Question: A system consists of three servers as shown in Fig. Arriving customers first enter the queue preceding server 1, and after completing service they are routed to either server 2 or server 3. The routing policy is to always send a customer to the server with the shortest queue, and in case of a tie to send to server 2. Customers completing service at servers 2 and 3 leave the system. A customer arriving from the outside is accepted into this system only as long as the total number of customers present is less than or equal to 2; otherwise, customers are rejected. Build an automaton model of this system.
