The average CRI-length of a controlled ALOHA collision resolution algorithm
type: Item
instance of: scholarly article
title: The average CRI-length of a controlled ALOHA collision resolution algorithm
zbMATH Open document ID: 0781.68027
DOI: 10.1016/0304-3975(93)90195-Y
author: Ulrich Schmid
published in: Theoretical Computer Science
publication date: 1993-05-16T00:00:00Z
review text: The paper investigates some properties of a hybrid conflict resolution algorithm proposed for a network with a controlled ALOHA protocol. The algorithm adjusts the retransmission probability to the number of colliding stations. It consists of two steps, namely, the estimation of the number \(n\) of collisions and the collision resolution phase, being the ordinary S-ALOHA algorithm which the retransmission probability \(p=1/n\) and delayed transmissions of newly generated packets. The author estimates the number of collisions and gives the average conditional length of CRI for a given number \(n\) of colliding stations. Next, using the Mellin transform technique he proposes an asymptotic analysis of the average value of CRI. The author proves that the average CRI length is of order \(O(n\log n)\) as \(n\) tends to infinity. This result gives some insight to the instability of the described controlled ALOHA algorithm, namely, it shows that even controlling the retransmission probability is not sufficient to guarantee the stability of the considered protocol.
Mathematics Subject Classification ID: 68M10
Mathematics Subject Classification ID: 94A05
Mathematics Subject Classification ID: 90B18
zbMATH DE Number: 166966
zbMATH Keywords: controlled \(S\)-ALOHA
zbMATH Keywords: conflict resolution algorithm
zbMATH Keywords: Mellin transform
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: CRI length
reviewed by: Józef Woźniak
MaRDI profile type: Publication
cites work: Q3661894
cites work: Q5850027
cites work: Q3704890
cites work: A perspective on multiaccess channels
cites work: Estimating the multiplicities of conflicts to speed their resolution in multiple access channels
cites work: &lt;tex&gt;Q&lt;/tex&gt;-ary collision resolution algorithms in random-access systems with free or blocked channel access
cites work: On the asymptotics of the average CRI length of the slotted ALOHA collision resolution algorithm
cites work: Q3844537
description: scientific article; zbMATH DE number 166966