6.4.6 A time-shared computer system has three terminals that are attached to a central processing unit (CPU) that can simultaneously handle at most two active users.

If a person logs on and requests service when two other users are active, then the request is held in a buffer until it can receive service. Let X.t/ be the total number of requests that are either active or in the buffer at time t. Suppose that X.t/ is a birth and death process with parameters

Determine the long run probability that the computer is fully loaded.

and = [ 10 for k 0, 1,2, for k 3 [ku k = 12 fork 0, 1,2, = for k = 3.