Processor related communications

A compute device can access local or remote accelerator devices for use in processing a received packet. The received packet can be processed by any combination of local accelerator devices and remote accelerator devices. In some cases, the received packet can be encapsulated in an encapsulating packet and sent to a remote accelerator device for processing. The encapsulating packet can indicate a priority level for processing the received packet and its associated processing task. The priority level can override a priority level that would otherwise be assigned to the received packet and its associated processing task. The remote accelerator device can specify a fullness of an input queue to the compute device. Other information can be conveyed by packets transmitted between and among compute devices and remote accelerator devices to assist in determining an accelerator to use or other uses.