completly hypothectical question:
A Imperial navy BatRon (in this case 6 ships strong) is deploying to the Macguffin system on the edge of the imperium (which edge is unimportant) for an extended time. It is not expecting a full combat situation, but at the same time, it is expecting to see some form of action (be it anti-pirate, police actions, etc).
what would be the size and composition of the defensive screen attached to it? would it even have a screen (i assume so, but am not familar enough with traveller large scale space combat to know if thats plausible)
I suppose first you'd have to decide what definition of a BatRon you want to go by. For example MT's Fighting Ships of the Shattered Imperium defines a Batron as 4 battleships/dreadnaughts, 3 scouts, 2 auxilaries, 2 transports and 1 tanker.
Given that, I'd have the scouts put out a web of sensor sats with the CICs of those capital ships monitoring them. A thick screen of sensor sats is cheap, easily carried by a transport and deployed by the scouts and effective for giving plenty of warning. Additionally, I don't know of any restriction against one or more of those battleships actually being a fleet carrier of a similar size (for example a dreadnaught sized fleet carrier, 3 battleships, with 2 auxillaries (possibly filled by destroyers) would be a pretty formidable carrier group). Lots of fighter patrols would make a good picket screen as well.
But that all assumes you accept the definition from FSSI, some may not. There would also be the question of what, if any, attached assets were included in the task force. For example, some decriptions of SDBs (CTs FightingShips, p25) gives the example of many of these 200 Td boats being loaded into a transport and deployed that way, so maybe one of the transports is loaded with 60 of these SDBs (assuming a 20k Td transport with about 12k Td cargo, if you have bigger transports... well...

). Seems plausible and there's presedence for it. Or you could attach a squadron of destroyer escorts. Even a TankRon is listed as having a cruiser, 2 auxillaries, 4 escorts (destroyers), 4 scouts and 2 transports in addition to 4 tankers... that would beef up their screen quite a bit.
Personally, when I'm doing such things for a campaign I start by working out an overall table of organization and equipment for whatever area or force I'm dealing with (not just talking Traveller here, I do the same if I'm dealing with say a Baron or Earl for Harn), then I dispatch forces based on what they have available, their mission, and what other missions that same main force is having to cope with.
So if we were talking the Spinward Marches just as an example, I'd rough out the sector / domain fleet, then rough out what squadrons are where doing what, including not just that force but what forces might be nearby in other systems or subsectors. I do the same for the attacking force. That way I'm fairly well prepared no matter what the PCs do or what unexpected strategy they cook up (cause you know how players have a knack for wanting to try that one strategy you didn't think of

). Sometimes what ships get sent aren't the ideal mix, task forces are based as much on what was available as they are ideal military doctrine and organization. Having an idea what is going on in the theatre area and what the main force has to manage helps me sort out what is reasonably available which I think adds a touch of realism whether its Traveller, Steel Panthers or Harn.
The above might work well for you particularly if you want to run a campaign with smaller ship tonnages for the fleets or using reserve fleets, etc.