Question

Suppose within your Web browser you click on a link to obtain a Web page. The IP address for the associated URL is not cached in your local host, so a DNS lookup is necessary to obtain the IP address. Suppose that a DNS server is visited with RTT1=2.1ms before your host receives the IP address from DNS. Further suppose that the Web page associated with the link contains exactly one object, consisting of a small amount of HTML text. Let RTTO-3.2ms denote the RTT between the local host and the server containing the object. Assuming zero transmission time and processing time of the HTML object, how much time elapses from when the client clicks on the link until the client receives the HTML object?

(please fill in numbers in millisecond (ms) in the space provided.)
A. Time to receive the html object
Now, suppose the HTML file references 8 image objects on the same server. The transmission time of each image object is 2 ms. Neglecting processing time, how much time elapses under the following protocols. (Assuming DNS cache doesn't existing in your local host in each case).
B. Persistent HTTP with pipelining (default)?
C. Non-persistent HTTP with no parallel TCP connections?
D. Non-persistent HTTP with up to 10 parallel connections?

Answer 1

The probability of events in Web traffic with exponential distribution can be calculated using the exponential formula for continuous intervals and the Poisson distribution for counting discrete events in a fixed interval.

Step-by-step explanation:

When analyzing Web traffic and durations between site visits with an exponential distribution, we can apply the memoryless property of the exponential distribution and its probability density function to calculate the desired probabilities.

a. The probability that the duration between two successive visits to the website is more than 10 minutes is determined using the exponential distribution formula P(T > t) = e-λt, where λ is the rate of visits per minute, and t is the time in minutes. Since there are 12 visits per hour, the rate λ equals 12/60 visits per minute. For 10 minutes, the calculation would be P(T > 10) = e-(12/60)*10.

b. The top 25 percent of durations can be found by determining the time at which the cumulative distribution function (CDF) equals 0.75 and solving for t.

c. The memoryless property of the exponential distribution implies that the probability of a visit occurring within the next five minutes is the same as if no time had passed at all. Therefore, the calculation is the same as in part a, but for 5 minutes: P(T ≤ 5) = 1 - e-(12/60)*5.

d. The probability of fewer than seven visits occurring within a one-hour period can be calculated using the Poisson distribution, where the mean λ is equal to 12 visits per hour. We sum the probabilities of having 0 to 6 visits in the given hour.