I'm not sure that is going to work. GSM is time division multiplexed with a co-ordinating channel that issues the time slots to stations in the vicinity. If you introduce delays it will stop working and by extending the range you risk more than one device 'grabbing' the same time slot. I think GSM repeaters have to be based on "store and forward" principles, basically, your repeater is seen as a mobile device from the first cell station and connects normally then passes the data packets to a second cell station to increase the range. I don't think analog signal boosters will work.
I may be wrong, I was involved in the designing GSM base stations in the USA back in the 1980s but I haven't worked on it for many years.
Brian.