An arrangement for use with a plurality of runnable processes that send messages to each other, and means for sending a message from a sending process on a sending one of the processors to a destination process on a different destination one of the processors, each process having a priority selected from a plurality of different priorities, the arrangement comprising;
- a plurality of storage means each corresponding to a different priority of the plurality of priorities, for storing messages;
- first means for running a selected process;
- and
- second means responsive to a message sent by a sending process on a sending one of a plurality of processors to a destination process on a different destination one of the plurality of processors, for effecting delivery of the message to the destination process if the priority of the sending process is greater than the priority of a process which is presently selected to run on the destination processor, and for storing the message in one of the storage means corresponding to the priority of the sending process if the priority of the sending process is lower than the priority of the process which is presently selected to run on the destination processor,
- the second means further responsive to a change of process which is presently selected to run on the destination processor from one process to another process, for effecting delivery to destination process on the destination processor of messages stored in storage means corresponding to priorities at least as high as the priority of the other process.