The zig-zag strategy seems trivially obvious - but it might not be the better strategy in a particular situation. I suggest rather than asking under what conditions this strategy is preferable, you ask under what conditions the counter-intuitive straight-line strategy is preferable.
The advantage of zig-zagging is that it presents a smaller "collision cross-section" both in terms of target area (side-on) and time (an arrow following the runner remains "on target" longer). The advantage of the straight-line path is that it gets the runner out of range in the shortest time. It also minimises the relative speed of impact, thus minimising damage - though in realistic scenarios this is unlikely to be significant.
The question needs further specification, in particular regarding the speed $c$ of the arrows, the time $\tau$ between shots (which includes reloading and aiming), and their range $R$.
I presume that B cannot try to dodge the arrows as they fly. But there are many other factors to consider. For example :
How much of a head start is B given?
How accurate (in terms of angular spread) is the archer's aim?
Does B follow a predetermined zig-zag path known to A (as in your conditions), or are his turns made at random?
Is gravity to be taken into account? The disadvantage of the straight-line path is then reduced as B gets further from A, requiring the arrow to be aimed away from the target and into the sky.
What cover is available? Reaching cover might be less risky than getting out of range.
The relative cross-sections presented by B to hits from the back, side and above. This could include any body armour or exposure of weak points.
Complications could be piled on indefinitely to make the mathematical model more realistic. Judicious simplifications are necessary, as in your model, to avoid unnecessary effort towards spurious accuracy. But without the minimum specifications suggested above ($c$, $\tau$, $R$) it is not possible to decide which strategy is best.
Generally: In the unrealistic case that the speed of arrows $c$ is less than the speed of the runner $v$, the direct route is clearly preferable. Even when $c > v$ the direct route might be preferable if it takes B out of range much quicker, presenting significantly fewer opportunities for shots to be taken.
Presumably B is given a "head start". This time is best used running directly away from A, and only then (possibly) zig-zagging. Likewise, while A is reloading B should run directly away from A.
Developing your model : I assume the 'head start' is the time $\tau$ between shots.
1. For the straight-line option, arrows are fired at times $n\tau$ where $n=1, 2, 3,...$, and reach B at times $t_n = n\tau \frac{c}{c-v}$. B is then distances $y_n=vt_n$ from A. 537
The number N of shots arriving within range is given by $y_N < R$.
I shall assume that the probability of hitting a target is proportional to the solid angle which it presents. Suppose A is certain to hit B if face-on and within a distance $y_0$. Then the probability of hitting B at distance $y$ is approx. $(\frac{y}{y_0})^2$ provided that $y>y_0$. So for this strategy the probability of B being killed is
$P_1 = \Sigma^N_1 (\frac{y_n}{y_0})^2$.
I assume that all hits are ultimately fatal. More realistically you could assign a probability of a hit being fatal; if non-fatal it reduces B's speed by a certain factor.
1. For the zig-zag option at angle $\theta$ to the straight-line direction, the speed of separation of B from A is now approx. $v_y=v\cos\theta$. To simplify calculations, I assume the length of the zig-zags is much smaller than the distance AB. Arrows reach B at times $t_n = n\tau \frac{c}{c-v_y}$. B is then distances $y'_n=v_y t_n$ from A. The number M of shots arriving within range is given by $y'_M < R$.
Since B is now slightly side-on to the arrows the target area is smaller by a factor of approx. $\cos\theta$. This assumes that B is a 'cardboard cut-out'. In realistic situations this factor could be ignored, except perhaps for shots from above.
The probability of hitting B is now approx. 586