Question: Consider a two-server system with exponentially distributed inter-arrival and service times. Let λ be the mean arrival rate and μ be the mean service rate of each server. The system has a limit of 3 jobs at any time. The servers work on jobs independently (only one server is working when there is only one job in the system).
(a) Develop the labeled directed arc network for this system.
(b) Write a system of equations, balance and norming equations, for this system.
(c) Solve this system for the general form of the steady-state probabilities.
(d) Write the equation for server utilization in terms of the steady-state probabilities.
(e) What is the mean number of jobs lost per unit time due to the limited system capacity?
(f) What is the system throughput rate? Note that throughput means completed jobs.