Problem
Consider a (small) data center with 2 servers. The server center also has 3 users, of which one user can only use one server at a time. A single user is modeled as an on-off process, where the idle period is exponentially distributed with the parameter v = 1 (1/hour) and the service time (activity period) is exponentially distributed with the parameter u = 1/2 (1/hour), and both are mutually independent of everything. If the incoming user is blocked, a new idle period begins. Let X(t) 6 {0, 1, 2} be the number of users in the system, which is a Markov process.
1. Draw the state transition diagram of the process. Which model is it with Kendall's notation?
2. Solve the equilibrium distribution of the process X(t).
3. What is the probability that the customer will be blocked upon arrival, i.e., call blocking Bc?