A system comprising: a first device comprising a processor and a Wi-Fi module ; and a remote processing system coupled to the first device via a wireless connection across a network , wherein the first device is configured to switch, during operation, between: a first operating mode in which the processor performs packet processing for the wireless connection on behalf of the first device , and a second operating mode in which the processor is in a reduced power state and the Wi-Fi module performs packet processing for the wireless connection on behalf of the first device , characterised in that the system is configured such that: when the first device switches from the first operating mode to the second operating mode , a then-current sequence number associated with packets transmitted over the wireless connection is transferred from a computer-based memory in the first device to the Wi-Fi module, or when the first device switches from the second operating mode to the first operating mode , a then-current sequence number associated with packets transmitted over the wireless connection is transferred from the Wi-Fi module to an operating system for the processor. a first device comprising a processor and a Wi-Fi module ; and a remote processing system coupled to the first device via a wireless connection across a network , wherein the first device is configured to switch, during operation, between: a first operating mode in which the processor performs packet processing for the wireless connection on behalf of the first device , and a second operating mode in which the processor is in a reduced power state and the Wi-Fi module performs packet processing for the wireless connection on behalf of the first device , a first operating mode in which the processor performs packet processing for the wireless connection on behalf of the first device , and a second operating mode in which the processor is in a reduced power state and the Wi-Fi module performs packet processing for the wireless connection on behalf of the first device , characterised in that the system is configured such that: when the first device switches from the first operating mode to the second operating mode , a then-current sequence number associated with packets transmitted over the wireless connection is transferred from a computer-based memory in the first device to the Wi-Fi module, or when the first device switches from the second operating mode to the first operating mode , a then-current sequence number associated with packets transmitted over the wireless connection is transferred from the Wi-Fi module to an operating system for the processor. when the first device switches from the first operating mode to the second operating mode , a then-current sequence number associated with packets transmitted over the wireless connection is transferred from a computer-based memory in the first device to the Wi-Fi module, or when the first device switches from the second operating mode to the first operating mode , a then-current sequence number associated with packets transmitted over the wireless connection is transferred from the Wi-Fi module to an operating system for the processor. <EOS>