A petrol station in the capital Kingstown has a single pump manned by one attendant. Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an average. Assume the arrival rate is Poisson probability distribution and service rate is exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and sales, station loses about $15 per hour of customer time spent waiting for the attendant to service and order. Part A Answer the following questions: a. What is the probability that no customers are in the system (Po)? b. What is the average number of customers waiting for service ( Lq)? c. What is the average number of customers in the system (L)?
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!
Question 4
A petrol station in the capital Kingstown has a single pump manned by one attendant. Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an average. Assume the arrival rate is Poisson probability distribution and service rate is exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and sales, station loses about $15 per hour of customer time spent waiting for the attendant to service and order.
Part A
Answer the following questions:
a. What is the probability that no customers are in the system (Po)?
b. What is the average number of customers waiting for service ( Lq)?
c. What is the average number of customers in the system (L)?
d. What is the average time a customer waits for service(Wq)?
e. What is the average time in the system (W)?
f. What is the probability that a customer will have to wait for service (Pw)?
g What is the probability that there is exactly 2 customers in the system?
h) What is the probability that there are more than 3 customers in the system?
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