Consider a service system in which customers arrive as a Poisson process of rate 3 (per unit time). There are two servers in the system, labeled 1 and 2. For both, the service time has the same exponential distribution with mean 1/2 (time units). All service times are i.i.d. When both servers are busy, an arriving customer waits in a queue, whose capacity is assumed to be infinite. The queue is served in the first-in-first-out order. The service policy is such that server 1 is the "main" one, and server 2 is a "helper." This means that:

(a) if a customer arrives in the empty system, it goes to server 1, not 2;

(b) if a customer arrives in the system when server 1 is working and server 2 is idle, this customer goes to server 2;

(c) when any server completes service, it will take for service the next customer waiting in queue if any;

(d) if server 1 completes a service when there is nobody waiting in the queue, but server 2 is working on a customer, then server 1 "takes" this customer from server 2, and serves it to completion as if it were a new customer. In particular, these rules imply that if there is exactly one customer in the system, it is served by server 1, not 2; if there are two or more customers in the system, both servers are working.

How would I find the continuous markov chain distribution? I thought it would go to separate nodes, but I feel like it doesn't because when there is 1 customer, it always automatically goes to the first server. Also, how would I go about finding the stationary distribution? I am so confused. Also, how would I know which customers leave the system with which server?