Logged in time ticks down at the normal rate.
Logged out time ticks down half as fast.
Completing different tasks through mini-game UI's would reduce prison time and would also give logged-in users something to do as opposed to watching Netflix on their second monitor. These tasks could include:
Collecting litter - Walk around the open prison area, empty trash cans and take the bag to a recycling center at the other end of the prison, rewarded per item dropped off.
Cleaning cells - Walk around each cell and use a command to put you in a mop animation, empty and refill your mop bucket in a mainetance cupboard, rewarded per mop bucket refilled.
Mining - Speaks for itself
Cutting trees - Same as the existing lumber job at Mount Chiliad, rewarded per item dropped off.
Painting - Walk around different areas of the prison and touch up the paintwork in corridors, just trigger a suitable animation against a wall, rewarded per animation.
Crafting clothes/shoes - Collect materials from one end of the prison, take them elsewhere, sew the clothes together and then drop them off somewhere else, rewarded per item crafted.
Playing chess - Chess minigame, rewarded for time spent playing (maybe a bit more for winning?).
Playing poker - Same script as tequila-la-la, rewarded for time spent playing (maybe a bit more for winning?).
Repairing DOC vehicles - Same script as mechanic shop, per repair you get reward (wouldn't necessarily have to be vehicles that are being used, could just spawn them in for RP sakes, i.e. service & MOT)
Cooking food - Collect materials from one end of the kitchen, take them elsewhere, cook the ingredients together and then drop them off somewhere else, rewarded per item crafted.
None of the above tasks would necessarily bring about a resulting item or monetary reward but it just gives people something to do and communicate over. Even fun social games such as chess or poker could provide reduced jailtime as it would incentivise players to engage with one-another rather than isolate themselves. At the end of the day the purpose of the game is to bring enjoyment to player and in its current state prison does not do that to any extent.