Performance Dependencies

Based on the architecture and the layout model described in Section 3, we know that the design space of probe-based storage is relatively complex and involves many parameters such as the number of active tips per device, mover's movement range, and acceleration. To choose one configuration over another, we must understand how the physical configuration affects the performance. Therefore, we analyze the dependencies in the model between these parameters and the service time, which we wish to minimize.

Figure 4 is a dependency graph showing how performance is related to probe-based storage parameters [21]. The graph edges represent the dependencies, the leaf nodes are parameters, and the remaining nodes are intermediate variables. The dependencies in this graph reflect the parameters and layout presented in Section 3, although other models could be used both for the layout and for the physical behavior of the device [10]. The target in the graph is the service time, which is the sum of seek time and transfer time, as shown in Equation 1. We model each of these components separately:

$$t_{service} = t_{seek} + t_{transfer}$$ (1)

Our model for seek time, described in Section 4.1.2, assumes uniformly distributed requests. To adjust for sequentiality in workloads, we parameterize Equation 1 with the runlength calculated from the trace. To compute the runlength, we calculate the length, in bytes, of each sequential run in the trace and average these runs to compute the runlength in bytes, $r_l$.

Only the first request of a sequential run will require repositioning the mover, incurring seek time. Thus the ratio of average request size ($r$) to runlength ($r_l$) represents the fraction of requests that require seeks. We modified the service time equation (1) to use the runlength and obtained Equation 2:

$$t_{service} = \frac{r}{r_l} t_{seek} + t_{transfer}$$ (2)

Figure 4: A simplified design space parameter dependency graph. The head of the graph represents the service time, which is the minimization target. From the graph we can identify the parameters (represented by the leaves) on which service time depends.