Question: Redo Problem under the assumption that the group size is one with probability 1/2 and two with probability 1/2.
Problem: Jobs arrive at a single machine for processing. Jobs arrive in groups of two (always) with an exponentially distributed time between groups with mean rate λ. The single server works on individual jobs. The service time is exponentially distributed with a mean rate μ. Let be the probability that there are n jobs in the system in steady-state. Note that there is no limit to the number of jobs allowed into this system. Draw the state diagram with labeled arcs and write the steady-state equations for states 0, 1, 2, 3, 4, and 5. What is the relationship between λ and μ that guarantees that a steady-state exists?