Arrivals of a customers to payment counter in a bank follow poisson distribution with an average of 10 per hour. The service time follows negative exponential distribution with an average of 4 minutes. (a) What is the average number of customers in the Queue? (b) The bank will open one or more counter when the waiting time of a customer is at least 10 minutes. By how much the flow of arrivals should increase in order to justify the second counter?
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!
Problem #01: Arrivals of a customers to payment counter in a bank follow poisson distribution with an average of 10 per hour. The service time follows negative exponential distribution with an average of 4 minutes.
(a) What is the average number of customers in the Queue?
(b) The bank will open one or more counter when the waiting time of a customer is at least 10 minutes. By how much the flow of arrivals should increase in order to justify the second counter?
Problem #02: On the desk of an office of a Banking Company, the arrivals of the customers follow poisson law and an average at every 10 minutes a customer arrives. The officer responsible takes on an average 6 minutes to serve a customer, assuming the exponentially distributed. Find out the average arrival rates for
(a) 1 hour
(b) 15 minutes
(c) 8 hours
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