Suppose users share a 2 Mbps (i.e., 2×106 bits per second) link. Also suppose each user transmits continuously only at 1 Mbps when transmitting, but each user transmits only 20% of the time. a)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 queueing delay if three users transmit at the same time? b)Note that the probability that a given user is transmitting is 0.2 (i.e., 20% of time). Suppose now there are three users. Find the fraction of time during which the queue grows.

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter20: Queuing Theory
Section20.10: Exponential Queues In Series And Open Queuing Networks
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Suppose users share a 2 Mbps (i.e., 2×106 bits per second) link. Also suppose each user transmits continuously only at 1 Mbps when transmitting, but each user transmits only 20% of the time.
a)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 queueing delay if three users transmit at the same time?
b)Note that the probability that a given user is transmitting is 0.2 (i.e., 20% of time). Suppose now there are three users. Find the fraction of time during which the queue grows.

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