Up to this point, the performance analysis of both pure-ALOHA and channel hopping protocols has been focused on the number of GWs on the network. In this section, we will focus our attention on the impact of the channel time allocation on the network performance. In the previous section, the time allocated by the GWs, per cycle, to each channel was static. Thus, despite the varying number of EDs and the number of GWs covering the network, the amount of time set to each channel remained unchanged, distributing the time unfairly.
5.1. Channel Time Allocation for a Single GW Network
To obtain the time allocation that grants the best network fairness, we first considered a single GW network with a variable number of EDs. For each network size, several channel time distributions were evaluated in order to find the ones that grant similar chances of channel access opportunities.
Table 4 presents the channel time allocations for each network size which yield the best fairness indicator. As expected, the channel time allocated to the Fast-Rate must be lower than for the other channels, regardless the network size, as the data rate is faster, and thus the EDs have more chances to access the medium.
Figure 10 illustrates the Jain’s network fairness according to the channel allocation times presented in
Table 4, where we can see that by using a customized time channel allocation time, according to the number of EDs in the network, the protocol is considerably fair when compared to a blindsided version of it, with a fixed allocation time. In particular, for a network of 2000 EDs, the network fairness index increased from
to
. As explained before, by using a fair channel allocation time we are reducing the channel time allocated to the fastest channel because the data rate is higher, thereby granting the same channel access opportunities to EDs in other zones. Naturally, such a reduction has an impact on the network goodput, as illustrated in
Figure 11, because EDs in faster zones are the ones that contribute more to the network goodput.
5.2. Channel Time Variation for Multiple GW Networks
By increasing the number of GWs, the number of EDs optimally using the Standard channel decreases. Therefore, in order to keep the network fair, the time allocated to the Standard channel must be reduced. To analyze the impact of the channel time variation in the scenario of multiple GWs, we decreased the amount of time initially given to the Standard channel and distributed to the non-Standard channels following the proportion of non-Standard times obtained for a single GW (hereafter simply denoted as percentage of decrease, or simply PoD). Therefore, the Standard channel time was decreased from 2.5% to 50%.
Let us start by analyzing a network with 2 GWs. As shown in
Figure 12, for large networks, the fairness index increases with the PoD until a maximum value is observed. For example, for a network size of 1500 EDs, this maximum is achieved when the PoD is around 15%, and for a network size of 100 EDs, the fairness peak is registered when the PoD is around 2.5%. When we remove more time from the Standard channel and give it to the non-Standard channels, i.e., when we increase the PoD, the fairness drops due to the lack of channel access opportunities of the EDs using the Standard channel as the optimal one.
As the EDs can transmit their packets at a higher data rate, competing for the medium more often, the network goodput improves with an increase in the PoD, as shown in
Figure 13. However, as the EDs that use channels with slower data rates have fewer transmission opportunities, network fairness is negatively affected.
When we install a third GW, the behavior of the network fairness, as shown in
Figure 14, is identical to the prior behavior. The PoD from which the network fairness starts to decrease is about 15% when the network has 1500 EDs, the same value registered for the 2 GWs scenario. However, the peak occurrence with the network growth does not always have increasing behavior. The network with 100 EDs, regardless of initially being the fairest scenario, was surpassed when the decrease surpassed 38%. This new threshold occurred later than in the 2 GWs network (34%).
Similarly to what happened in the scenario with 2 GWs, the network goodput for a 3 GWs scenario, illustrated in
Figure 15, increased with the time allocated to the faster channels, namely, the Fast-Rate channel, which allowed the EDs to access the medium more often.
At last, we present the results regarding the time allocation in a 5-GWs scenario. As shown in
Figure 16, we can see an increase in the network fairness until the PoD of the Standard channel time surpasses 25%, for a network with 1500 EDs. This time, the fairness in less populated networks, namely, 100 EDs, increases for a PoD below 25%.
The interception between the curves of 100 EDs and 250 EDs happened for a higher PoD, approximately 44%, as shown in
Figure 16. Furthermore, PoD above 40% had a more negligible influence on the fairness of networks with 1500 EDs. Like the networks with three GWs, the fairness peak does not always increase with the network growth; it starts to decrease above about 500 EDs.
Regarding the network goodput, the behavior is very similar to that registered for scenarios with two and three GWs: increasing with the time allocated to faster channels, as shown in
Figure 17.
To easily compare the network fairness,
Figure 18 presents the fairness behavior for each tested scenario and the different PoD of the Standard channel time. Due to the fairer distribution of GWs by the network, the scenario with five GWs was only outperformed for percentages below 15% and in networks with under 500 EDs.
The results also show an overlap between the three tested scenarios. First, the scenario with two GWs achieved better fairness than the others, followed by the network with three GWs. and last, the one with five GWs. This behavior is supported by
Figure 19, in which the curve representing the 0.95 fairness index moves towards higher PoD as the number of GWs increases. As seen, for a network with 100 EDs, the higher fairness achieved with the original time allocation occurred with a scenario with two GWs. However, as the number of EDs increased, better fairness was guaranteed by the scenario with three GWs when the PoD was around 5%. Then, above a PoD of about 13.4%, as the 0.95 fairness lines of three and five GWs intersect, the fairness of the latter scenario became the best.
When the scenario with five GWs had 1500 EDs, the fairness peak was at , as the PoD was equal to 25%. For the same PoD and network size, the fairness values verified for the other scenarios were and , for two GWs and three GWs, respectively. This is a clear difference, which is as marked as the time allocated to faster rate channels, per GW cycle.
As shown in
Figure 20, by comparing the goodput for all the tested scenarios, an increase was noticeable with the number of GWs, which became more accentuated with increases in the PoD and the network size, due to the decrease in the channel access competition of each GW. Along with this, the number of EDs in the ideal channel increases in the Fast-Rate channel, which results in an increase in the number of channel accesses for the same period of time. The transmissions are faster than in slower channels, leading to smaller restriction periods.
Figure 21 illustrates the percentage of collision for every tested scenario. The network with five GWs had the lowest number of channel access collisions when considering every medium access performed by the EDs. As referred to before, the main reason for this behavior is the reduction in the number of EDs sharing the channel and the lower probability of two or more EDs choosing the same time slot to transmit. Another reason is the decreasing possibility of the hidden-terminal problem. As the number of GWs increases, the EDs transmitting to a given GW, with a specific channel, are more within reach of the other EDs that also transmit to the same GW. Thus, the control packets are more likely to be received by the generality of the EDs, decreasing the number of situations where two EDs transmit at the same time because none of them receive the control packet sent by the other.