Assume that at a bank teller window the customer arrives at an average rate of 20 per hour according to poission distribution. Service rate of the bank teller is calculated 2 minutes per transaction. Assume also that the bank teller spends a distributed customer who arrive from an infinite population are served on a first come first services basis and there is no limit to possible queue length. what is the value of utilization factor? What is the expected waiting time in the system per customer? 3.what is the probability of zero customer in the system
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 customer arrives at an average rate of 20 per hour according to poission distribution. Service rate of the bank teller is calculated 2 minutes per transaction. Assume also that the bank teller spends a distributed customer who arrive from an infinite population are served on a first come first services basis and there is no limit to possible queue length.
- what is the value of utilization factor?
- What is the expected waiting time in the system per customer? 3.what is the
probability of zero customer in the system?
Question 2
ABC company has one hob regrinding machine. The hobs needing grinding are sent from company’s tool crib to this machine which is operated one shift per day of 8 hours duration. It takes on the average half an hour to regrind a hob. The arrival of hobs is random with an average of 8 hobs per shift.
- Calculate the present utilization of hob regrinding machine.
- What is average time for the hob to be in the regrinding section?
- The management is prepared to recruit another grinding operator when the utilization of the machine increases to 80%. What should the arrival rate of hobs then be?
Question 3
In a bank with a single sever, there are two chairs for waiting customers. On an average one customer arrives 12 minutes and each customer takes 6 minutes for getting served. Make suitable assumption, find
- The probability that there are more than two customers in the queue,
- The probability that there are exactly two customers in the queue
- Expected waiting time of a customer.
Question 4
At a certain petrol pump, Customer arrive according to a passion process with an average time at 5 min between the arrivals. The service time is exponential distribution with mean 2 mins on the basic of this information.
Find out: -
- Traffic intensity or utilization
- What would be the average number of customers in the queue?
- What is the expected number of customers at petrol pump?
- What is the expected number time one spends at petrol pump?
- What would be the proportion time the petrol pump is idle?
Question 5
In a bank cheque are cashed at a single ‘teller’ counter. Customers arrived at the counter in a Poisson manner at an average rate of 30 customers /hour. The teller takes on an average, a minute and a half to cash cheque. The service time has been shown to be exponentially distributed
- Calculate the percentage of time the teller is busy.
- Calculate the average time a person is expected to wait in the queue.
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