Heavy Traffic Characteristics of a Circular Data Network

Traffic behavior in the Pierce loop for data transmission is studied under assumptions of heavy loading. A deterministic mathematical model for describing traffic flows is developed and analyzed. The mathematical problem is of a linear complementarity type which has not been dealt with in the literature of mathematical programming. An effective procedure, the load-and-shift algorithm, for determining traffic flows is proposed. The procedure yields all feasible solutions for traffic flows and reveals the possibility of stations grouping into dominating classes and preventing other stations from using the system. This property, which can be eliminated by exercising appropriate control, also may affect the stochastic behavior of the system when heavy traffic conditions do not prevail and therefore deserves careful investigation. The paper includes two numerical examples illustrating use of the load-and-shift algorithm and numerical results from a simulation showing some of the effects of dominating classes when heavy traffic conditions do not prevail.