A network switch buffer and link is modeled as a M/M/1 queue and server. At 3pm

Question

A network switch buffer and link is modeled as a M/M/1 queue and server. At 3pm the arrival rate of packets was 100 packets/sec (packets can be transmitted at a rate of 200 packets/sec) and at 4pm the arrival rate was 150 packets/sec. (i) What was the utilization of the server at 3pm? (ii) What was the utilization of the server at 4pm? (iii) By how much did the mean sojourn time of a packet increase from 3pm to 4pm? (iv) What is the probability that a packet does not have to wait in the buffer upon arrival at 3pm? (v) Suppose that at 3pm the arrival rate at another link was 200 packets/sec and that the server can transmit at 400 packets/sec. Without calculation state whether or not the mean queue length remains the same in this latter link.

Explanation / Answer

Solution:

i) Utilization of the server at 3 pm is = (Arrival packet rate at 3 pm/ packets transmitted rate at 3 pm)x100

(100 / 200)x100 = 50 %

ii) Utilization of the server at 4 pm is = (Arrival packet rate at 4 pm/ packets transmitted rate at 4 pm)x100

( 150 / 200 ) x 100 = 75 %

iii) The sojourn time of a packet increase from 3 pm to 4 pm is = [(packet rate at 4pm - packet rate at 3pm)/packet rate at 4pm] x 100

[ (150 - 100) / 150 ] x 100 = 33.33 %

iv) The probability that a packet does not have to wait is = arrival packet rate / transmitted packet rate

= 100 / 200 = 0.5

v) The mean queue length remains the same.

The reason is the probability will remain the same and the packets ratio rate also same

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