Question: Consider a single-server system with two types of jobs. The system has a limited capacity of three total jobs in the system at any time. The job classes have different mean arrival and service rates, but all are assumed to be exponentially distributed. Let λ1 be the mean arrival rate and μ1 be the mean service rate of job type 1, and let λ2 be the mean arrival rate and μ2 be the mean service rate of job type 2. Job class 1 are high priority items and, as such, they have preemptive priority over jobs of type 2 on the server.
Space within the system limit of three jobs is on a first-come first-service basis; thus, once a low-priority job is in the system, it cannot be replaced by a high-priority job. Although all low-priority jobs must wait until all high-priority jobs have been processed, even if they arrive when a low-priority job is being serviced. Develop the labeled directed arc network for this system.
Hint: there are ten different states and the number of each job type must be accounted for separately.