Assume that at a bank teller window the customers arrive in their cars at the average rate oftwenty per hour according to a Poisson distribution. Assume also that the bank teller spendsan average of two minutes per customer to complete a service, and the service time is exponentially distributed. Customers, who arrive from an infinite population, are served on a first-come-first-served basis, and there is no limit to possible queue length. a. What is the expected waiting time in the system per customer? b. What is the mean number of customers waiting in the system? c. What is the probability of zero customers in the system? d. What value is the traffic intensity?
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!
Assume that at a bank teller window the customers arrive in their cars at the average rate oftwenty
per hour according to a Poisson distribution. Assume also that the bank teller spendsan average of
two minutes per customer to complete a service, and the service time is exponentially distributed.
Customers, who arrive from an infinite population, are served on a first-come-first-served basis,
and there is no limit to possible queue length.
a. What is the expected waiting time in the system per customer?
b. What is the
c. What is the
d. What value is the traffic intensity?
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