Average Deadheading Energy Consumption (ADEC)

• Average Deadheading Energy Consumption (ADEC) is a metric that quantifies energy used during non-revenue segments, capturing overhead in both mobility systems and IEEE 802.11ah networks.
• The metric employs formal definitions with calibrated coefficients, integrating factors like distance, travel time, and protocol-specific parameters to compute energy overhead.
• Empirical analyses show significant energy savings, with reductions up to 72% in urban mobility and halved overhead in wireless systems through optimized parameter tuning.

Average Deadheading Energy Consumption (ADEC) is a quantitative metric for evaluating the energy cost associated with non-revenue movements—termed "deadheading"—in both wireless sensor networks and urban mobility systems. In two distinct research contexts—IEEE 802.11ah WLAN energy modeling (Bel et al., 2015) and electric vehicle fleet simulation for on-demand mobility in Chengdu (Wu et al., 8 Nov 2025)—ADEC serves as the primary indicator of system efficiency, capturing overhead energy expenditure not directly linked to successful payload exchange or passenger service.

1. Formal Definition and Mathematical Formulation

ADEC is rigorously defined as the average energy consumption attributable to deadheading segments, computed per evaluation cycle or per served trip. In mobility systems (Wu et al., 8 Nov 2025), the definition is as follows: Let $U_{\mathrm{served}}$ denote the set of all trips served in a period ($N = |U_{\mathrm{served}}|$). For each trip $u$, the deadheading distance $md_u$ (distance from previous dropoff $d_{u-1}$ to next pickup $o_u$), and travel time $td_u$, yield the segment energy

$$DEC(md_u,td_u) = B_1\,md_u + B_2\,\Bigl(\frac{60\,md_u}{td_u}\Bigr)^2 md_u,$$

with calibrated coefficients $B_1 = 0.132$, $B_2 = 5\times10^{-6}$, resulting in energy in kWh. The ADEC is then

$$\mathrm{ADEC} = \frac{1}{N} \sum_{u=1}^{N} DEC(md_u, td_u).$$

In the 802.11ah wireless context (Bel et al., 2015), ADEC is derived as the subset of per-cycle energy consumption corresponding to all "overhead" periods: $$\mathrm{ADEC} = P_{RX}\cdot t_{RX}^{hdr} + P_{ID}\cdot t_{ID}^{hdr}$$ where $t_{RX}^{hdr}$ and $t_{ID}^{hdr}$ capture intervals of beacon listening, multicast reception, and protocol-mandated wait times.

2. Underlying Energy Models

In urban mobility simulation (Wu et al., 8 Nov 2025), the vehicle energy model is drawn from De Cauwer et al. (2015), combining a constant per-kilometer term (rolling resistance, accessory loads) and a velocity-squared term reflecting speed-related inefficiencies: $$DEC(md,td) = 0.132\,md + 5\times10^{-6}\,\Bigl(\frac{60\,md}{td}\Bigr)^2 md$$ All distances $md$ are in kilometers, times $td$ in minutes. This provides sensitivity to route geometry and urban congestion.

For 802.11ah (Bel et al., 2015), the device energy model partitions energy by operational mode (TX, RX, idle, sleep), with deadheading defined as periods when the station is active but not engaged in payload transfer—specifically, beacon listening and contention wait times: $$E_{avg} = P_{RX} t_{RX} + P_{TX} t_{TX} + P_{ID} t_{ID} + P_{SL} t_{SL}$$ ADEC isolates the header-related RX and idle contributions, using explicit formulas for beacon durations and occurrence probabilities.

3. Empirical Values and Comparative Reductions

Quantitative assessments reveal significant gains in energy efficiency from strategic deadheading reduction:

• In Chengdu’s ride-hailing simulation (Wu et al., 8 Nov 2025), traditional street-hailing taxis record ADEC ≈ 0.33 kWh/trip; ride-hailing achieves ≈ 0.095 kWh/trip, a 72.1 % decrease.
• 802.11ah model optimization (Bel et al., 2015) shows that optimal settings (DTIM interval, TIM grouping) can halve ADEC while maintaining service guarantees.

Spatially and temporally, ADEC reduction via ride-hailing is most pronounced in low-density zones (e.g., 98 % reduction at the Airport) and during midnight/early-morning hours, corresponding to longer unproductive relocations.

4. Sensitivity to System Parameters

ADEC is strongly influenced by the configuration of operational parameters:

Parameter	Effect on ADEC	Context
DTIM Interval $T$	Larger $T$ lower ADEC ∝ $p_{MC}$	WLAN (Bel et al., 2015)
TIM Groups $N_{TIM}$	Increase minimizes beacon overhead	WLAN (Bel et al., 2015)
Fleet Size	Increasing fleet yields diminishing returns	Mobility (Wu et al., 8 Nov 2025)
Geofencing	Improves ADEC in center, worsens overall	Mobility (Wu et al., 8 Nov 2025)
Demand Management	No significant ADEC change for trip rejection	Mobility (Wu et al., 8 Nov 2025)

For wireless sensor networks, increasing $N_{TIM}$ reduces the TIM beacon overhead, with optimal energy found around $N_{TIM}\approx8$. Expanding the DTIM interval $T$ suppresses multicast overhead but is bounded by latency and success requirements.

In mobility systems, fleet size has quickly saturating benefits: beyond 1.8× baseline, further ADEC reduction is negligible. Geofencing tightens dispatch in dense subregions, lowering local ADEC, but overall system efficiency declines due to fragmentation. Demand-side policies (e.g., trip removal) are neutral on ADEC, affecting only passenger waiting times.

5. Component Analysis of Deadheading Overhead

ADEC encapsulates, by construction:

• In urban fleets: energy cost for each repositioning move absent passengers, computed as the sum of segment-wise DEC across all served trips, isolating infrastructure and operational inefficiency.
• In 802.11ah WLANs: overhead resulting from mandatory protocol activity—DTIM/TIM beacon reception, multicast waiting, and protocol backoff (DIFS)—which does not result in a successful data exchange.

Practically, the main contributors to ADEC in both domains are those processes required for protocol fidelity or operational readiness but which directly detract from revenue or payload throughput.

6. Limitations, Extensions, and Methodological Considerations

Both papers identify limitations inherent to macro-level ADEC modeling. In mobility (Wu et al., 8 Nov 2025), assumptions include that all vehicles are homogeneous and electric, auxiliary loads (HVAC, charging losses) are not explicitly captured, and repositioning between trips ignores tactical route optimization. Deadheading is not decomposed by vehicle platform (ICE/hybrid/electric).

For WLANs (Bel et al., 2015), ADEC does not include payload or contention-related idling, and specific per-device variations (due to battery health, environmental factors, or proprietary power-saving firmware) are not modeled.

Recommended refinements include: integrating fine-grained, trace-based energy models (e.g., real-world brake-regeneration profiles); explicit routing or parking optimization between deadheading segments; dynamic demand-side feedback loops such as dynamic pricing for ride-hailing; mixed-fleet analysis spanning electric and non-electric systems.

7. Broader Implications and Future Directions

ADEC is emerging as a critical performance metric in energy-aware design for both urban mobility and wireless IoT deployments. Its explicit calculation allows quantification and targeted reduction of non-productive infrastructure energy cost, enabling comparative assessment of service modes (e.g., ride-hailing vs. cruising) or protocol configurations (802.11ah beacon intervals). In both domains, future research may focus on integrating demand-responsive strategies, dynamic repositioning, and heterogeneous device models to enhance the granularity and practical impact of ADEC-based analyses. A plausible implication is that further optimization of ADEC will lead to not only lower operational energy budgets but also improved service quality via more effective resource allocation and scheduling.