Consider two queueing systems. The first has one server and no limit on the length of the queue. Customers arrive according to a Poisson process with rate a. The service time is exponentially distributed with rate Mk Mk is proportional to the number of people in the system. That is, where k is the number of people in the system and u is a constant.

Mk = ku a = 1.5 u = 1.6

Determine the steady-state probability at P(1).

Calculate the average number of people in the system.

Calculate their average time in the system.