Consider a single$-$server queueing system that can hold a maximum of two customers excluding those being

served. The server serves customers only in batches of two, and the service time $($for a batch$)$ has an exponential distribution with a mean of $1$ unit of time. Thus if the server is idle and there is only one customer

in the system, then the server must wait for another arrival before beginning service. The customers arrive

according to a Poisson process at a mean rate of $1$ per unit of time.