Assume that a bank teller window the customer arrives at a average rate of 20 per hour according to Poisson Distribution. Assume also that the bank teller spends a distributed customers who arrive from an infinite population are served on a first come first service basis and there is no limit to possible queue length. 1. What is the expected waiting time in the system per customer 2. what is the probability of zero customer in the system
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Step 1
The expected waiting time in the system per customer: The arrival rate (λ) is 20 customers per hour. The service rate (μ) is not given in the question, so let's assume it as x customers per hour. The formula for the expected waiting time in the system (W) is Show more…
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Customers arrive at a bank counter manned by a single cashier according to a Poisson distribution with a mean arrival rate of customers per hour. The cashier attends to the customers on a first-come, first-serve basis at an average rate of customers per hour, with the service time exponentially distributed. Find the probability of the number of arrivals (0 through 5) during (i) a 5-minute interval and (ii) a 30-minute interval. Also, find the probability that the queuing system is idle, the probability associated with the number of customers (0 through 5) in the queuing system, the probability that there are more than customers in the queuing system, the time a customer should spend in the queue, and the time a customer spends before leaving the bank counter.
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