Graph neural network-based cell switching for power optimization in ultra-dense heterogeneous networks

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Following the analysis setups, this part covers the experimental consequence evaluation for the proposed GBCSS, in contrast with different benchmarks. Qualitative discussions concerning GBCSS with some state-of-the-art options are additionally included on this part.

For learning-based options (GNN and FA), an offline coaching stage was first carried out. The skilled GNN and FA’s coverage had been then exported to provide statistical outcomes (i.e. metrics (E_{saving}) and (Lambda _{%}) with respect to (N_{sc})) utilizing the validation dataset. Lastly, the 2 day samples within the take a look at dataset is used to emulate the web deployment for cell-switching execution that gives outcomes for (P_{tot}) all through the day (24 h). Until in any other case acknowledged, the outcomes for every (N_{sc}) case are generated utilizing the GNN skilled with the dataset generated for that case. Notice that throughout the on-line execution part, it’s attainable to replace the educational fashions utilizing the newest collected knowledge to additional enhance the fashions’ performances. Nevertheless, such on-line mannequin updating is past the scope of this paper.

Earlier than presenting the outcomes concerning every metric, it is usually necessary to investigate the convergence behaviors of the GNN coaching. Utilizing the configured GNN setups, the loss operate worth outlined in Eq. (18) was collected throughout the coaching stage. For all thought-about (N_{sc}), the GNN mannequin managed to converge inside the first 20 epochs for 7 out of 8 (N_{sc}) circumstances, with the minimal epochs for convergence being 5, and the utmost epochs round 55. Because the loss information for all 8 (N_{sc}) circumstances can’t be summarized clearly in a graphical method, the important info has been offered above.

Statistical outcomes from validation set

Determine 3 exhibits the outcomes of metrics (E_{saving}), (Lambda _{%}), and (eta _{%}) with respect to (N_{sc}). The typical values utilizing the 4 day samples within the validation dataset are calculated for the metrics. It’s noteworthy that the ES algorithm has solely been executed for (N_{sc} in {4, 8, 12, 16 }) as a result of time consumption burden because the algorithm is very computationally demanding with a complexity of (O(2^{textbf{N}})). Which means that the processing time for the ES algorithm doubles for each unit (N_{sc}) increment. In distinction, GBCSS learns to discover a sub-optimal answer that approximate to the optimality as a lot as attainable whereas sustaining a a lot decrease computational complexity of (O(textbf{N})).

The metric (E_{saving}) is the optimization goal for cell switching options in accordance with the issue definition in Eq. (11), and is a vital metric to think about. It may be seen in Fig. 3a that the every day whole power saved will increase when (N_{sc}) is raised for all cell-switching strategies, based mostly on the truth that deploying extra SCs results in elevated energy consumption, whereas creating extra potentialities for offloading and cell switching when the MC has adequate useful resource to take over, and therefore bigger power saving.

For (N_{sc} in {4, 8, 12, 16}), the saved power utilizing the ES algorithm is the best among the many thought-about options, and could be anticipated to stay so for bigger (N_{sc}) values if ES was to be executed. For GBCSS, the power saved is decrease than that of ES. For (N_{sc} in {4, 8, 12, 16}), the GBCSS achieves 53.97%, 63.04%, 66.82%, and 60.08% of ES’ (E_{saving}) efficiency, leading to a 62% (E_{saving}) efficiency for the 4 (N_{sc}) circumstances. Furthermore, the GNN is ready to additional improve the (E_{saving}) for a lot of deployed SCs because the slope of the (E_{saving}) curve has clearly elevated for (N_{sc} in {24, 28, 32}). The detailed dialogue concerning this side is roofed within the one-day efficiency evaluation with extra supporting outcomes.

Apparently, the (E_{saving}) utilizing the FA benchmark is clearly bigger than that of GBCSS for many thought-about (N_{sc}) circumstances apart from (N_{sc} = 8) and 12, during which each options lead to comparable (E_{saving}). GBCSS can obtain a most 103.61% and a minimal of 62.28% (E_{saving}) performances in contrast with utilizing the FA, with a mean of 86.60% (E_{saving}) efficiency in contrast with utilizing the FA for all (N_{sc}) circumstances. This implies that the FA benchmark outperforms GBCSS in uncooked power saving.

Nevertheless, it’s equally necessary to additionally take into account the metric (Lambda _{%}), which signifies how a lot of the unique site visitors load with out cell switching (i.e. All-on) could be preserved utilizing totally different cell-switching answer and represents the optimization constraint outlined in Eq. (12). Based on its definition, the utmost worth for (Lambda _{%}) is 100%, which signifies that all authentic site visitors load is preserved after cell switching execution.

Determine 3b exhibits this metric with a reference purple dashed line of the All-on technique stands for the higher certain. It may be seen within the determine that ES has (Lambda _{%} =100%) for (N_{sc} in {4, 8, 12, 16}), and is cheap to imagine this development shall be constant for different (N_{sc}) circumstances. As compared, utilizing the proposed GBCSS ends in a mean (Lambda _{%}) of 99.63% for all 8 (N_{sc}) circumstances, with a most of 99.88% and minimal of 99.31%. This implies that the GNN learns to protect the person QoS as a lot as attainable when lowering the HetNet unit’s power consumption.

In distinction, it may be seen that the (Lambda _{%}) utilizing FA decreases from 99.77% for (N_{sc} = 4) to 78.30% for (N_{sc} = 32). Which means that in comparison with GBCSS, the additional power saved when utilizing the FA benchmark as proven in Fig. 3a will value 21% of the unique site visitors load and therefore the person QoS within the worst case. The reason being that utilizing the offline skilled FA algorithm for on-line choice making results in rather more frequent choice making that causes the MC to overload and thus person QoS downgrade, as solely the MC can take over the site visitors load of a SC in accordance with the issue formation.

Contemplating each power consumption and site visitors masses, Fig. 3c exhibits the normalized every day power effectivity (eta _{%}) for the thought-about cell switching options with respect to All-on. It’s clear that (eta _{%}) of utilizing the ES algorithm is the best and achieves a mean (eta _{%}) of 13.74% among the many (N_{sc}) circumstances, with a most power effectivity achieve of 16.25% in comparison with that of All-on, whereas (eta _{%}) utilizing the FA answer drops repeatedly and turns into even decrease than that of All-on as a result of a big proportion of authentic site visitors load being sacrificed to realize greater energy saving. As compared, GBCSS achieves a mean and most (eta _{%}) of 8.50% and 10.41% respectively in comparison with All-on. The development of (eta _{%}) utilizing GBCSS is much like that of ES based mostly on the outcomes for (N_{sc} in { 4, 8, 12, 16}) in accordance with Fig. 3c, whereas total the power effectivity achieve utilizing the GNN is about 62% for these (N_{sc}) circumstances. Furthermore, assuming the typical (eta _{%}) (13.74%) utilizing the ES is preserved for (N_{sc} in {20, 24, 28, 36}), the GNN can obtain a most 75.76% of ES’ efficiency concerning power effectivity achieve.

However, the FA benchmark nonetheless outperforms the proposed GBCSS when (N_{sc} = 4) with FA’s (eta _{%}) being round 2.5% bigger as in Fig. 3c. A possible motive is that the GNN shouldn’t be in a position to additional approximate to the optimum answer when the gradient calculated by way of the loss operate Eq. (18) turns into too small, as studying to at all times change on the MC results in a big ({mathscr{L}}) enchancment when coaching the GBCSS. As compared, the FA benchmark avoids such state of affairs because the motion for the MC has predefined to be at all times ON. Nevertheless, the relative underperformance of GNN on this case could be thought to be insignificant as the general power saved on this case is low as a result of solely 4 SCs had been deployed.

Take a look at set efficiency outcomes

The outcomes generated with the take a look at dataset for one-day energy consumption utilizing every answer are offered for 3 (N_{sc}) circumstances (i.e. (N_{sc} in { 4, 12, 32})) that represents situations of a small, medium and huge variety of deployed SCs inside the thought-about (N_{sc}) circumstances. The outcomes of node dimension generalization take a look at for the GNN can be lined on this part.

Efficiency comparability on workday samples

Determine 4 exhibits the facility consumption per time slot utilizing GBCSS and different benchmarks all through a workday (from 00:00 a.m. to 11:59 p.m.) for the three (N_{sc}) circumstances. As a result of identical computational complexity motive as for statistical outcomes evaluation, the ES algorithm shouldn’t be executed to generate outcomes for (N_{sc} = 32).

Based on Eqs. (2) and (3), the facility consumption calculation is a linear transformation of (lambda) when no BS is put into sleep. Due to this fact, a HetNet unit’s site visitors load development all through a day could be inferred by the facility consumption development of the All-on technique. It may be seen in Fig. 4 that the HetNet unit’s energy consumption is comparatively low earlier than daybreak with solely a small variety of lively customers, whereas the site visitors load begins to rise round 8 a.m. and peaks earlier than noon, resulting in an elevated energy consumption interval with much less potential for energy saving. Later, the site visitors load begin to decline extra considerably within the late afternoon (4 p.m.), main to a different interval for power effectivity optimization utilizing cell switching.

As proven in Fig. 4a, all 3 cell-switching options are in a position to considerably scale back the facility consumption from 0 a.m. to eight a.m.. Throughout this era, the facility consumption utilizing GBCSS extremely mirrors the conduct of the ES algorithm. Through the high-traffic hours, GBCSS turns to observe the technique of All-on, which is a suboptimal technique for this time interval. From 4 p.m. till midnight, the GNN additionally learns to scale back the HetNet unit’s energy consumption, however the efficiency shouldn’t be as important because it does within the time interval earlier than daybreak in comparison with the optimum outcomes computed by way of ES. In distinction, the FA benchmark additionally mirrors the conduct of ES over the day, and total outperforms GBCSS particularly after 4 p.m.. Furthermore, throughout the busy hours between 9 a.m. and 4 p.m., it may be seen that for a while slots, the facility consumption of utilizing the FA benchmark turns into lower than that utilizing ES. As a result of ES produces the optimum cell switching selections for energy saving whereas sustaining the unique site visitors masses within the HetNet unit, it may be inferred that FA’s additional power-saving comes from sacrificing the person QoS.

For the (N_{sc} = 12) case in Fig. 4b, the conduct of the ES algorithm stays the identical as within the (N_{sc} = 4) case, whereas a bigger hole could be discovered in contrast with the facility consumption of All-on, suggesting a bigger potential for power effectivity optimization. Equally, GBCSS additionally demonstrates comparable outcomes constant to these in Fig. 4a, with the efficiency after 4 p.m. additionally improved in comparison with that within the (N_{sc} = 4) case. Nevertheless, the outcomes of the FA benchmark begin to have extra important fluctuations in Fig. 4b, with clearly decrease energy consumption in contrast with utilizing the ES throughout the busy hours. Combining with the ends in Fig. 3b, which means that the FA benchmark begins to output extra selections that causes person QoS sacrifices.

As for the (N_{sc} = 32) case in Fig. 5c, the fluctuation within the outcomes of the FA benchmark has even worsen with the variety of selections sacrificing the person QoS additional rises. An apparent rationalization to this development is that the FA benchmark makes use of the linear operate approximation approach to signify the worth operate, which can not have sufficient expressiveness for situations with greater complexity. In distinction, GBCSS exhibits rather more steady outcomes that’s constant to these for (N_{sc} = 4 ,{textual content {and}}, 12). Furthermore, GBCSS additionally begins to change off SCs throughout the busy hours, and the facility consumption throughout this era turns into smaller than that of All-on for (N_{sc} = 32) in accordance with Fig. 4c. That is rather more much like the technique that ES produces based mostly on ends in Fig. 4a,b. As mentioned within the above part, the primary motive to it may be that the loss operate can’t be considerably optimized when (N_{sc}) is small, following the calculation in Eq. (18). Furthermore, cell switching throughout a time interval with intensive site visitors primarily ends in marginal energy consumption enchancment for small (N_{sc}), as proven by the outcomes utilizing the ES algorithm. In distinction, a bigger (N_{sc}) results in extra potential for a major loss discount throughout the busy hours. This may be thought to be a bonus to take advantage of, as a result of the envisioned ultra-dense HetNet improvement for past 5G will lead to considerably giant numbers of SCs to be deployed, the place the GNN might discover nice potential in approximating to the optimum cell switching choice. All the outcomes offered on this part to date correspond to the discoveries in Fig. 3.

Moreover, it may be seen in Fig. 4 that typically utilizing GBCSS and the FA benchmark ends in extra energy consumption than utilizing the All-on technique throughout the busy hours for (N_{sc} = 4) and eight. This raises one other query as it’s counter-intuitive to have such observations that switching off some BSs causes extra energy consumption than at all times maintaining all of the SCs on. Nevertheless, contemplating Eq. (2) along with the parameters in Desk 1, it’s attainable for sure cell switching selections to trigger an total bigger energy consumption by offloading to the MC. For instance, switching off a half-loaded femto BS ends in a 2.1W energy consumption discount underneath the experiment configuration, however the MC taking up the offloaded site visitors (assuming adequate useful resource) could have its energy consumption raised by 47W, which results in a -44.9 W energy consumption achieve. A proper mathematical proof could be present in¹² that makes use of the identical energy mannequin and BS energy profiles.

In abstract, the proposed GBCSS is ready to carefully approximate the optimum cell switching selections computed by the ES algorithm when the overall site visitors load on the HetNet unit is low, whereas tends to generate a suboptimal methods throughout the time interval with intensive site visitors. However, such suboptimal technique throughout the busy hours could be improved when (N_{sc}) turns into bigger (Fig. 4c), when the GNN begins to reflect the behaviors of ES as in Fig. 4a,b. The one-day efficiency analysis on a workday produces outcomes that carefully correspond to the statistical outcomes generated from the validation dataset.

Efficiency comparability on vacation samples

Underneath the identical setup, Fig. 5 exhibits the facility consumption utilizing totally different cell switching options on the New yr’s day vacation (2014/01/01). The trending within the figures corresponds with the occasion of individuals celebrating the brand new yr’s eve, resulting in a lot of lively customers and therefore excessive energy consumption all through the early hours after midnight. As compared, the general energy consumption throughout daytime is extra steady in contrast with that throughout the workday pattern in Fig. 4.

Moreover, it’s clear that utilizing cell switching options ends in important energy financial savings throughout the daytime. That is much like the 2 power-saving time durations in Fig. 4, suggesting that in such a vacation, cellular service requests throughout the regular busy hours should not as intensive in comparison with that in a workday. Furthermore, in Fig. 5a, the facility consumption utilizing each GNN and FA is almost similar to the optimum outcomes utilizing the ES benchmark. As well as, the GNN makes no selections that trigger the facility consumption to be greater than All-on and FA additionally performs considerably higher on this regard. The reasoning to this phenomenon is that learning-based options study to seize the facility saving potential throughout low-activity time durations higher than throughout the high-activity durations, mixed with the ends in Fig. 4.

Different outcomes present in Fig. 5 are extremely corresponding to the findings in Fig. 4, such because the outcomes utilizing the FA benchmark have fluctuations with the magnitude will increase for a bigger (N_{sc}), whereas the GNN is extra steady on this regard. As these elements are already mentioned within the workday case, this part consists of no additional gildings.

Generalization functionality on node dimension

A outstanding characteristic of GNN fashions is their node dimension invariance, indicating that so long as the info with the same underlying topology could be expressed utilizing the identical graph illustration, a GNN mannequin skilled utilizing knowledge of node dimension i could be immediately use to provide outcomes for node dimension j ((i ne j)). This characteristic enormously boosts the generalization functionality of GNN fashions in contrast with different ML fashions, resulting in a major value discount when deploying GNN fashions to totally different situations for an outlined activity.

Due to this fact, this part presents the node dimension generalization take a look at to the proposed GBCSS. The workday knowledge samples within the take a look at dataset is used. Two GNN fashions skilled with coaching knowledge of (N_{sc} = 4) and 32 are utilized on this take a look at, whereas the node dimension for the take a look at case is (N_{sc} = 12) for each fashions to present a clearer comparability. As a result of RL-based options want to verify the characteristic house and/or motion house that can’t be naturally prolonged by the mannequin itself with out reapplication, the FA benchmark is therefore not relevant on this analysis.

The one-day energy consumption outcomes of this take a look at is proven in Fig. 6. These outcomes exhibits that each fashions skilled with totally different node sizes (each bigger and smaller node dimension throughout the coaching stage) could be immediately utilized within the (N_{sc} = 12) state of affairs. For the 2 lower-traffic durations, 0 a.m. to eight a.m. and after 4 p.m., each fashions generate comparable outcomes to that in the identical node dimension situations in Fig. 5b. Moreover, it may be seen that the fashions observe some element from what discovered within the authentic node dimension state of affairs. For instance, the GNN mannequin skilled with (N_{sc} = 4) produces some sub-optimal selections that result in greater energy consumption round 9 a.m., much like that in Fig. 4a, whereas the GNN mannequin skilled with (N_{sc} = 32) tends to lead to giant energy consumption round 0 a.m., which comparable to the conduct in Fig. 4c. Sadly, the mannequin skilled with (N_{sc} = 32) doesn’t keep the technique to change off some SCs for energy saving as in Fig. 4c for (N_{sc} = 12), whereas retains mirroring All-on throughout the busy hours, much like that in Fig. 4b. The rationale to this may increasingly nonetheless be the discovered loss operate traits, {that a} smaller (N_{sc}) results in insignificant loss enchancment for cell switching throughout busy hours, as mentioned for the workday case.

The node dimension generalization take a look at outcomes counsel that fashions skilled with one node dimension could be immediately utilized to the same state of affairs with one other node dimension. Though the efficiency is probably not optimum, this characteristic can enormously scale back the price of mannequin switch, as the entire GNN mannequin could be immediately utilized with none preparatory steps. After the switch, the mannequin could be up to date utilizing knowledge collected within the new state of affairs to study the underlying patterns to enhance efficiency.