Assume that in a two server system, a customer is serviced by server 1 then by server 2. The service times are exponentially distributed with means and , respectively. Further assume that if server 2 is busy, then the customer in server 1 will remain there until server 2 becomes free (blocking any other customer from entering the system until server 2 becomes free). After being serviced by server 2 the customer then leaves the system. Suppose that you arrive to find server 1 and 2 busy, what is the expected time you spend in the system?
for your service it would merely be
now for the waiting time, I basically reasoned it as follows:
Assume that there is only one customer and he's at server 2, leaving server 1 empty.
so his expected time in the system will be (where I get the probability from http://www.mathhelpforum.com/math-he...tribution.html)
using the above result would yield:
where the last term is your wait time given that you finished with server 1 before the customer finished with server 2.