M/M/m/m. M/M/m - compulsory test

1. Consider an M/M/m/m system with a=4.5 offered load and m=5 servers. The average service time is 1 time unit.

a) What is the arrival intensity of the customers (that is, the offered traffic)?

b) Assume that the system is in blocking state, that is, all the servers are busy. What is the expected time for the system to stay in blocking state? Motivate your answer.

c) Give the blocking probability with the help of Erlang tables and calculate the average number of customers in the system.

2. Consider now that we add an infinite buffer for the system in problem 1.

a) Motivate that this system is stable.

b) Calculate the probability that an arriving customer has to wait and calculate the average number of customers in the system, with the help of the equations that we derived in class.

c) Compare the average number of customers in the first and in the second system. Which one is higher? Why?