Service Time Model

In  Section 4.1.2 and Section 4.1.1 we obtained expressions for the seek and transfer times. We can now substitute these equations (19 and 8) for $t_{seek}$ and $t_{transfer}$ in Equation 2. This gives us an expression for the service time as shown in Equation 20:

$${t_{service}(\delta_x, \delta_y, T_{active}, T_y, r, r_l) =}$$

$$\frac{r}{r_l(\sqrt{\delta_x} + \sqrt{\delta_y} + 8 t_{settle} \sqrt{\frac{5}{\pi}})}$$

$$\big( (\sqrt{\delta_x} + 8 t_{settle} \sqrt{\frac{5}{\pi}}) (\frac{1}{8} \sqrt{\frac{\pi \delta_{x} }{5}} + t_{settle}) +$$

$$\delta_y \frac{1}{8} \sqrt{\frac{\pi}{5}}\big) +$$

$$\frac{8 r d_b}{T_{active}} (\frac{1}{\delta_y} (t_{TA} + \frac{t_{XM}}{T_y}) + \frac{1}{v_0})$$