A small bank has two tellers, one for deposis and one for withdrawals. The service time for each teller is exponentially distributed, with a mean of 1 min. Customers arriving at the bank according to a poisson process, with mean rate 40 per hour; it is assumed that depositors and withdrawers constitute separate poisson processes, each with mean rate 20 per hour , and that no customer is both a depositor and a withdrawer.
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 small bank has two tellers, one for deposis and one for withdrawals. The service time for each teller is exponentially distributed, with a mean of 1 min. Customers arriving at the bank according to a poisson process, with mean rate 40 per hour; it is assumed that depositors and withdrawers constitute separate poisson processes, each with mean rate 20 per hour , and that no customer is both a depositor and a withdrawer. The bank is thinking of changing the current arrangement to allow each teller to handle both deposits and withdrawals. The bank would expect that each teller's mean service time would increase to 1.2 min, but it hopes that the new arrangement would prevent long lines in front of one teller while the other teller is idle, a situation that occurs from time to time under the current setup. Analyze the two arrangements with respect to the average idle time of teller and the expected number of customers in the bank at any given time.
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