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A company has positions for three employees. Applicants for these jobs appear at a Poisson rate of two per year. If all jobs are filled, they look elsewhere. Those who hold a job do so for an exponentially distributed time with mean one-half year. a. Determine the proportion of applicants that are turned away. b. What is the average number of employees?

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Karabo99

Answer and Explanation:

Let πj denote the steady-state probabilities. Assume that these values are known.

a). Determine the proportion of applicants that are turned away.

Because Poisson arrivals see time averages (PASTA), the proportion of applicants that are turned away is equal to the fraction of the time that the company is fully staffed.

Therefore, π3 ←

b). What is the average number of employees?  

From the definition of expected value, 0π0 + 1π1 + 2π2 + 3π3 ←

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