Sensitivity Analysis

maximum allowed share count SC over the ranges [1.5, 3], [0.3, 0.8], and [5, 15], respectively.

Figure 7plots the performance of ZS (for single storage hotspots) in terms of both the QoD improvements and the QoS overheads encountered for the different parameter values. Before describing the selection process of the default values for the different ZS parameters, we first illustrate the reasons for selecting each of these ranges.

We study the effect of changing the C threshold between 1.5 and 3. The selection of this range is based on the role of C in the ZS process. Recall that the pre-migration load of donor to the collective pre-migration load of the receiver and the migrator should be more than, or at least equal to, C for the ZS to take place (Inequality 4.1). Furthermore, the size of the traded zone to the pre-migration load of the migrator should be larger than, or at least equal to, C as well (Inequality 4.2). Thus, selecting a value for C which is lager than 3 will result in highly reducing the probability of satisfying the DMC, and in a consequent high reduction in the number of zone shares taking place in the network. Similarly, setting C to a small value would highly increase the number of zone shares and may cause cyclic migrations. We study the performance for C values ranging from 1.5 to 3 with an 0.1 increment. We only present the results for a subset of these values that captures the main learned lessons from the study.

We study the effect of changing the E parameter between 0.3 and 0.8. The selection of this value range is based on the role of E in the ZS process. Recall that the energy needed to send the traded zone to the pre-migration energy of donor should not exceed E (Inequality 4.3). Thus, E should definitely be less than 1 so that the donor does not deplete all its energy.

In fact, it should make sure to leave the donor with a good amount of energy. That’s why we select a value of 0.8 as the maximum for this threshold as to make sure that the donor has a least a fraction of 0.2 of its energy remaining after the zone sharing process. Furthermore, The energy of needed by the migrator in the zone sharing process (which comprises the energy needed to send its pre-migration load plus the energy needed to receive the traded

zone) to the energy of the migrator should not exceed E (Inequality 4.4). Thus, E should guarantee that the migrator is left with energy after the zone sharing process, exactly as it was discussed for the donor. The same argument follows for the receiver (Inequality 4.5).

As for the lower bound, selecting a very low fractional value for E will be too restrictive and would result in decreasing the probability of applying the ZS process, especially after the energy of the sensor nodes across the network is about to be fully consumed. In light of this, we selected a lower bound of 0.3 for E. Specifically, we study the performance for E values ranging from 0.3 to 0.8 with an 0.1 increment. We only present the results for a subset of these values that captures the main learned lessons from the study.

In addition to studying the ZS performance for SC = 1, i.e., testing the SHZS perfor-mance, we study the effect of changing the SC value between 5 and 15 hops (i.e., shares per zone). The reason for selecting 5 as the lower bound is to set a clear distinction between MHZS and SHZS. Based on our experiments, a smaller SC value, e.g., 2 or 3, is not sufficient to highly improve (or degrade) the performance of the SHZS scheme. In fact, our results show that pushing a hot zone only 2 or 3 hops away from its original storage sensor does not highly differ from pushing it for only one hop. In all these cases, the ZS ability to decompose the hotspot is limited. As for the upper bound for SC, setting SC to a very large value will result in completely disturbing the DCS index structure. This would result from the fact that hot zones will be sent very far from their original destination. Additionally, all mappings and routing decisions will be based on our ZS scheme rather than based on the underlined DIM scheme. To avoid this, we set the upper bound for SC to be 15. Specifically, we conducted experiments for SC values ranging from 5 to 15 with an increment of 1. We only present the results for a subset of these values that captures the main learned lessons from the study.

We now move on to discuss the results of our sensitivity analysis. We started our analysis by studying the effect of C on SHZS. To limit the effect of E, we set it to the maximum value of 0.8. This experiment resulted in a peak SHZS performance for C = 2, namely a 20% improvement on QoD with a 3.5% overhead on QoS. Thus, we select a default value of 2 for the C parameter.

Moving forward, we set C = 2 and study the effect of E on the SHZS performance. This

Figure 7: QoD Improvements vs QoS Overheads of the Different ZS Versions

resulted in a performance improvement that is inversely proportional to the value of E. The peak performance was achieved for E = 0.3 with a 25% QoD improvement and a 3% QoS overhead. Thus, we select a value of 0.3 to be the default value for E.

Using the default values for both C and E, we move on to study the performance of MHZS with SC = 5. As a first step, we verify that the default values already computed for SHZS achieve the best performance for MHZS as well. We start by studying the different C values while setting E to 0.3. For this study, the best performance is achieved when C = 2.

QoD improvements are about 55% and QoS overheads are around 5%. Similarly, we test the MHZS performance for the different E values. The value of E = 0.3 continued to score the best MHZS performance. This verifies the selection of the default values for C and E.

Finally, we study the effect of SC on the MHZS performance. We present the results for SC values of 10 and 15 (while setting the C and E to their default values). The results show that SC has a limited effect on the MHZS performance. The MHZS performance was almost identical for the two SC values, 10 and 15, with a 50% QoD improvement and an 8%

QoS overhead. Thus, we set the default value of 5 for the SC parameter.

Using the default values for C = 2, E = 0.3, and SC = 5 (right most point on Figure 7), we test the ZS performance against the different hotspot types and settings. Our exper-imental results are shown in Figures 8 to 28. In these figures, we compare the performance of the basic DIM versus the performances of both SHZS and MHZS, with respect to our different performance measures. It is important to mention that we only included the DIM as the sole reference scheme as our simulations have shown that it completely outperform both the LS and the GHT schemes. Thus, in order to present more accurate and complete graphs, we only plot the results for our ZS scheme and those for DIM.

4.1.8.2 Single Static Storage Hotspots The following three results compare the ZS