It has been concluded that a single-server queuing system with exponentially distributed service and interarrival times can be modeled as a birth-and-death process with statedependent mean service and arrival rates, ILn and Ii", respectively.

f1 = {n for n = 0,1,2,3 n 0 otherwise I\. = {3 -n n 0

a. Construct the corresponding rate diagram.

for n = 0,1,2,3 otherwise

b. Calculate the stationary probabilities for finding exactly n customers in the system, lPn, n = 0,1,2,3, ... }.

c. Determine the expected number of customers in the queuing system, L, and in the queue, Lq. Also determine the expected time a customer spends in the system, W, in the queue, W q, and in the service facility, Ws'