I have M/M/4 queue with an arrival rate of λ= 1.5 per minute and an expected service time of 1/γ= 2 minutes. At arrival four persons are being served and 10 are waiting in line.
Q: What distribution does the time from you arrive to you move up one space in the que have? What is the expected time to move up one space?
So my thinking: This would be the same as the distribution for one customer being served moves out of the system. So it would be exponential distribution? I am unsure of the expected value though. I assume it is either 1/γ= 2 minutes or γ = 0.5 minutes, but I am not quite sure. Help?