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,...

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