Cloud offloading has recently attracted a substantial amount of attention from both industry and academia. This new generation of service, beyond conventional task scheduling and management, utilizes the abundant computation capacity from the public clouds and takes it as a part of external resource on the mobile devices. In this paper, we find that the cloud offloading can potentially increase the running latency of the offloaded tasks. Our measurement shows that the cloud offloading systems, such as Gaikai, can introduce up to 400ms communication latency between the customers and the remote offloading servers. This creates a severe bottleneck to offload the delay sensitive tasks. To mitigate such a challenge, we suggest Cloud Offloading on Customer-Provided Resources, which utilizes the local resources of the customers, such as their home PCs, to minimize the latency during the task offloading. We discuss the framework design based on our commercial system SpotCloud and propose a travel-aware protocol to further address the latency problems when the customers are traveling far from their home PCs. Our model analysis and trace-based simulation indicate that the task execution latency can be reduced by 60% when using the customer-provided offloading service. It is reasonable to believe that such a framework can serve as a useful complement to the conventional cloud offloading on pubic clouds.