Suppose four active nodes—nodes A, B, C and D—are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to transmit in each slot with probability . The first slot is numbered slot 1, the second slot is numbered slot 2, and so on.   (a) What is the probability that node A succeeds for the first time in slot 5?  (b) What is the probability that some node (either A, B, C or D) succeeds in slot 4? (c) What is the probability that the first success occurs in slot 3?  (d) What is the efficiency of this four-node system

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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  1. Suppose four active nodes—nodes A, B, C and D—are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to transmit in each slot with probability . The first slot is numbered slot 1, the second slot is numbered slot 2, and so on.

 

(a) What is the probability that node A succeeds for the first time in slot 5? 

(b) What is the probability that some node (either A, B, C or D) succeeds in slot 4?

(c) What is the probability that the first success occurs in slot 3? 

(d) What is the efficiency of this four-node system? 

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