A resource conflict resolution problem formulated in continuous time

Abstract

In many situations involving data transmission from diverse sources there can be conflict for a limited number of channels or other facilities. Uncoordinated attempts by several sources to use a single facility can result in collision, the destruction of all participants in the collision, meaning the loss of the transmission, and hence the need for re-transmission. An important problem concerns the development of workable procedures for alleviating the conflict and corresponding message delay problems. Often such problems are viewed as occurring in discrete time: slots of equal length occur in temporal succession, and each slot can handle just one packet of data at a time, if two or more packets try to use the same slot simultaneously, a collision occurs that somehow must be resolved. A recent paper analyzed a stack protocol for handling such a situation, but there are many other proposals. This report is concerned with some simple models for a single facility (channel), and for contention or conflict resolution. The models are formulated in a continuous-time manner: messages, or numbers of packets constituting messages, are long, meaning that they occupy many consecutive slots on the average if a single transmission is occurring. Additional keywords: Queueing theory; Congestion theory; ALOHA; Communications traffic