To a certain degree, the answer is "both." Repeating the same subject in each of several sentences in a paragraph does have the ability to build continuity, but it can also get rather repetitive (and thus boring to the reader). I wouldn't say that it's redundant, per se, unless you actually repeat the semantics of one sentence in a following sentence.
This is the beauty of pronouns, which allow you to use a word other than the same noun phrase over and over. You can also break up your writing with synonyms, introductory prepositional phrases and modifiers, use of compound sentences, and so forth. For example:
A passenger arrived; he entered the train station. Immediately, he was checked by government agents, after which the disgruntled traveler promptly left the station.
On the other hand, there are valid reasons for specifically repeating words from one sentence in a following sentence; usually this is a deliberate rhetorical device to reinforce the parallels and connection between the sentences.
At the end of the day, it's a stylistic choice on the part of the writer. There is nothing grammatically wrong with what you have written, but you'll want to be conscious of how the reader will accept it.
EDIT: You mentioned that this is part of a "process." Documentation that describes processes, including manuals, handbooks, and so forth, are far more likely to eschew narrative flow in favor of clarity and the lack of redundancy. Thus, if the purpose is to capture a specific sequence of unambiguous steps, then the repetition of the noun phrase is usually viewed much more favorably, especially in a numbered list. For example, suppose you were writing the process for travelers going through security:
- The passenger takes off his shoes and coat.
- The passenger places all small items (watch, wallet, etc.) in an available container.
- The passenger places all suitcases on the x-ray machine belt.
Note that the fact that this is a numbered list (or bullet list) is significant, because it specifically is not attempting to serve as narrative.
This may also be a good question for the Writers Stack Exchange.