1. A hardware logic system for directing incoming processing data units, with such units referred to as packets, to instances of a set of locally hosted application programs referred to as the applications, the system including: at any given one of a set of processing systems, each of which hosts its assigned groups of instances of the applications, a hardware logic subsystem for producing, for each given one of the applications, (1) an expression of availability of instances hosted at the given processing system that are accepting packets with no destination instance specified, with such packets referred to as no-instance-specified NIS packets, and (2) an indication of which instances of the given application are accepting NIS packets; and at an inter-processing-system load balancer among a set of such load balancers, a hardware logic subsystem for: examining whether an incoming packet destined for a given one of the applications has a destination instance of that given application identified, and if so, directing the packet toward a processing system that hosts such an identified destination instance, while otherwise, selecting an appropriate processing system to which to forward the packet, at least in part based on the expressions, from individual processing systems of said set, of availability of instances for the given application for NIS packets, and directing the packet to a such selected processing system; and at a second-stage load balancer specific to the processing system to which the packet was directed to by the inter-processing-system load balancer, a hardware logic subsystem for examining whether the packet has an instance of its destination application identified, and if so, directing the packet toward a processing resource associated with such an identified destination instance, while otherwise, determining an appropriate instance of said destination application among the group of instances of that application hosted on the processing system, at least in part based on said indication of which instances of said destination application are accepting NIS packets, and directing the packet toward a processing resource associated with such determined instance of that application.