An exercise on Markov process

A Life Insurance Company offers various retail Insurance products. But the business is not as good as expected.

Top management decides to set up a task force to analyze the reasons and suggest corrective measures. After a detailed study, the team submits the report indicating the need to design the claim management system scientifically.

It is found that the claims are reported at an average rate of 500 per week following Poisson distribution. The Claims Processing rate too follows Poisson distribution.

Analyze following alternatives and offer your recommendation.

1. How will the system behave if the claims management system is designed to have claims processing rate as 400 per week Poisson?

2. How will the system behave if the claims management system is designed to have claims processing rate as 500 per week Poisson?

3. How will the system behave if the claims management system is designed to have claims processing rate as 800 per week Poisson?

4. How will the system behave if the claims management system is designed to have claims processing rate as 1200 per week Poisson?

5. Management wants the average number of claims in the system at a time to not exceed 25. What do you recommend to achieve this?