Sandwich shop : a queuing net work with finite disposable resources queue and infinite resources queue

As I take the queuing system course, I become interested in the queuing systems in our life, for example, the cafeteria in the school. In this project, I want to model an interesting queuing system I observed in some cafeteria on campus, and study the behaviour and performance of the queuing system at the cafeteria. When I go to the Jazz Café in Darrin Communications Center, I noticed that there are two types of customers. Some of the customers quickly pick up some prepared food or drinks and join the check-out line, while some of them order sandwiches or coffee that take some time to be ready for pick-up. The prepared food usually serves in a limited amount, so it happened to me that the prepared sandwich is sold out. In that case, I would need to decide to get a fresh made sandwich or leave and make purchase somewhere else. So I model such queuing network as a sandwich shop. Each day during the peak hour, 11:30 a.m. to 1:30 p.m., the sandwich shop have K prepared sandwich available in the refrigerator, and enough raw materials to make customized sandwich for all the arriving customers. The customer who wants customized sandwich is called customer of type 1 and arrives following a Poisson Process with rate λ1. And the customer who wants to pick up a prepared sandwich and check out soon is called customer of type 2 and arrives following a Poisson process with rate λ2. When a type 1 customer arrives, he goes to the queue at the food counter, and wait for his turn when a staff will make his customized sandwich. Once he gets his sandwich, he proceeds to the checkout queue to pay for the food. There is one staff at the food counter, and his service time has exponential distribution with rate μ1. When a type 2 customer arrive, he goes to the queue in front of the refrigerator to wait for his turn to pick up a prepared sandwich. The time each type 2 customer needs to choose and take the prepared sandwich is also exponentially