The interfacial transition zone, or ITZ, is the cement industry’s version of a chain’s weakest link. In ordinary concrete, this porous, calcium hydroxide-rich region between aggregate and mortar is where damage typically begins. Measuring its thickness, however, has always been messy. The classic backscattered electron porosity-gradient method suffers from inconsistent grayscale thresholds that can shift results by 10 to 20 micrometers, while the calcium-to-silicon ratio approach depends on subjective judgments about where a plateau begins and ends. Existing automated tools, developed for normal-weight concrete, break down when confronted with the low calcium content and pore-induced signal noise characteristic of lightweight aggregates. The Chinese team’s solution, dubbed HMM-SF, chains together a Gaussian hidden Markov model and Sigmoid fitting to read elemental line scans from energy-dispersive X-ray spectroscopy and pinpoint interface boundaries without any human annotation at all.

The clever part of the algorithm lies in how it exploits chemistry. Among ten elements profiled across the interface, calcium turned out to be the ideal reference signal, because the cement paste is the only calcium-rich phase in the entire system: the Portland cement contains 57.04 percent calcium oxide, while the coal gangue aggregate shell holds just 3.37 percent and the core a mere 2.32 percent. That steep, well-directed gradient, combined with the relatively high signal-to-noise ratio of calcium’s characteristic X-ray line, gives the model a clean fingerprint to track. The workflow first identifies and interpolates across pores that would otherwise corrupt the signal, then uses a two-state hidden Markov model with Viterbi decoding to classify each measurement point as aggregate or mortar, fuses multi-element gradients to locate candidate boundaries, and finally fits Sigmoid curves to the calcium and calcium-to-silicon profiles, defining the ITZ as the interval between 10 percent and 90 percent of the elemental transition.

The validation exercise is a textbook demonstration of why each algorithmic component matters. In a five-level ablation experiment, a naive K-means clustering baseline catastrophically over-predicted 226 interfacial zones, achieving an F1 score of just 0.308. Swapping in a three-state hidden Markov model cut predictions to 76 but inflated the mean thickness to an implausible 105.4 micrometers, because treating the interface as a discrete state cannot capture its graded nature. Introducing Sigmoid fitting corrected the mean width to a physically sensible 41.6 micrometers, artifact filtering suppressed spurious detections, and the final multi-element gradient fusion lifted the complete model to a precision of 0.926, a recall of 0.969, and an F1 score of 0.947 against 65 manually annotated reference positions across 33 specimens.

With the tool validated, the researchers quantified 68 interfacial zones across eight mix proportions and discovered that their thicknesses follow a lognormal distribution with remarkable consistency. The global mean came out at 44.9 micrometers, the median at 27.5 micrometers, and the extremes ranged from 9.4 to 148.8 micrometers, a strongly right-skewed spread. A Kolmogorov-Smirnov test on pooled, group-centered residuals returned a p-value of 0.972, confirming that all eight mixtures share the same distributional shape parameter of 0.761, with only the location parameter shifting between mixes. Strikingly, even at the highest water-to-binder ratio and aggregate volume fraction tested, no abnormal interfacial thickening appeared, suggesting the porous coal gangue aggregate may actually help optimize the interface rather than degrade it.

That counterintuitive behavior traces back to the aggregate’s internal curing. Scanning electron microscopy revealed that cement particles and fly ash cenospheres embed themselves in the rough aggregate surface’s open pores, which range from 8 to 135 micrometers, anchoring calcium silicate hydrate gel that grows outward and interlocks with the paste. Unconnected pores act as tiny water reservoirs, absorbing and slowly releasing moisture that refines the interface and suppresses the growth of coarse, detrimental calcium hydroxide crystals. Connected macropores, by contrast, release moisture too quickly, locally raising the water-to-binder ratio and promoting excessive ettringite formation that increases interfacial porosity. The mix design variables left clear fingerprints: fly ash at 25 percent produced the densest interfaces, a water-to-binder ratio of 0.2 yielded the thinnest mean zone at 20.2 micrometers, and aggregate volume fraction showed a U-shaped optimum near 40 percent.

The cross-scale analysis delivered the study’s most commercially significant insight: interfacial thickness alone does not control strength. Within the fly ash series, mixes with 22.5 to 89.9 percent thicker mean zones lost only 6.8 to 13.0 percent of their compressive strength, while the water-to-binder ratio series showed strength dropping 18.3 percent despite a mere 8.5 percent thickening. The volumetric picture proved far more predictive. The ratio of interfacial zone volume to mortar volume correlated most strongly with 28-day compressive strength, with a Pearson coefficient of negative 0.766, and strength rose 33.0 percent as that ratio fell from 5.94 percent to 1.26 percent. The average mortar thickness between aggregates, which stretches from 1007 to 2447 micrometers across the mixes, correlated positively, because thicker mortar layers dissipate stress and lengthen crack paths. A power-law regression combining the three representative parameters achieved an R-squared of 0.858, though the authors caution that eight group-level observations make these exploratory relationships rather than universal laws.

Perhaps the most visually compelling results came from overlaying digital image correlation strain maps onto microstructural images of the loaded specimens. In normal-weight concrete, the interfacial zone consistently lit up first, entering the high-strain state from the 0.4 peak-displacement stage onward and confirming the classic ITZ-dominated damage nucleation described in the literature. In the coal gangue concrete, the three phases evolved almost synchronously, with inter-phase differences in high-strain area fraction as low as 1 to 5 percent at peak load. The team interprets this as a weak-phase competition mechanism: whichever of aggregate, interface, or mortar is locally weakest fails first and steers the damage direction, while the interface merely acts as a boundary condition reshaping the competition. Crack skeleton analysis reinforced the story, with 57.8 percent of total crack length running through the mortar and only 0.6 percent through the interface, and crack densities 18 to 41 percent lower than in normal-weight concrete across all three phases.

For a field racing to absorb mountains of coal mining waste into structural materials, the implications are twofold. Practically, the study points toward mix designs with roughly 25 percent fly ash replacement, water-to-binder ratios between 0.20 and 0.30, and aggregate volume fractions of 30 to 40 percent as the sweet spot where strength and interfacial quality align. Methodologically, the open-source HMM-SF algorithm, available on GitHub, offers the first objective, annotation-free route to quantifying interfacial zones in porous lightweight aggregate systems, removing a long-standing source of subjectivity that has plagued cross-scale modeling. The authors are careful to note the limits: the method assumes a monotonic elemental transition and would need recalibration for high-calcium aggregates, and the small interfacial area fraction of about 2 percent limits statistical resolution at the current imaging scale. Even so, by fusing hidden Markov statistics, sigmoid mathematics, and full-field strain imaging, the work transforms a fuzzy microscopic boundary into a measurable, predictable design variable, and brings carbon-saving coal gangue concrete one large step closer to code-worthy credibility.

Subject of Research: Automated identification of the interfacial transition zone in coal gangue lightweight aggregate concrete and its correlation with compressive strength and cracking behavior

Article Title: Interfacial transition zone in coal gangue lightweight aggregate concrete: Automated identification, strength correlation, and cracking behavior

Article References: Zhao, X., Wu, T., Wang, Z., & Fan, S. (2026). Interfacial transition zone in coal gangue lightweight aggregate concrete: Automated identification, strength correlation, and cracking behavior. Case Studies in Construction Materials, 25, Article e06581. https://doi.org/10.1016/j.cscm.2026.e06581

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06581

Keywords: coal gangue, lightweight aggregate concrete, interfacial transition zone, hidden Markov model, EDS line scanning, digital image correlation, compressive strength, crack propagation, lognormal distribution, fly ash, internal curing, solid waste utilization

The N×On-Off/D/1 model describes a single server with deterministic service times, fed by N independent sources that each alternate between active ON periods, during which they emit packets, and silent OFF periods. This structure matters because real network traffic is nothing like the smooth, memoryless arrivals assumed in textbook models. Since the landmark measurements of Ethernet traffic by Leland and colleagues in the 1990s, engineers have known that packet streams are bursty and correlated, and that burstiness is precisely what inflates queues and delays. The On-Off source model captures this correlation in a tractable way, making it a workhorse for teletraffic engineering in broadband and wireless systems alike.

Before trusting any simulator, the researchers had to prove it reproduces known results. Their first validation stage used the M/D/1 queue, the classical model with Poisson arrivals and deterministic service, as a baseline. For this model, the asymptotic decay rate of the queue-length tail distribution is known in closed form, giving an exact mathematical benchmark. Across utilization levels rho ranging from 0.7 to 0.95, the simulator matched the theoretical decay rate to within one percent. That level of agreement is the kind of result that separates a credible simulation framework from a toy, and it established the foundation for everything that followed.

The second validation stage tackled the harder target: the Burst Scale Decay Rate, or BSDR, a closed-form approximation that predicts how quickly the probability of large queue buildups decays when many On-Off sources feed the buffer. Here the simulator tracked the approximation within 2.2 to 12.5 percent across the tested configurations. Crucially, the team did not treat that residual gap as an embarrassment. By running multiple independent replications and constructing confidence intervals, they showed that the discrepancy is a systematic property of the closed-form approximation itself, not random simulation noise. In other words, the simulator is more accurate than the approximation it was being tested against, a subtle but important inversion that gives engineers a clearer picture of how much to trust the analytical shortcut.

With the framework validated, the researchers turned to the central question: what does the distribution of per-packet queueing delay actually look like under bursty load? They examined three different ON/OFF configurations at utilization levels from 0.89 to 0.98, deep in the congested regime where wireless networks spend much of their operating life. Each operating point was simulated with five independent replications totaling roughly 700 million packets, an enormous dataset by any statistical standard. The scale matters because the question they were asking, whether a delay distribution follows a particular mathematical form, is exactly the kind of question where insufficient data produces misleading answers.

The verdict came from four independent distance measures: the Kolmogorov-Smirnov statistic, the Anderson-Darling statistic, the coefficient of determination between cumulative distribution functions, and the Bhattacharyya overlap coefficient. All four measures told the same story. As the load increases, the queueing delay distribution steadily approaches a lognormal shape. The Kolmogorov-Smirnov distance shrank to 0.051 at the highest loads, and the fixed-sample Anderson-Darling statistic, which is especially sensitive to the tails of a distribution, dropped by factors of three to seven. For network engineers, this is a genuinely useful regularity: the lognormal distribution, whose parameters can be estimated from a mean and a variance, offers a compact closed-form description of delay behavior that grows more accurate precisely where delays matter most, near saturation.

Yet the study is equally emphatic about the limits of that regularity. Bootstrap-corrected goodness-of-fit tests rejected exact lognormality at every single operating point, no matter how close the visual and distance-based agreement appeared. The authors therefore present the lognormal as an approximation with quantified accuracy rather than an exact law, a distinction that reflects a mature statistical philosophy. To test whether some other two-parameter distribution might do better, they systematically compared the lognormal against Weibull, gamma, log-logistic, and Lomax alternatives. The result was nuanced: at moderate loads the lognormal could lag behind the best competitor for a given configuration, but as load increased it became competitive with, and in some cases the best among, all the two-parameter candidates.

Configuration mattered too. The team’s sensitivity analysis showed that OFF-dominated or symmetric traffic patterns, where the silent period is at least as long as the active period, produced better lognormal agreement at moderate loads. Near saturation, however, this dependence weakened, suggesting that extreme congestion washes out the details of the source structure and drives the delay distribution toward a common heavy-tailed form regardless of how the bursts are shaped. This finding has practical implications for traffic engineering, because it tells operators when they can rely on a simple lognormal fit and when the specifics of their traffic mix demand a more careful analysis.

Perhaps the most consequential result concerns the tails, the extreme delays that determine whether a system meets the stringent latency budgets of 5G, the tactile internet, and ultra-reliable low-latency communications. Above a utilization of roughly 0.95, the fitted lognormal consistently overestimated the empirical 95th, 99th, and 99.9th percentile delays in every configuration tested, at P99.9 by factors ranging from 3.6 to 9.6 times the observed values. At moderate loads, by contrast, the sign of the tail error depended on the traffic configuration, sometimes underestimating the true risk. The authors frame the heavily loaded overestimation as a virtue: the lognormal acts as an empirically conservative closed-form tool for delay budgeting, erring on the safe side exactly in the regime where network dimensioning decisions are made.

The broader significance of the work lies in its marriage of large-scale simulation with rigorous uncertainty quantification. Rather than declaring a new universal law of network delay, the study delivers something more useful: a validated simulator, a calibrated understanding of when the BSDR approximation can be trusted, and a quantified recipe for using the lognormal as a delay-budgeting tool with known error bounds. As wireless networks absorb everything from factory robots to remote surgery, the difference between a guessed delay distribution and a statistically verified one translates directly into either wasted capacity or violated service guarantees. This research gives the engineers building that future a sharper instrument, and a candid account of its precision.

Subject of Research: Queueing-theoretic modeling and statistical validation of packet delay distributions in bursty wireless network traffic

Article Title: Validation of burst scale decay rate and analysis of lognormal delay distribution in NxOn-Off/D/1 queueing models for wireless network performance

Article References: Enisoglu, R., Inan, B. A., & Ugurlu, S. Y. (2026). Validation of burst scale decay rate and analysis of lognormal delay distribution in NxOn-Off/D/1 queueing models for wireless network performance. Cluster Computing, 29(13), Article 780. https://doi.org/10.1007/s10586-026-06591-y

Image Credits: AI Generated

DOI: 10.1007/s10586-026-06591-y

Keywords: queueing theory, N×On-Off/D/1 model, burst scale decay rate, lognormal distribution, packet delay, QoS provisioning, wireless networks, tail probability estimation, goodness-of-fit testing, network dimensioning, discrete-event simulation, 5G latency