ON THE STABILITY OF 5 TYPES OF SLOTTED ALOHA SYSTEMS WITH CAPTURE ANDMULTIPLE PACKET RECEPTION

stability of slotted ALOHA systems with various types of capture pheno mena and multiple packet reception capability is discussed in conjunct ion with the cusp catastrophe. The slotted ALOHA systems considered ar e classified into; 1) single packet reception with geometric capture, 2) independent multiple packet reception with geometric capture, 3) si ngle packet reception with M-out-of-N capture (M less than or equal to N), 4) multiple packet reception with M-out-of-N capture, and 5) sing le packet reception with perfect capture. First, general expressions f or the cusp points and the bifurcation sets are derived. Then, we pres ent explicit formula for the stability of slotted ALOHA systems for th e five types of capture and multi-packet reception capability and demo nstrate how the bistable behavior is mitigated due to capture effect a nd multi-packet reception capability.