In queuing theory, (with a single queue and a single server) writing $A$ for the service rate (of customers) and $B$ for the arrival rate (of customers) we know that the average time a customer waits in the system is given by,
What is the intuitive interpretation of this equation?
What I understand from basic intuition is that $A$ customers gets service in 1 sec (as $A$ is the service rate) so, one customer should get service in $1/A$ seconds.
Now, $B$ means, $B$ customers comes in 1 second (the arrival might be bursty or not depending on the probability distribution). So, $(A-B)$ is , how many more customers can the server serve per second, right?
So, why is the waiting time $W=1/(A-B)$?
How can I understand this relationship intuitively?