on the properties of the wireless link. We formulate two optimization problems corresponding to two transmission strategies: (1) Outage-constrained, and (2) Latency-constrained. We derive the optimal system parameters under a reliability criterion. We show that the obtained results are superior compared to the ones based on the optimization of the expected latency.