For the M/M/1 queue with ρ < 1 of Example 9.23, suppose that the number of customers pr...

For the M/M/1 queue with ρ < 1 of Example 9.23, suppose that the number of customers present when the first customer arrives has the following discrete distribution:

which is the steady-state distribution of the number of customers in the system. Compute the distribution function of D₁ and its mean. In this case, it can also be shown that D_i for i ≥ 2 has this same distribution.

Example 9.23