Simple Exponential distribution problem....need help

[rkruz]

problem:
Service time is exponentially distributed with mean 30 minutes.
1st customer arrived at t=0 min.
2nd customer arrives at t=5 min
what is expected duration from arrival of 1st to departure of the 2nd customer?

Can you help provide some hints on how to solve this?

thank you.

 

[tkhunny]

Exponentials are "Memoryless".

5+30 maybe?

Actually, it's a little harder than that since we don't know what kind of service system we have.

If it has two servers, 5+30 is good enough.

If there is only one server, #2 has to wait for #1 to finish. 5 + 25 + 30?

 

[rkruz]

i thought it was a queue problem to. but apparently it only requires Littles law to solve.

 

[tkhunny]

Great. Quote the "Law" and let's see how it applies.

Alse, what does "service time" mean? Is that door to out or server to out?

I'm not quite convinced that Little can answer such an ambiguous question.