1) Determine the blocking probability, that is the probability that a random call will be blocked. (2) On average, how many calls are rejected per hour? Substantiate your answer. (3) What is the proportion of time that all the 10 output lines are available.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A telephone switch has 10 output lines and a large number of incoming lines. Upon arrival
a call on the input line is assigned an output line if such line is available { otherwise the
call is blocked and lost. The output line remains assigned to the call for its entire duration
which is of exponentially distributed length. Assume that 180 calls per hour arrive in
Poisson fashion whereas the mean call duration is 110 seconds.
(1) Determine the blocking
blocked.
(2) On average, how many calls are rejected per hour? Substantiate your answer.
(3) What is the proportion of time that all the 10 output lines are available.
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