1. In a system for allocating access to a demand-shared facility among a plurality of units wherein each unit has an assigned unique n digit priority number for determining facility access during concurrent requests by said units, said system comprising; an arbitration bus interconnecting all of said units, means in each of said units for requesting access to said demand-shared facility, a plurality of multistate logic devices in each of said units, control means for selectively and combinationally switching said logic devices from a first to a second state in each of said units under control of specified parameters representing the current dynamic state of said units, a register in each unit means for forming a dynamic priority number for each of said units by applying the outputs of said logic devices as parameter digits to the more significant digit positions of said unit's register and by applying the digits of said assigned priority number to the lesser significant digit positions of said unit's register, a mask bus interconnecting said units, means for applying a mask signal at selected times to said mask bus, means in each of said units currently requesting access to said demand-shared facility for concurrently superimposing the corresponding digits of the associated dynamic priority number onto said arbitration bus sequentially digit by digit, means in each requesting unit responsive so long as said mask signal is extant on said mask bus for disabling said superimposing means so that no parameter digits of a requesting unit are superimposed on said arbitration bus, means for comparing the digit values on said arbitration bus with the corresponding digit values applied by each of said requesting units, and means for removing from facility access contention a requesting one of said units upon the detection of a prescribed comparison result between a bus digit value and the corresponding digit value applied by said unit, said disabling means also being effective so that said preference for facility access between said requesting units is determined by any parameter bits applied to said bus and by the applied bits of said assigned priority numbers of said requesting units.