A service station consists of two back-to-back stations S1 a…

A service station consists of two back-to-back stations S1 and S2. Customers follow this workflow: Customers first arrive at S1​, are served, and then proceed to S2​. After service at S2​, with probability 0.1, a customer is sent back to S1​ for rework (reentrant flow). Otherwise, with probability 0.9, the customer leaves the system. Assume the following conditions: The arrival process follows a Poisson distribution with rate 10 per hour. The service times at S1 and S2​ follow exponential distributions with means 5 minutes and 6 minutes​, respectively. S1 has a single server and S2 has two servers. Both have infinite queue capacity.

Consider a drive-through restaurant where all orders are pro…

Consider a drive-through restaurant where all orders are processed by one order kiosk with virtually unlimited space for the cars to line up. Suppose one car arrive every 3 minutes, while it takes 90 seconds on average to take the order. Show your work on the scratch paper when answering Q20-Q22.