Exercise 2: A hardware system has two processors P1 and P2 that are identical. Time in the system is divided into slots. The system is governed by the following set of rules: With a probability pa, a maximum of one job arrives each time slot in an independent way. The job starts immediately on a free processor (idle) if any. If both are free the job starts at P1. Jobs are not buffered. If P1 and P2 are busy, arriving jobs are lost. A job is ended by a processor in a slot with probability pe. Since job completion is independent, the possibility that both processors end their jobs at the same time slot is pe 2 .

A processor can end a job in a time slot and starts another. a) Represent the problem as a Markov chain. Hint: Consider the following states: State 0: No jobs, State 1: one job in the system (in P1) and State 2: 2 jobs in the system. Hint: you need to think about all possibilities when looking for the transition probability.