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
Section: Chapter Questions
Problem 1PE
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Suppose 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 p = 0.6. The first slot is numbered slot 1, the second slot is numbered slot 2, and so on.

 

  1. 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?

 

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

 

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