Transient Solution of a two-processor heterogeneous systems

A two-processor system heterogeneous with Poisson arrival of jobs having exponentially distributed execution times is considered. Here, the service rates of these processors are not identical. Each job requires exactly one processors for its execution and the scheduling policy is FCFS. When both the processors are idle, the faster processor is scheduled for service before the slower one. For this system, exact time-dependent system size probabilities are obtained using a suitable probability generating function. Finally, some important performance measures are also obtained.