There are m users who share a system. Each user alternates between "thinking" intervals whose durations are independent exponentially distributed with parameter LAMBDA, and an "active" mode that starts by submitting a service request. The server can only serve one request at a time, and will serve a request completely before serving other requests. The service times of different requests are independent exponentially distributed random variables with parameter MU, and also independent of the thinking times of the users. We can describe this process via a continuous-time Markov chain model where the states are the number of pending requests.
a) What is the number of states in the states space as a function of m and what values can they take?
b) For a state i, with 1 <=i <= m, what is the transition rate to state i - 1?
c) For a state i, with 1 <= i <= m - 1, what is the transition rate to state i + 1?
d) Give the steady-state balance equations.