A method comprising: exchanging fabric packets selectively over a plurality of virtual channels between a plurality of processing elements interconnected as a fabric, each fabric packet comprising a virtual channel specifier identifying one of the virtual channels, each processing element comprising a fabric router and a compute element enabled to perform dataflow-based and instruction-based processing associated with each of the virtual channels, each compute element comprising a memory enabled to store one or more associated instructions for each of the virtual channels and further enabled to provide at least one of the one or more associated instructions to the compute element for execution; in each processing element, managing a local respective virtual queue for each of the virtual channels; in each processing element and in accordance with predetermined criteria, picking ones of the virtual channels for associated processing, the predetermined criteria comprising selecting from a pool of local currently active ones of the virtual channels; in a first processing element of the processing elements, performing an activate operation specifying one of the virtual channels; in the first processing element and responsive to the performing, locally activating the specified virtual channel; in the first processing element and subsequent to the locally activating, locally picking the specified virtual channel in accordance with the predetermined criteria; and in the first processing element and responsive to the locally picking, initiating the associated processing of the specified virtual channel, the associated processing of the specified virtual channel comprising the first processing element obtaining and executing the at least one of the one or more of the associated instructions from the memory of the compute element of the first processing element. exchanging fabric packets selectively over a plurality of virtual channels between a plurality of processing elements interconnected as a fabric, each fabric packet comprising a virtual channel specifier identifying one of the virtual channels, each processing element comprising a fabric router and a compute element enabled to perform dataflow-based and instruction-based processing associated with each of the virtual channels, each compute element comprising a memory enabled to store one or more associated instructions for each of the virtual channels and further enabled to provide at least one of the one or more associated instructions to the compute element for execution; in each processing element, managing a local respective virtual queue for each of the virtual channels; in each processing element and in accordance with predetermined criteria, picking ones of the virtual channels for associated processing, the predetermined criteria comprising selecting from a pool of local currently active ones of the virtual channels; in a first processing element of the processing elements, performing an activate operation specifying one of the virtual channels; in the first processing element and responsive to the performing, locally activating the specified virtual channel; in the first processing element and subsequent to the locally activating, locally picking the specified virtual channel in accordance with the predetermined criteria; and in the first processing element and responsive to the locally picking, initiating the associated processing of the specified virtual channel, the associated processing of the specified virtual channel comprising the first processing element obtaining and executing the at least one of the one or more of the associated instructions from the memory of the compute element of the first processing element.