12.5 Consider an m-server queueing system that operates in the following manner. There are two types of customers: type 1 and type 2. Type 1 customers arrive according to a Poisson process with rate λ1, and type 2 customers arrive according to a Poisson process with rate λ2. All the m servers are identical, and the time each takes to serve a customer, regardless of its type, is exponentially distributed with mean 1=μ. As long as there is at least one idle server, all arriving customers are served without regard to their type. However, when all m servers are busy, type 2 customers are blocked; only type 1 customers may form a queue. When the number of customers in the system decreases to k , m following an incidence of type 2 customer blocking, type 2 customers will once again be allowed to enter the system. Define the state of the system by ða; bÞ, where a is the number of customers in the system and b is the phase of the system that takes the value 0 when both types of customers are allowed to enter the system and the value 1 when only type 1 customers are allowed. Give the state transition rate diagram of the process and determine the Q-matrix, including the D submatrices.