Answered: Suppose users share a 2 Mbps link. Also…

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

Problem 7P

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Question

Suppose users share a 2 Mbps link. Also suppose each user transmits continuously at 1
Mbps when transmitting, but each user transmits only 20 percent of the time. a. When circuit switching is used, how many users can be supported?
b. For the remainder of this problem, suppose packet switching is used. Why will there be
essentially no queuing delay before the link if two or fewer users transmit at the same
time? Why will there be a queuing delay if three users transmit at the same time?
c. Find the probability that a given user is transmitting.
d. Suppose now there are three users. Find the probability that at any given time, all three
users are transmitting simultaneously. Find the fraction of time during which the queue
grows.

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