On the Stability of Five Types of Slotted ALOHA Systems with Capture and Multiple Packet Reception

Katsumi SAKAKIBARA  Michiru HANAOKA  Yoshiharu YUBA 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E81-A  No.10  pp.2092-2100
Publication Date: 1998/10/20
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Spread Spectrum System
Keyword: 
slotted ALOHA,  capture effect,  stability,  cusp catastrophe,  cusp point,  bifurcation sets,  multiple packet reception, 

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Summary: 
The stability of slotted ALOHA systems with various types of capture phenomena and multiple packet reception capability is discussed in conjunction with the cusp catastrophe. The slotted ALOHA systems considered are classified into; 1) single packet reception with geometric capture, 2) independent multiple packet reception with geometric capture, 3) single packet reception with M-out-of-N capture (M N), 4) multiple packet reception with M-out-of-N capture, and 5) single packet reception with perfect capture. First, general expressions for the cusp points and the bifurcation sets are derived. Then, we present explicit formula for the stability of slotted ALOHA systems for the five types of capture and multi-packet reception capability and demonstrate how the bistable behavior is mitigated due to capture effect and multi-packet reception capability.