For this example we will be studying one of the Van Gogh class of mobile logistics platform: The Paul Cézanne.
In the story, the asteroid belt has two mega-cities. One in orbit around Psyche, and the other on the surface of Ceres. Those mega-cities allowed smaller vessels to operate around the belt, coming in to port every few months to exchange raw resources they harvest for fresh supplies, lifestyle diversions for the crews, and services to maintain and upgrade the vessels themselves. The ships were generally floating refineries with smallish crews.
In between the mega-cities and the tramp harvesters was a class of mega-vessel known as the Hokusai. These logistics bases / towns of 2000 or so permanent residents and crew who could accomodate up to 20000 guests at a time. These ships were built with the same propulsion system as the battleships that protected the asteroid belt, but instead of carrying missiles and strike craft they contained farms and repair facilties. These ships travelled in regular routes reaching the under-served areas of the Asteroid belt. It was cheap and cheerful for an austere harvester to send a chunk of its crew to one of these ships that were in the area for shore-leave. Those same shuttles could bring back consignments of fresh food that boosted the morale of those on-board (as no matter how well prepared, shelf-stable rations get tiresome).
The vessel utilizes the same propulsion plant as a Carr Class battleship. But instead of missiles, strike craft, and a legion of troops, the vessel carries farms, factories, a civilian shipyard, and leisure facilities. In times of crises, the Hokusai could be sent in a timely manner to provide disaster relief. In times of war, they were paired with a battleship to provide logistics support. The Battleship was the castle with all the guns, the Hokusai was the town outside that grew the food and had all of the bars full of wenches.
When it came time to settle the Kupier Belt and beyond, the ISTO built the Van Gogh class. This was an enlarged Hokusai with a number of other improvements. The first series of books takes place in and around the vessel Paul Cezzane the third of the Van Gogh vessels built. It also plays a pivotal roll in diplomacy and scientific exploration in the Solar System.
The Cezzane has a population of about 2500. This is based on the population of Wrangell, Alaska. One of the oldest oldest non-native settlements in Alaska. They are actually a perfect model for an asteroid mining operation. They exist on the frontier. Their economy is mainly based on the exploitation and trade of raw materials. (Fish and lumber.) They have a healthy pattern of growth. And that's the key: a stable population is a growing population. It may be growing slowly, but it needs to be growing.
The Paul Cézanne is a bit of an odd duck, because it is basically a resort town. The 2500 full time inhabitants/crew regularly interact with hundreds or even thousands of crew from other settlements and vessels. As designed it operates as a "big city" to the villages and ships of the Asteroid belt. This model gets stretched to breaking when it is placed on the edge of the Solar System to act as an anchor for development in the Kuiper belt. (It also nearly starts a war with Krasnovia when it was decided to station the ship near The the Kuiper Belt object we call Pluto. We joke about demoting the status of planets. In some realities this dispute was taken a bit more seriously.)
The population is going to be going through a regular series of booms and busts as the contracts for the workforce expire, and new crew are recruited as those on board sometimes stay and sometimes move on to other jobs.
One of the problems was that of recruiting. When the ship operated around the asteroid belt, crews could count on being able to get on or get off at the port of their choice almost immediately after their contract expired. The Cézanne was now going to operate at the edge of the Solar system. It was a 9 month journey on most of the commercial fusion vessels. Though a high performance passenger craft could potentially reach the outpost in "only" 4 months.
The Cézanne was chosen partly because the intended ship Salvadore Dali was a new class with teething issues. But mostly because the ship was an experiment using traditional agricultural practices. The farmers on board where Swiss practitioners of what we today would recognize as Amish and/or Mennonite practices. They formed a tight-nit community who stayed with the ship for the decades it was in operation up until the Pluto mission.
The Cézanne was also a retirement community for Mages. They booked passage on the ship as a sort of permanent cruise. The mages could also act as expert consultants on those few occasions where the crew had to solve a problem that required old age and treachery.
Neither population required a continuous communications link with the outside world. The Neo-Amish adapted their concept of Rumspringe / Walkabout into a time period long enough for their children to take a ship back to "Civilization" and return after they (found themself/finished college/did their stint in the Spacey). They call it "Raumgang" a mashup of (Raum for Space and Rundgang for walkabout). These children, if they came back, usually brought a spouse who was open to the idea of living in a little town on the edge of the Solar System.
To get the sign-off from the shareholders of the Cézanne (who were predominately the farmers on the ship) ISTO had to guarantee a vessel would be arriving and departing from the core system at least every 6 months. If for nothing else, to allow their young adults a chance to engage in Raumgang.
The Cézanne would travel for 9 months out to the Kuiper belt, operate for 3 years, and then return. During the ship's scheduled maintenance the crew would have a chance to transfer on or off the vessel. The "townies" stayed on board, as the vessel was basically their home. The habitats would be operated on port power while the engine and reactors were refurbished, or replaced.