Reducing planning time in swarm exploration via quorum sensing and discrete-event scheduling

 Corresponding author: Fredy Hernán Martínez Sarmiento Copyright © 2025 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0. Reducing planning time in swarm exploration via quorum sensing and discrete-event scheduling Fredy Hernán Martínez Sarmiento * Facultad Tecnológica, Universidad Distrital Francisco José de Caldas, Bogotá, Colombia. Global Journal of Engineering and Technology Advances, 2025, 24(03), 021-033 Publication history: Received on 22 July 2025; revised on 28 August 2025; accepted on 1 September 2025 Article DOI: https://doi.org/10.30574/gjeta.2025.24.3.0258 Abstract This paper presents an event-driven framework for multi-agent exploration that couples a lightweight scheduler and blackboard with a Quorum Sensing (QS) coordination layer. Robots emit and sense a diffusive field using two scalar probes and a contact signal, select one of four motion primitives from local gradients, and make fully asynchronous, arrival-triggered decisions without global rounds. The QS field is integrated on a grid with explicit diffusion, decay, and no-flux obstacle boundaries, while motion uses arrival-time timestamps to reduce intermediate events and avoid idle time. Across six layouts (200×300 cells) and swarms of 4–20 agents, the QS policy lowered planning time by about 33% and route imbalance by about 31% relative to an asynchronous non-QS baseline; average path length remained competitive and repeated length fell by roughly 17%. Ablations (no circumnavigation, fixed emissions, single-probe sensing) degraded at least one metric, clarifying the role of each mechanism, and scheduler wall-time scaled nearly linearly up to six threads. Because sensing and actuation are minimal and decisions are local, the controller maps cleanly to differential-drive robots and short-range signaling, enabling transfer to low-cost platforms while preserving reproducibility. Keywords: Asynchronous coordination; Discrete-event simulation; Multi-agent exploration; Quorum sensing; Swarm robotics 1. Introduction Cooperative exploration in unknown indoor environments remains a central problem in cyber–physical systems, where sensing constraints, limited compute budgets, and the need for reproducible evaluations converge [1–3]. Teams of small, differential–drive robots must build actionable knowledge of the space while avoiding prolonged idle periods and unnecessary revisits [1, 4]. Traditional formulations depend on global maps or round–based coordination, both of which tend to induce contention and latency in practical deployments [5]. In contrast, local decision rules that exploit short– range information offer a path to scalable behavior on modest hardware. This study adopts that perspective and places the emphasis on methods that can be transferred to real platforms without extensive instrumentation [6–8]. The problem addressed here is to explore two–dimensional layouts with multiple agents while reducing coordination overhead and maintaining path efficiency [9, 10]. Four metrics guide the analysis: planning time (PT), average path length (APL), route imbalance (SPL), and repeated length (RPL) [11]. Agents are equipped with a contact signal for obstacle incidence and one or two scalar probes that read a synthetic concentration, used as a proxy for neighborhood density. Decisions are taken asynchronously on arrival events, avoiding global synchronization barriers that stall progress when a subset of agents faces difficult geometry [12, 13]. The intent is to balance minimal sensing with principled scheduling so that throughput remains high as team size grows. Global Journal of Engineering and Technology Advances, 2025, 24(03), 021-033 22 A gap persists between lightweight coordination schemes and simulation frameworks that expose their performance under realistic constraints. Centralized or frontier–heavy approaches increase communication and memory load, and synchronous rounds leave robots waiting even when local opportunities exist [14, 15]. Moreover, many simulators do not couple the coordination rule with an event–driven core that can attribute costs to scheduling and policy separately [16, 17]. The approach proposed in this paper fuses a thread–pooled discrete–event engine with a Quorum Sensing (QS) strategy in which each robot emits and senses a diffusive field obeying a simple balance of diffusion, decay, and point sources [18]. By relying on thresholds over that field and local gradient estimate, agents select motion primitives without recourse to a global planner or explicit task assignment. The central hypothesis is that QS–based local thresholding lowers PT and improves SPL relative to an asynchronous non–QS baseline while keeping APL and RPL competitive [19, 20]. The method rests on three pillars: an event scheduler that timestamps the next arrival rather than advancing in small fixed steps, a constant–time blackboard that provides structured access to shared state, and a controller that combines dual–probe gradient estimation with circumnavigation when obstacles block direct ascent. Mode–dependent emissions shape the field so that useful regions sharpen and stale concentrations dissipate at a controlled rate, while an activation cap limits crowding. The evaluation spans six layouts and swarms of four to twenty agents, includes ablations that remove individual mechanisms, and measures scheduler behavior under increasing thread counts. Together these elements provide a transparent account of where improvements arise and how they scale. Assumptions and scope are stated up front to frame the discussion and guide future extensions. The environment is planar with static, opaque obstacles; diffusion is isotropic with constant coefficients; agents are homogeneous and execute four motion primitives at nominal speeds. These choices align with entry–level hardware, where the QS scalar can be approximated by short–range radio or infrared intensity and contact is available through bumpers or short– range rangefinders. Reproducibility is supported by fixed seeds, explicit parameter ranges, and configuration files that capture both simulation and controller settings. The remainder of the paper is organized as follows: Section 2 details the system architecture; Section 3 presents the modeling choices and algorithms; Section 4 reports results and analyses; Section 5 discusses implications and limitations; and Section 6 concludes the paper. 1.1. System Overview This work addresses cooperative exploration of unknown two–dimensional layouts using a discrete–event simulation engine that embeds a Quorum Sensing (QS) coordination layer. The targeted objective is to shorten the overall planning time (PT) while keeping the average path length (APL) competitive, reducing route imbalance (SPL), and limiting repeated traversals (RPL). Agents are modeled as differential–drive robots equipped with minimal sensing: a border/contact detector (CS) and one or two scalar intensity probes (IS) for QS. Coordination is fully local and asynchronous; each robot decides upon arrival events without waiting for global rounds, thereby avoiding idle time typical of synchronous schemes. Figure 1 summarizes the architecture and its main data paths, highlighting the separation between the event–driven core, the blackboard, and the service layer that implements visibility, QS field dynamics, and optional route planning. The engine follows a priority–queue dispatch by timestamps and a thread–pool executor for parallel handling of ready events. Each agent, the QS field service, and the metrics module register their own event types; the scheduler packs ready events and dispatches them to idle workers, which improves CPU utilization on multicore hosts. Shared state is exchanged through a blackboard that stores fixed–layout arrays for agent attributes, field tiles, and cached visibility masks, enabling 𝑂(1) lookups and writes via index views. The service layer offers four capabilities: (i) a grid map with occluding obstacles and ray–casting visibility, (ii) a QS field simulator with diffusion and decay, (iii) an optional A* routine for diagnostic comparisons, and (iv) a metrics/logging utility that aggregates PT/APL/SPL/RPL and QS–specific indicators. To keep the control loop lightweight, only the agents and the QS field run at fine event granularity; map and metrics are invoked on demand or on coarse schedule. Global Journal of Engineering and Technology Advances, 2025, 24(03), 021-033 23 Figure 1 High–level architecture. A thread–pooled event scheduler drives models and services. Agents publish/subscribe to a constant–time blackboard (pose, mode, local QS samples, emissions), while services expose visibility queries, QS field updates, metrics, and optional A* The QS field represents the local “autoinducer” concentration sensed and emitted by robots. In continuous form, with position 𝑥 ∈𝛺 ⊂ ℝ2, the field ℎ(𝑥,𝑡) evolves as: 𝜕ℎ 𝜕𝑡 =𝐷𝛻2ℎ−𝛾ℎ+∑𝑠𝑖 𝑁 𝑖=1 (𝑡) 𝛿(𝑥−𝑝𝑖(𝑡)) (1) where D>0 is the diffusion coefficient, γ∈(0,1) is the decay factor, s_i (t)≥0 is the emission of agent i, and δ(⋅) is the Dirac impulse at the agent position p_i (t). Obstacles enforce a no–flux boundary condition 𝛻ℎ(𝑥,𝑡)⋅𝑛(𝑥)=0, 𝑥 ∈𝜕𝛺𝑜𝑏𝑠 (2) with n the outward normal at the obstacle boundary. In the simulation, (1) is discretized on a uniform grid with spacing Δ and explicit time step Δt, yielding ℎ𝑢,𝑣 𝑡+1 =(1−𝛾𝛥𝑡) ℎ𝑢,𝑣 𝑡+𝐷𝛥𝑡 𝛥2∑ (ℎ𝑎,𝑏 𝑡−ℎ𝑢,𝑣 𝑡) (𝑎,𝑏)∈𝒩4 +∑𝑠𝑖𝑡 𝑁 𝑖=1 1[(𝑢,𝑣)= 𝑝𝑖𝑡] (3) where 𝒩4 is the 4–neighborhood and 1[⋅] is the indicator function; zero–normal flux at obstacles is enforced by mirroring boundary samples. Two IS taps separated by 𝛥𝑑 along the robot frame provide a local gradient estimate: 𝛻ℎ (𝑝𝑖𝑡) ≈ [ ℎ(𝑝𝑖𝑡+𝛥𝑑 𝑒𝑥)−ℎ(𝑝𝑖𝑡) 𝛥𝑑 ℎ(𝑝𝑖𝑡+𝛥𝑑 𝑒𝑦)−ℎ(𝑝𝑖𝑡) 𝛥𝑑 ] (4) which is robust enough for mode switching and motion selection when combined with the contact signal. Agents implement a compact state machine with five modes: wild (ergodic exploration with small random perturbations), gradient ascent (follow 𝛻ℎ ), circumnavigation (wall–following when CS is active), grouping (stabilize near a field maximum), and active/virulent (elevated emission). Activation is triggered by a density threshold while keeping an upper bound on concurrently active units, modeled as: 𝑎𝑐𝑡𝑖𝑣𝑎𝑡𝑒𝑖(𝑡) = 𝕀[ℎ(𝑝𝑖,𝑡)> 𝜂 ∧ |𝑊(𝑡)| <𝑇] (5) Global Journal of Engineering and Technology Advances, 2025, 24(03), 021-033 24 where 𝜂 is the concentration threshold, 𝑊(𝑡) is the set of active agents, and 𝑇 is a population cap. A reproduction logic at the simulation level activates nearby idle nodes when density is low and proximity holds, which accelerates coverage without altering the local sensing assumptions. Emission is adjusted by mode, for example 𝑠𝑖(𝑡)=𝑠𝑏𝑎𝑠𝑒 in wild/grouping and 𝑠𝑖(𝑡)= 𝑠ℎ𝑖𝑔ℎ in active, which sharpens maxima and speeds up convergence. Motion relies on four primitives Forward, Backward, TurnLeft, and TurnRight selected from the sign and orientation of the estimated gradient in the body frame and the contact flag. The event system schedules motion by arrival time rather than by fine time–stepping: if a primitive advances the robot by ∥𝛥𝑥𝑖∥ at nominal speed 𝑣𝜋𝑖, the next event is: 𝑡𝑎𝑟𝑟,𝑖 = 𝑡𝑛𝑜𝑤 +∥𝛥𝑥𝑖∥ 𝑣𝜋𝑖 (6) which reduces the number of intermediate events and lowers scheduling overhead. Primitive selection can be expressed as where 𝜃𝑖 is the robot heading, 𝑣𝑖 is the forward unit vector, and 𝜖 > 0 rejects weak gradients. Figure 2 depicts the event loop: perception, QS update, policy switch, primitive execution, and scheduled arrival, with no global barriers between agents. Figure 2 Event flow for one agent and the QS field service. Decisions are taken on arrival events; perception and field updates run as separate ready events. Asynchrony eliminates idle periods due to global synchronization The blackboard records per–agent pose, mode, last primitive, local samples (ℎ,𝛻ℎ ), emission 𝑠𝑖, and timestamps; field tiles are stored as contiguous arrays with halo cells to implement (9) by reflection. Visibility caches speed up line–of– sight queries for contact prediction, while optional local/ global belief maps can be maintained for analysis without influencing the QS controller. Event insertion/removal is 𝑂(𝑙𝑜𝑔𝐸) on a binary heap with 𝐸 enqueued items, whereas Global Journal of Engineering and Technology Advances, 2025, 24(03), 021-033 25 blackboard reads/writes are amortized 𝑂(1) by using fixed offsets and strided views. A thread–pool worker model (one worker per ready batch) and the absence of global coordination barriers sustain throughput as the number of agents grows. Faults are naturally contained because decisions are local: removing an agent does not invalidate others’ control loops or the QS service. Table 1 summarizes symbols and principal configuration parameters. Maps use a 200×300 grid; the perception radius is chosen so that the visible window is roughly one tenth of the environment by area, which keeps sensing costs moderate. QS diffusion and decay are tuned for stability of (3) under the explicit update, and thresholds (𝜂,𝑇) control activation pressure and limit crowding. Primitive speeds and step sizes determine the cadence of arrival events through (13), which influences PT directly. Radio–based or infrared short–range signaling can approximate the QS scalar for hardware transfer, while the contact sensor maps to bumpers or short–range rangefinders. Table 1 Core symbols and configuration parameters Symbol / Parameter Meaning 𝐷, 𝛾 QS diffusion coefficient and decay factor 𝜂, 𝑇 Activation threshold and active–set cap 𝑠𝑏𝑎𝑠𝑒, 𝑠ℎ𝑖𝑔ℎ Emission levels by mode 𝛥, 𝛥𝑡 Grid spacing and integration time step 𝛥𝑑 Probe spacing for gradient estimate 𝑣𝜋 Nominal speed for each motion primitive Map size 200×300 cells (4–neighborhood) Perception radius ≈20 cells (ray–casting visibility) Threads Scheduler worker count (CPU–bound) 2. Methods The study adopts a two–dimensional grid world with static, opaque obstacles and ray–casting visibility, and models each robot as a differential–drive agent endowed with minimal sensors. A contact signal (CS) reports border or obstacle incidence, and one or two scalar probes (IS) sample a synthetic Quorum Sensing (QS) field used as a local coordination medium. All decisions are taken asynchronously on arrival events; no global synchronization barriers are introduced, and a lightweight coordinator is retained only for logging and metrics. Spatial discretization relies on a uniform lattice of size 200×300 cells, with a neighborhood limited to four orthogonal adjacencies to keep computations predictable. The QS field ℎ(𝑥,𝑡) represents a local concentration that diffuses, decays, and receives point injections from agents. In continuous form and with 𝑥 ∈ 𝛺 ⊂ ℝ2, the dynamics read (1) with 𝐷 > 0 the diffusion coefficient, 𝛾 ∈ (0,1) the decay factor, 𝑠𝑖(𝑡)≥0 the emission of agent 𝑖, and 𝑝𝑖(𝑡) its position. Obstacles enforce Neumann boundary conditions to prevent spurious flux across opaque walls (2) where 𝑛 is the outward unit normal. On a grid with spacing 𝛥 and time step 𝛥𝑡, an explicit scheme using the four–neighbor Laplacian gives (3) where 𝒩4 denotes the orthogonal neighbors and 1[⋅] is the indicator function. Stability is preserved by choosing 𝐷𝛥𝑡/𝛥2≤ 1 4 ⁄ for the explicit stencil and by clamping the field to a finite interval [0,ℎ𝑚𝑎𝑥] to avoid numerical drift. No–flux boundaries are implemented by mirroring halo samples at 𝜕𝛺𝑜𝑏𝑠, which keeps the discrete gradient orthogonal to obstacle faces and reduces artifacts near corners. Local sensing is obtained from two intensity samples displaced by a small offset 𝛥𝑑 along the robot frame, which permits estimating a forward–finite–difference gradient. With 𝑒𝑥 and 𝑒𝑦 unit vectors in the body frame (4), and a weak– gradient threshold 𝜖 > 0 rejects noisy directions that lack consistent ascent. Measurement noise is modeled as additive bounded disturbance 𝑛𝑡 with |𝑛𝑡|≤𝜈, which is handled by clipping the sample before differencing. The contact signal 𝐶𝑆 ∈{𝑡𝑟𝑢𝑒,𝑓𝑎𝑙𝑠𝑒} is triggered by an impending collision predicted by the visibility service, and serves as a mode guard toward wall–following. This sensing set stays within the capabilities of low–cost platforms while providing enough directional information for a stable policy. Each agent runs a compact state machine with five modes: wild (ergodic exploration with small randomized headings), gradient ascent (follow 𝛻ℎ ), circumnavigation (wall–following when 𝐶𝑆 =𝑡𝑟𝑢𝑒), grouping (stabilize near a field Global Journal of Engineering and Technology Advances, 2025, 24(03), 021-033 26 maximum), and active/virulent (increased emission). Activation follows a density threshold with an upper bound on concurrent active units (5) with 𝜂 the concentration threshold, 𝑊(𝑡) the active set, and 𝑇 a cap that limits crowding. A reproduction logic at the simulation level activates nearby idle nodes when density is low and proximity holds, which accelerates coverage without changing the local sensing model. Emission 𝑠𝑖(𝑡) depends on the mode, e.g., 𝑠𝑏𝑎𝑠𝑒 in wild/grouping and 𝑠ℎ𝑖𝑔ℎ in active, with a first–order smoothing 𝑠𝑖(𝑡)←(1−𝛼)𝑠𝑖(𝑡−)+𝛼𝑠𝑖⋆ to avoid oscillations. The combination of thresholds, caps, and emission smoothing yields predictable transients and limits the formation of unstable clusters. Control uses four motion primitives {FORWARD, BACKWARD, TURNLEFT, TURNRIGHT} at nominal speeds {vF, vB, vL, vR}, and a selector that maps the estimated gradient and the contact flag to a specific action. The simulator schedules motion by arrival time rather than by fine time–stepping: if a primitive advances the robot by ∥ 𝛥𝑥𝑖∥ at speed 𝑣𝜋𝑖, the next event is (6), which reduces the number of intermediate events and maintains throughput under load. The selection rule is (7) with 𝜃𝑖 the heading and 𝑣𝑖 the forward unit vector. Deterministic tie–breaking and small dithering are used in wild mode to preserve ergodicity without biasing the ascent decision when a reliable gradient appears. The discrete–event engine maintains a priority queue keyed by timestamps, packs ready events into batches, and dispatches them to a thread–pool executor. Event types include Perception, QSFieldUpdate, PolicySwitch, MotionPrimitive, Arrival, and EmissionUpdate, each with a fixed handler signature and constant–time access to shared state. The blackboard stores per–agent pose, mode, last primitive, local samples (ℎ,𝛻ℎ ), emission 𝑠𝑖, and timestamps; field tiles and visibility caches are exposed as strided arrays. Consistency is preserved by a single–writer discipline per slot and versioned reads, which avoids explicit locking for the common case. Push and pop operations on the queue cost 𝑂(𝑙𝑜𝑔𝐸) for 𝐸 enqueued items, whereas blackboard reads and writes are 𝑂(1) in the amortized sense. This combination sustains performance as the number of agents grows and keeps planning time low under multicore execution. Algorithm 1 summarizes the per–agent control loop, while Algorithm 2 lists the QS field update with boundary handling. Both routines use only local information and communicate via the blackboard, which simplifies instrumentation and facilitates reproducibility. The agent loop senses, estimates a gradient, switches modes under thresholds and caps, chooses a primitive, schedules its arrival, and updates emission with smoothing. The field update integrates diffusion and decay, applies mirrored halos at obstacle boundaries, and injects emissions at agent locations. The pair forms a closed loop in which the density–dependent signal steers the robots and the robots reshape the signal in return. Parameterization follows conservative stability bounds and practical sensing constraints. Table 2 lists default values and ranges used during tuning, which cover diffusion and decay, activation threshold and cap, probe spacing, primitive Global Journal of Engineering and Technology Advances, 2025, 24(03), 021-033 27 speeds, perception radius, and thread counts. The tuning protocol starts from 𝐷𝛥𝑡/𝛥2 at one fourth and reduces it when oscillations are detected near high–contrast interfaces; 𝜂 and 𝑇 are explored on a coarse grid to balance activation pressure and crowding. Probe spacing 𝛥𝑑 is set to the smallest value that yields a reliable finite difference given the noise level, whereas primitive speeds are selected to keep arrival intervals within a narrow band that preserves scheduler efficiency. These choices keep the controller simple while making the simulation stable and reproducible across seeds. Table 2 Default parameters and tuning ranges Parameter Symbol Default Range Diffusion Coefficient D 2.25×10-2m2/s [1.25, 3.00]×10-2m2/s Decay rate γ 1.0 s-1 [0.5, 2.5] s-1 Activation threshold η 0.55 (norm. by hmax=1) [0.45, 0.65] Active-set cap T [0.5 N] {[0.3N], [0.5N], [0.7N]} Probe spacing Δd 2 cells [2, 4] cells Primitive speeds vπ linear: 0.20 m/s angular: 90°/s linear: [0.15, 0.25] m/s angular: [60°,120°]/s Perception radius - 20 cells {15, 20, 25} cells Time step Δt 20 ms [10, 25] ms Threads - CPU cores {2, 4, 6, 8} Notes: Cell size Δ=0.05 m (map 200×300 cell⇒10×15 m). The default ratio satisfies DΔt/Δ2=0.18 with the explicit stability bound DΔt/Δ2≤1/4. Field values are clipped to hmax=1; η is expressed in normalized units. Linear speed apply to Forward/Back; angular speeds to TurnL/TurnR. For comparability and ablation, a non–QS asynchronous baseline is implemented with a random walk biased only by frontier visibility, plus three ablated QS variants: (i) no circumnavigation, (ii) fixed emissions without mode dependence, and (iii) single–probe sensing that suppresses the gradient estimate. Metrics include planning time (PT), average path length (APL), route imbalance (SPL), and repeated length (RPL), computed per run and reported as mean±standard deviation across five seeds. Additional QS indicators are tracked for analysis: time–to–quorum for a given fraction 𝑝 (TTQ), fraction of gradient–aligned steps (GRA), cluster cohesion as distance to nearest local maximum (CA), activation ratio |𝑊|/|𝑊0| over time (AR), and reproduction rate per unit time and area (RR). Statistical analysis uses Welch’s 𝑡–test or ANOVA depending on homoscedasticity checks, and reports 95% confidence intervals with Holm–Bonferroni correction when multiple pairwise tests are issued. Reproducibility is supported by fixed random seeds, capped run length of 2000 steps, exact map sizes, and a deterministic scheduling mode for debugging. 3. Results We evaluated the proposed QS–based exploration policy on six layouts (Empty, Parking, Hilbert, Classroom, Living, and House) using swarms of {4,8,12,16,20} agents and five independent seeds per configuration. Primary endpoints were planning time (PT), average path length (APL), route imbalance (SPL), and repeated length (RPL), computed per run and then aggregated as mean ± standard deviation. Additional indicators specific to QS were tracked to explain mechanism behavior: time–to–quorum (TTQ) for a target coverage fraction, rate of gradient–aligned steps (GRA), activation ratio over time (AR), and cluster cohesion distance to local maxima (CA), together with the reproduction rate (RR). Statistical comparisons between the QS policy and an asynchronous non–QS baseline used Welch’s 𝑡–test with Holm–Bonferroni correction across layouts and swarm sizes; effect sizes were reported with Cliff’s 𝛿 when distributions were not assumed normal. All results below follow the simulation protocol and numerical settings presented in the previous sections, including stability limits for the explicit stencil and arrival–time scheduling for motion events. The first set of results concerns PT and SPL, which capture coordination overhead and load sharing, respectively. Aggregated over all layouts and swarm sizes, the QS policy reduced total PT from 14.8±4.2 s to 9.9±3.1 s (−33.1% relative change; 𝑝 < 0.001, 𝛿 = 0.62) and lowered SPL from 178±40 to 122±32 cells (−31.5%; 𝑝 < 0.001, 𝛿 = 0.58). Per–layout improvements in PT were consistent: Empty (−21%), Parking (−28%), Hilbert (−35%), Classroom (−31%), Living (−27%), and House (−30%), with a similar pattern for SPL reductions. These reductions reflect the absence of Global Journal of Engineering and Technology Advances, 2025, 24(03), 021-033 28 global barriers and the self–selection of goals by local gradients, which keeps agents productive even when others are still in transit. Figure 3 summarizes PT as a function of the number of agents. Figure 3 Planning time (PT) versus number of agents, aggregated across six layouts. Lines show mean values with shaded 𝟗𝟓% confidence intervals over five seeds per configuration. The QS policy consistently decreases PT, with larger relative gains in Hilbert and Classroom scenarios The second set of outcomes focuses on path efficiency (APL) and redundancy (RPL), which tend to be more sensitive to obstacle geometry than PT or SPL. Across all tested conditions, APL remained comparable between methods, with a slight advantage for QS: 598±90 versus 612±95 cells (relative change −2.3%; 𝑝 = 0.08), which indicates that the gradient–based policy does not pay a significant price in distance to preserve asynchrony. RPL, measured as the percentage of revisited steps, decreased from 19.7±4.1% to 16.3±3.6% (−17.3%; 𝑝 = 0.004), most notably in Parking and House, where local detours are frequent. These findings suggest that circumnavigation, coupled with a weak–gradient rejection threshold, reduces unnecessary oscillations near obstacles and sharp corners. Table 3 reports the main metrics aggregated over layouts and swarm sizes, together with relative changes against the baseline. Table 3 Primary metrics aggregated over all layouts and swarm sizes (mean ± std over 𝟔×𝟓×𝟓 runs). Relative change is computed as 𝜟% = Baseline−QS Baseline ×𝟏𝟎𝟎 Metric Baseline (Async) QS (Ours) 𝜟% PT [s] 14.8±4.2 9.9±3.1 +33.1 APL [cells] 612±95 598±90 +2.3 SPL [cells] 178±40 122±32 +31.5 RPL [%] 19.7±4.1 16.3±3.6 +17.3 To attribute the gains to specific mechanisms, we conducted an ablation study with three variants: (i) no circumnavigation, (ii) fixed emissions (mode–independent 𝑠𝑖), and (iii) single probe (no 𝛻ℎ  estimate). Removing circumnavigation increased APL and RPL (+11% and +14%, respectively) and raised PT by +6%, particularly in labyrinthine Hilbert layouts. Fixing emissions raised PT by +12% and SPL by +9% due to weaker maxima and slower group formation, while leaving APL essentially unchanged. Using a single probe reduced gradient fidelity and increased SPL by +13% and APL by +7%, indicating poorer alignment between headings and useful directions. Table 4 compiles the aggregated deltas versus the full QS policy. Global Journal of Engineering and Technology Advances, 2025, 24(03), 021-033 29 Table 4 Ablation study: aggregated relative changes (%) with respect to the full QS policy (negative is better than QS, positive is worse) Variant PT APL SPL RPL No circumnavigation +6 +11 +5 +14 Fixed emissions +12 +3 +9 +2 Single probe +9 +7 +13 +5 Mechanism–level indicators provide additional insight into why PT and SPL improve under QS. Median TTQ for 𝑝 =0.6 was 58 steps with an interquartile range (IQR) of [42,76], which shows that a majority of agents reach the activation threshold in a relatively short horizon. The rate of gradient–aligned steps (GRA) reached a median of 0.71 with IQR [0.65,0.77], consistent with sustained ascent once a reliable direction emerges. The activation ratio 𝐴𝑅(𝑡) at 𝑡 = 500 steps was 0.62 [0.55,0.68], and cluster cohesion (CA) measured as median distance to the nearest field maximum stabilized near 11.3 cells [8.4,15.0]. The reproduction mechanism remained modest, with 3.2 [2.4,3.9] activations per 103 steps, supporting coverage without flooding the map with active units. Table 5 summarizes these quantities for completeness. Table 5 QS–specific indicators reported as median [IQR], aggregated over layouts and swarm sizes Indicator Definition Value TTQ (𝑝 = 0.6) [steps] time to reach quorum fraction 58 [42,76] GRA [ratio] gradient–aligned step rate 0.71 [0.65,0.77] AR at 𝑡 = 500 [ratio] |𝑊|/|𝑊0| at step 500 0.62 [0.55,0.68] CA [cells] distance to nearest ℎ–maximum 11.3 [8.4,15.0] RR [/103 steps] reproduction activations 3.2 [2.4,3.9] Scalability was assessed by measuring scheduler wall–time and event throughput under thread counts {2,4,6,8} on the Classroom layout with 20 agents. The event scheduler exhibited near–linear improvements up to six threads, with wall– time decreasing from 6.2 s (2 threads) to 3.7 s (4 threads) and 2.6 s (6 threads), and then saturating at 2.5 s (8 threads). This behavior matches expectations for batch dispatch with diminishing contention on shared structures and confirms that the event–driven design scales well under moderate parallelism. The combination of arrival–time scheduling and an 𝑂(1) blackboard keeps per–event costs bounded, which limits queue churn even when agent counts grow. Figure 4 presents the scheduler curve with 95% confidence bands over five runs. A brief sensitivity sweep was performed to examine robustness to the main parameters of the QS field and the activation logic. Varying 𝐷𝛥𝑡/𝛥2 in [0.10,0.25] revealed a shallow minimum in PT near 0.18, with instability observed only beyond 0.25 as expected for the explicit stencil. Adjusting the activation threshold 𝜂 over a 20% band around the default showed a monotone PT trade–off: lower thresholds speed up TTQ but increase RPL due to premature clustering; higher thresholds delay activation and raise SPL. Changing the cap 𝑇 from ⌊0.3𝑁⌋ to ⌊0.7𝑁⌋ indicated that moderate caps yield the best SPL without harming APL, while very high caps reduce cohesion and increase planner jitter. Probe spacing 𝛥𝑑 affected gradient fidelity; values below two cells amplified noise, whereas larger offsets smoothed useful detail near narrow passages. Lastly, we note edge cases and runtime characteristics to round out the evaluation. Gradient stalls on flat plateaus occurred in 3.1% of runs and were mitigated to 1.2% by the emission smoothing factor 𝛼 = 0.25 and the weak–gradient threshold 𝜖 =0.02. Over–activation events caused transient RPL spikes when 𝜂 was set 10% below the default, but caps at 𝑇 =⌊0.5𝑁⌋ contained the effect without requiring global coordination. Average simulation time per configuration on an 8–core workstation was 31±5 s, processing 1.8×106 events on average; logs and configuration files were retained for every run. Confidence intervals for PT and SPL improvements excluded zero across all layouts, confirming that the gains are not tied to a single map family or swarm size. Overall, the results align with the intended design: local, asynchronous decisions informed by a diffusive signal lower coordination costs while preserving path efficiency and reducing imbalance.