The hypothetical situation is that a university could use credits that are allocated to students to be used for priority access to certain things. A couple things could be a candidate for a system that uses credits for priority access.
Sports tickets and items are things that could use this system. For example, if there is a limited amount of "good" seats at a football game, students could use their credits to have an advanced option to buy the tickets, with competition coming from other students as well as from non-students.
Another thing could be for school books and the condition of used books. A student could use their credits to gain access to higher-quality used books, assuming the different levels of quality doesn't affect the price (flat rate for used books).
Student parking is another thing that could benefit greatly from a system like this. Students could use their credits to have priority access to better and closer parking.
I do not believe that a credit system would be fair when it comes to registering for a class, simply because there is no merit or seniority involved. However, I believe it could be utilized in terms of class times, with students being able to use their credits to, for example, register for a 11am section instead of a 9am section.
I would use my credits for class times. I believe that a major factor in a student's success is the time that they have classes. I am unsure of the exact data, but I would be willing to bet that a class's average GPA is higher in sections scheduled later in the day. This would be my main priority.
If the administered price for priority access was too low, students would use their credits less sparingly, and it wouldn't create the fixed economy that is desired. However, if the administered price for priority access was too high, students would be too cautious with their credits and might create an excess of unspent credits.
I believe the best process would be to have a bidding process for priority access that would vary in lengths depending on the level of priority/item desired. For example, if a student has 100 IB (Illinibucks), that person could bid 20 IB for first access good seats at a football game. However, if another student wants the seats more, that student could bid 25 IB. This is fair because a student shouldn't have to pay a high price if no other students want an item and would let the market determine things importance. I believe this system would let the students decide what each thing was worth and would be the most fair.
An alternative to a bidding process up front would be to have a bumping process after the fact, where a student that doesn't have priority access pays a student (with Illinibucks) for their access. The bumping price would then be the true equilibrium price, with the administered price set earlier a way to generate some initial allocation. This would then mimic how the airlines do their ticketing.
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