Mobile devices frequently move with different velocities. Task delegation to remote cloud servers becomes critical when the requesting device changes its location. The communication with the remote cloud server might be lost, and the user does not receive the result. To solve this problem, two analytical models are provided in this article. In the first solution, we propose an approach where the mobile device uses remote cloud servers for executing task. When the user changes location, the mobile device looses connection with the cloud instance. Once the result is ready, the cloud server pushes the result back to the device via push notification message when the device reconnects with the network. However, the mobile device can also get the result by serializing session information. In the second solution, the mobile device offloads code into cloudlets. When the mobile device changes location, virtual machine live migration happens. The present state of the instance is transferred from the previous cloudlet to the new cloudlet, where the offloading process resumes execution. It is observed that the proposed task delegation and code-offloading models reduce the power consumptions, respectively, by 30–63% and 61–78% approximately than the existing mobility-aware approach. Experimental results are obtained using mobile device with various velocities inside and outside the university building.