This paper modelled traffic as a time-delayed feedback control system.

The paper assumed a simple model of two networking devices, whose input is and respectively. The input will influent the queue length and . Their relationship is modeled as a feedback system: Queue length variable and increases the input and respectively (with time delay ) because when a queue is too long, rerouting will be triggered. Then the system can be modelled as

The block diagram is presented in the paper.

The paper then set to zero and eliminate in the above equation, then it deduced the notation of and deduced that the rerouting network is stable iff . By setting to be , i.e. assume queue length is the integration, it found the bound for (amplifying factor of the feedback signal) to stabilize the network.

Bibliographic data

@article{
   title = "Stability of Traffic Patterns in Broadband Networks",
   author = "R. M. Goodman and B. E. Ambrose",
   journal = "Journal of Network and Systems Management, Special Issue on Routing in Broadband Networks",
   howpublished = "J Network Sys Management",
   volume = "3",
   number = "4",
   pages = "371--380",
   month = "December",
   year = "1995",
}