Three recent methods for model reduction of linear discrete systems are presented. They are based on the impulse response gramian which contains information on the input-output behavior of the system. The corresponding low order approximants retain the first r Markov parameters and the first r×r elements of the impulse response gramian of the original system. To see the efficiency of each algorithm, these methods are implemented and several simulations are done. From an illustrative example, we can better appreciate their performances and the closeness of each reduced order model to original system.