A network uses a single 150 Mbs LAN with average LAN delay of 15 ms. The network

Question

A network uses a single 150 Mbs LAN with average LAN delay of 15 ms. The network is
connected through a 10 Mb/s access link to the Internet. The Internet experiences an average
delay time of 200 ms, while the delay (in seconds) on the access link is a function of its
utilization as below:
D =
10U
1 - U
Where U (from 0 to 1) is the bandwidth utilization fraction and D is the delay on the access link.
There are 29 requests every second generated on the LAN, and average size of request is 100 Kb.
(a) If no web caching is used, what is the average end-to-end delay to service a request?
(b) If a web cache is used in the network with a hit ratio of 80%, what is the average end-to-end
delay?
(c) If a web cache is used with a hit ratio of 30%, what is the average end-to-end delay?

Explanation / Answer

a.    Total number of requests for every second generated on the LAN is 29.

            Average size of request is 100kb.

                  U = 29 × 100K / 1M

b.      80% requests incur 10 ms delay, rest incur longer delay.

              U = 2.9 × 0.3 = 0.87

              D = 3.986 s

De = 0.8(0.01) + 0.3(3.986 + 0.2 + 0.01) = 1.2668 s

c.       30% requests incur 10 ms delay, rest incur longer delay.

            U = 2.9 × 0.8 = 1.52

             D = 19.85 s

De = 0.3(0.01) + 0.8(19.85 + 0.2 + 0.01) = 16.051 s

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