7. Consider a one-server queuing situation in which the arrival and service rates are given by An = 10 - n,n = 0,1,2,3 n

/-Ln = 2" + 5, n = 1,2, 3,4 This situation is equivalent to reducing the arrival rate and increasing the service rate as the number in the system, n, increases.

(a) Set up the transition diagram and determine the balance equation for the system.

(b) Determine the steady-state probabilities.

8. Consider the single queue model where only one customer is allowed in the system. Customers who arrive and find the facility busy never return. Assume that the arrivals distribution is Poisson with mean Aper unit time and that the service time is exponential with mean 1 time units.

Jl.

(a) Set up the transition diagram and determine the balance equations.

(b) Determine the steady-state probabilities.

(c) Determine the average number in the system.