On Bistable Region of Slotted-ALOHA Systems with Delay Constraints

Bistable behavior of slotted ALOHA systems has been extensively investigated. It is proved that bistable region can be eliminated by limiting the number of allowable transmission attempts per packet to eight or less. In this paper, we investigate bistable behavior of slotted ALOHA systems with delay constraints in terms of the catastrophe theory. A lifetime of a packet is confined within D slots, that is, a packet will be discarded after timer of D time-slots expired, unless packet transmission succeeds. Letting r be the packet transmission probability in a slot, we indicate that there exists bistable region, if the product Dr is greater than approximately 8.30, and that the system can operate with the unique stable equilibrium point, if Dr is less than approximately 8.30.