What is the z-domain transfer function of variable delay? Is it possible to obtain the transfer function of a signal that has a variable delay? 

For instance, I have a signal consisting of 10 samples:
0,1,1,1,1,0,0,0,0,1

If I would apply a unit delay to the signal, the transfer function would be z^-1 and the signal is now:

0,0,1,1,1,1,0,0,0,0

What would be the effect e.g. transfer function if I delay the rising edge of the pulse by 1 delay as above, but the falling edge would be delayed by 2 samples? The signal then would be:

0,0,1,1,1,1,1,0,0,0

Could this be derrived as a combination of z^(-1) and z^(-2) or this transfer function is non-linear?

Thank you for your answers.
A (discrete-time) system with a variable delay must be time-varying, and for this reason it cannot be described by a transfer function of the form

$$H(z)=\sum_{n=-\infty}^{\infty}h[n]z^{-n}\tag{1}$$

where $h[n]$ is the impulse response of the system.
Only linear time-invariant (LTI) systems can be described by a transfer function as given in $(1)$.