Modeling a signal through the environment
You can model frequency shift this way:


$s = s \circ exp(j \cdot 2\pi \cdot (f-\hat{f}) \cdot t)$,


where $\circ$ means Hadamard product and $s$ is input signal vector (e.g. frame or part of data stream of interest). You can implement this operation in the baseband or in carrier frequency. The effect will be generally the same. 

As you've told your signal time can increas if multipath exists. You can model it as FIR filter of the order of your impulse response length. Refer to the channel modeling techniques for details.

Also your signal time can vary (increase and decrease) if relative motion of receiver and transmitter exists. This effect appears in the case of so called wideband model, e.g. sonic channel in the underwater communications. For such a case signal bandwidth is comparable to carrier frequency so Doppler shift is very different for low frequencies and high ones in the band of interest. It causes varying of signal duration in the receiver end. If you deal with radio signals your signal model is probably narrowband so this effect is neglectable.