Alexander, Julius Caesar, Pompey - what are they to Diogenes, Heraclitus, Socrates? These men saw into reality, its causes and its material, and their directing minds were their own masters. As for the former, they were slaves to all their ambitions.
Even if you burst with indignation, they will still carry on regardless.
Do you ever want to know how important something is in the grand scheme of things? Marcus provides some advice: how will this decision I make (each action) sit with me? Will I regret it later? If so, then don't do it. Also, remember that you will shortly be dead and everything will return to dust. When I visited my therapy counselor in 2014, she gave me similar advice. How will this action or decision impact or matter one day from now? One week? A month? A year? Looking at actions and impacts of actions from that lens is quite helpful with decision making. One other thing, however; be mindful of the present and small, daily actions. Those turn into habits which then determine your character.
Marcus looked not to Alexander, Caesar and Pompey; rather he looked to Diognenes, Heraclitus and Socrates as sages and examples to follow. They were in charge of their directing mind and were not swayed by their monkey brains.
The last section above is an excellent point. Perhaps bursts of indignation can and do help change minds. But more often than not, "weeping in the hallways" and having outbursts does not change minds. Better to focus on action and what you can do rather than spending effort and time on complaining. I love this video below because Spock's reaction to his planet being destroyed is quite Stoic. Rather than weeping in the hallways, he chooses to act or focus on what is in his control.
(see also Citadel p. 295, 305)