Party representation on committees and reciprocity/logrolling are both elements of the congressional committee system that influence the legislative process greatly. Party representation on committees is when a committee such as congress is represented and leaning towards one party. In other words, what party the committee favors. Party representation on committees influences the legislative process because they will follow certian legislation based on the party's views. For example, if a committee is faced with an abortion issue, they will carry out leislation for abortion if their party representation is democratic or they will carry out legislation against abortion if they are rebublican. A committee becomes affiliated with a party depending on either the president at the time, (he appoints officials corresponding to his party), the majority stance of the committee, or the head of the commitee's party affiliation. Reciprocity is a mutual or cooperative interchange of favors or privileges, especially the exchange of rights or privileges of trade between nations, whereas logrolling is the exchanging of political favors, especially the trading of influence or votes among legislators to achieve passage of projects that are of interest to one another. This influences the legislative process because both it is when one committee says to the other, i'll vote in favor for you if you vote in favor for me. This way legislation can get passed due to majority vote due to logrolling/reciprocity.
Party leadership in Congress can influence the legislative process by passing certian legislation in correspondance to the views of the specific party as well as what legislation they pay attention to and what legislation they put to the side deemed as "unimportant." By passing certian legislation, they influence the overall process because they continuously change legislation according to their party affiliation. For example, pro abortion rights could have been passed with an overall democratic Congress. However, in a few years if Congress slides to a republican stance they will change legislation against abortion. Second, by focusing on some legislation important to the party and dismissing the other party's legislation, they are shifting the public policy of our nation. You see, if Congress is focused on Democratic issues, they will pass legislation in correspondance with that, shifting the way the nation functions. Overall, party leadership in Congress has a huge influence on the legislation process.