Consider the following arrival and departures of customers (in an M/M/1 queue with finite length of 1)
Customer 1 arrives during time 0 and leaves at time 4.
Customer 2 arrives during time 2 and leaves at time 9.
Customer 3 arrives during time 5 and leaves at time 11.
Determine each customer's service time.
I'm confused on how to solve this problem. For customer 1, I think $\mu$ would be 4 but I'm not sure what $\lambda$ would be. Also, I believe that every customer's service time is $\frac1{\mu-\lambda}$, for their respective parameters. How would I find those parameters though?
Since the queue length is $1$, I think the solution is straightforward. For first customer, waiting time $=0$, hence, service time$=4$. For second customer, waiting time$=2$, hence, service time$=9-4=5$. For third customer, waiting time is $=9-5=4$ and the service time$=11-9=2$.