Time result for my algorithm

The device time consists of multiple step, such as loading the circuit to the device, then the actual processor time and finally the return of the results.

Only the processor time scales with the number of shots, the device loading time, and result return are constant overhead. Thus it makes sense to see the behavior you saw; you have some constant time and then on top the time that scales linearly in the number of shots. You could find the time for the overhead if you do a linear fit to the total execution time, then the offset equals the overhead.

As a more concrete example, on a recent job the device load and return result together took about 10s and the processor time for 1024 shots was ~4s, and for 8192 ~28s (so even a little bit faster than 8x the 1024 shots time). Of course these numbers depend on the device you're using!