Customers arrive at a corner grocery store at a rate of 3 per minute and the Poisson

Question:

Customers arrive at a corner grocery store at a rate of 3 per minute and the Poisson distribution accurately defines this rate. A single cashier works at the store, and the average time to serve a customer is 15 seconds, and the exponential distribution may be used to describe the distribution of service times.

(a) What are λ and μ in this situation?

(b) Using Kendall notation, what type of queuing system is this?

(d) What percentage of time is the cashier idle?

(e) What is the average length of the line?

(f) How many minutes does the average customer spend waiting in line?

(g) How many minutes typically elapse from the time the person enters the line until the person pays the cashier and leaves the system?

(h) Find the probability that the number in the system is 1, 2, and 3.

Distribution
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