Dynamic Servicing. Customers randomly request service at a manufacturing facility during an eight-hour day according to a Poisson process with intensity λt. The requested orders are satisfied as soon...

Dynamic Servicing. Customers randomly request service at a manufacturing facility during an eight-hour day according to a Poisson process with intensity λt. The requested orders are satisfied as soon as possible, but may be delayed due to machine workloads, worker schedules, machine availability, etc. Past history shows that a request at time t will be satisfied either: (1) That day. (2) The next day. (3) Some time later. The request at time t is satisfied under scenario i with probability pi(t), and the expected revenue for such an order is ri, where i = 1, 2, 3. (a) Find the distribution of the number of requests in a day that are satisfied under each scenario i, where i = 1, 2, 3. (b) Find the daily expected revenue for satisfying the customers, and find the variance of this revenue. (This is an actual model of customer requests for orders of paper labels produced by a company.)