Unintrusive communication of status in a packet network in heavy traffic

We consider a packet switched network in the situation where communication resources are used close to capacity. Such heavy traffic may seem to present a dilemma. On one hand, at each node, the usefulness of status information about queues at other nodes is manifest. On the other hand, since the limitation of transmission resources causes backup, heavy load seems to be the worst situation in which to expend still more communication resources to convey status information. Under extremely general assumptions on inter-arrivals and services, a scaling appropriate for queueing processes in networks under heavy traffic has been established. Under these assumptions, we demonstrate that the status of the entire network can be communicated throughout the network, perfectly, in real time, without influencing the scaled queueing process. So, within a precise mathematical setting, we see that there is no dilemma: status can be conveyed at a negligible cost in a network operating at heavy load. Most of today's computer networks are designed for light-to-moderate loading. Yet heavy traffic analysis is growing in relevance, as is explained. A brief introduction to the subject of convergence of queueing systems is included.