If there are x number of devices that are wanting to transmit during a slotted Aloha protocol, what value of access probability (p) will maximize the amount of total throughput for the system? Also what happens to the value of throughput as the number of devices approaches infinity?

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter20: Queuing Theory
Section20.4: The M/m/1/gd/∞/∞ Queuing System And The Queuing Formula L = Λw
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If there are x number of devices that are wanting to transmit during a slotted Aloha protocol, what value of access probability (p) will maximize the amount of total throughput for the system? Also what happens to the value of throughput as the number of devices approaches infinity?

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