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Dynamic capacity allocation control for resource sharing networks (RSN) is studied when the networks are in heavy traffic. The goal is to minimize an ergodic cost with a linear holding cost function. Our main result shows that the optimal cost associated with an associated Brownian control problem provides a lower bound for the asymptotic ergodic cost in the RSN for any sequence of control policies. A similar result for an infinite horizon discounted cost has been previously shown for general resource sharing networks in Budhiraja and Conroy (in Modeling, stochastic control, optimization, and applications, 2019) and for general 'unitary networks' in Budhiraja and Ghosh (Ann Appl Probab 16:1962–2006, 2006). The study of an ergodic cost criterion requires different ideas as bounds on ergodic costs only yield an estimate on the controls in a time-averaged sense which makes the time-rescaling ideas of Budhiraja and Conroy (in Modeling, stochastic control, optimization, and applications, 2019) and Budhiraja and Ghosh (Ann Appl Probab 16:1962–2006, 2006) hard to implement. Proofs rely on working with a weaker topology on the space of controlled processes that is more amenable to an analysis for the ergodic cost. As a corollary of the main result, we show that the explicit policies constructed in Budhiraja and Johnson (Math Oper Res 45:797–832, 2020; Ann Appl Probab 34:851–916, 2024) for general RSN are asymptotically optimal for the ergodic cost when the underlying cost per unit time has certain monotonicity properties. [ABSTRACT FROM AUTHOR]

In this study, we explore optimal service allocation within the Chinese hierarchical healthcare system with green channels, providing valuable insights for practitioners to understand how optimal service allocation is affected by various realistic factors. These green channels are designed to streamline referrals from community healthcare centers to comprehensive hospitals. We aim to determine the optimal capacity allocation for these green channels within comprehensive hospitals. Our research employs techniques from queuing theory and stochastic processes, e.g., diffusion analysis, to develop a mathematical model that approximates the optimal allocation of resources. We uncover both closed-form and numerical solutions for this optimal capacity allocation. By analyzing the impact of various cost factors, we find that an increase in costs within the green channel results in a lower optimal service rate. Additionally, patient preferences for specific treatments influence allocation, reducing the optimal share of services provided by general hospitals. The optimal solution is also affected by the proportions of different patient types. Through extensive simulations, we validate the accuracy of our model approximations under heavy traffic conditions, further examining sources of error to ensure robustness. Our findings provide valuable insights into optimizing resource allocation in hierarchical healthcare systems, ensuring efficient and cost-effective patient care. [ABSTRACT FROM AUTHOR]

Both walk-in and online customers appear in many service systems such as restaurants. Online customers are often given a target time for pick up, and the quality of the food/beverage can degrade if it is ready before the arrival of online customers. This distinctive feature brings essential difficulties in the analysis and control of such systems. In "Technical Note: Asymptotically Optimal Control of Omnichannel Service Systems with Pick-up Guarantees," Gao, Huang, and Zhang study the optimal control problem of such service systems based on a two-class single server queueing model. The paper proposes a nearly-optimal policy that keeps the server idle when the queue of online customers drops below a threshold and there are no walk-in customers. Motivated by the recent popularity of omnichannel service systems, we analyze the joint admission and scheduling control of a queueing system with two classes of customers: online and walk-in. Unlike walk-in customers, online customers are given a target time for pick up upon placing an order. Thus, in addition to minimizing the waiting costs of walk-in customers and the rejection cost of both classes, we need to minimize the earliness and tardiness costs of online customers. Such a distinctive objective makes the control problem difficult to analyze. We develop a novel analysis by adopting the idea of proving H = λ G to establish an asymptotic relationship between the waiting time cost and the queue length cost under general control policies in the heavy-traffic regime. We also design a policy and show that it is asymptotically optimal. Funding: X. Gao's research is supported in part by the Hong Kong Research Grants Council [Grants 14201520, 14201421, and 14212522]. J. Huang's research is supported in part by the Hong Kong Research Grants Council [Grants 14500819, 14505820, and 14501621] and the National Natural Science Foundation of China [Grant 72222023]. J. Zhang's research is supported in part by the Hong Kong Research Grants Council [Grants 16208120 and 16214121]. [ABSTRACT FROM AUTHOR]

We consider multiclass make-to-stock production/inventory systems in which the manager makes three decisions, including pricing, outsourcing, and scheduling, to maximize the long-run average profit. For a sequence of systems in the heavy-traffic regime, with linear or strictly convex holding/waiting cost functions, we propose a sequence of policies and establish its asymptotic optimality. Our proof combines the lower bound approach and a thorough steady-state analysis of the systems. We also establish general results on the existence and tightness of the stationary distributions of the state processes under a more general family of policies. Funding: X. Gao's research is supported in part by the Hong Kong Research Grants Council [Grants 14201520, 14201421, and 14212522]. J. Huang's research is supported in part by the Hong Kong Research Grants Council [Grants 14500819 and 14505820] and the National Natural Science Foundation of China [Grant 72222023]. [ABSTRACT FROM AUTHOR]

Introduction. The paper analyses the causes of appearance and development of defects of the solid block with wing rails and welded rail ends (monoblock crossing) operating under heavy and intensive traffic conditions. Failure of such crossings is caused by crack initiation and development processes, as well as by metal pitting on the tread surface. One of the effective methods to increase the life of crossings is to harden their tread surface with blast wave energy.Materials and methods. The metal microstructure of the prototype crossings was investigated using metallographic equipment based on Zeiss Axiovert 25 microscope with Thixomet Pro software. Chemical etching of the surface of the samples used a reagent of 4% nitric acid solution in distilled water. Hardness of the hardened layer was determined by the Brinell method as per GOST 9012–59 on a TSh-2M hardness tester.Results. The author found that DS.30G.2 defects (Classifier of Defects and Damages of Turnout Elements) could be caused not only by oxide spots and cast seams in the metal but also by insufficient strength characteristics of the crossing structure, which should be eliminated when putting the product into production; increased dynamic loads not foreseen for the respective product. Microcracks formed in further operation in the overmoulded metal layer at the tread surface (without removing the defective layer) result in metal delamination and pitting. Thus, the turning of crossings should include the removal of the entire defective layer in addition to the removal of the swells. The research has shown that the most effective technology is explosive hardening of the crossing tread surface.Discussion and conclusion. The results show that crossing life could be improved by pre-hardening of the tread surface.

High concentration of heavy metals on tree leaves could disrupt mitosis in plant cells, leading to damage during cell division, and thereby reducing the number of stomata. Hence, this study evaluated the concentration of Pb, Zn and Cu in Leaves of Mangifera indica, Parkia biglobosa, Azadirachta indica, Delonix Regia, Schefflera arboricola, and Albezia. Lebbeck trees along Major Road Sides in Makurdi Metropolis, Benue State, Nigeria using standard methods. The concentrations of Pb, Zn, and Cu were significantly higher in A. Lebbeck, S. Actinophylla D. Regia than the rest of the plant species. The trend of metal concentration varied followed the order: Pb > Zn > Cu. Mean concentrations of Pb, Zn, and Cu were significantly higher in heavy traffic areas than other sampling areas. The results of the study suggest that the tree leaves samples could potentially serve as bioindicators for Pb, Zn, and Cu in environmental pollution area. [ABSTRACT FROM AUTHOR]

In this study, we explore optimal service allocation within the Chinese hierarchical healthcare system with green channels, providing valuable insights for practitioners to understand how optimal service allocation is affected by various realistic factors. These green channels are designed to streamline referrals from community healthcare centers to comprehensive hospitals. We aim to determine the optimal capacity allocation for these green channels within comprehensive hospitals. Our research employs techniques from queuing theory and stochastic processes, e.g., diffusion analysis, to develop a mathematical model that approximates the optimal allocation of resources. We uncover both closed-form and numerical solutions for this optimal capacity allocation. By analyzing the impact of various cost factors, we find that an increase in costs within the green channel results in a lower optimal service rate. Additionally, patient preferences for specific treatments influence allocation, reducing the optimal share of services provided by general hospitals. The optimal solution is also affected by the proportions of different patient types. Through extensive simulations, we validate the accuracy of our model approximations under heavy traffic conditions, further examining sources of error to ensure robustness. Our findings provide valuable insights into optimizing resource allocation in hierarchical healthcare systems, ensuring efficient and cost-effective patient care.

High concentration of heavy metals on tree leaves could disrupt mitosis in plant cells, leading to damage during cell division, and thereby reducing the number of stomata. Hence, this study evaluated the concentration of Pb, Zn and Cu in Leaves of Mangifera indica, Parkia biglobosa, Azadirachta indica, Delonix Regia, Schefflera arboricola, and Albezia. Lebbeck trees along Major Road Sides in Makurdi Metropolis, Benue State, Nigeria using standard methods. The concentrations of Pb, Zn, and Cu were significantly higher in A. Lebbeck, S. Actinophylla D. Regia than the rest of the plant species. The trend of metal concentration varied followed the order: Pb > Zn > Cu. Mean concentrations of Pb, Zn, and Cu were significantly higher in heavy traffic areas than other sampling areas. The results of the study suggest that the tree leaves samples could potentially serve as bioindicators for Pb, Zn, and Cu in environmental pollution area.

In this study, an attempt has been made to assess the influence of Corn Cob Ash (CCA) as filler in asphalt concrete mix. The effect of corn cob ash on mechanical properties of the asphalt concrete such as Marshall stability, flow, volumetric properties, and indirect tensile strength of asphalt concrete for heavy traffic roads has been evaluated. A total of thirty (30) asphalt concrete specimens were prepared with basaltic stone dust (BSD) and corn cob ash as a filler with bitumen content between 3.5% and 5.5% at varying increments of 0.5% and the Marshall stability test was performed on full mixes to determine the Optimum Bitumen Content (OBC) of the mixtures. From the test results, it is seen that specimens made with corn cob ash and basaltic stone dust are found to have satisfactory Marshall properties and moisture susceptibility showed that mixes using CCA filler provide better resistance to moisture effect than mixtures using BSD filler. Optimum bitumen content of CCA, and BSD were found out as 4.69%, and 4.86%, respectively. It is seen that maximum stability is observed by CCA filler materials. The value of stability of the asphalt concrete mixture using CCA and BSD is 11.4kN and 10.9kN, respectively, which satisfies the limiting value of 8.006 kN. Research findings indicated that the Indirect Tensile Strength Ratio (ITSR) of the paving mixes using basaltic stone dust was 93.71%, and corn cob ash was 97.04% which satisfies the criteria provided in the Ethiopian Road Authority (ERA) and Asphalt Institute Standard Specifications. Hence, it is generally concluded that the corn cob ash can effectively be used as filler in paving mixes in place of the most commonly used filler such as basaltic stone dust. Corn cob ash is a viable agriculture waste product that can be used as filler materials in the production of asphaltic concrete for heavy-trafficked roads. Overall, the use of corn cob ash as filler in hot mix asphalt concrete partly solves the significant agricultural waste disposal problem of the environment. [ABSTRACT FROM AUTHOR]

Increased production of wastes from different companies and agricultural areas creates severe surrounding trouble in terms of management and removal in Ethiopia. The utilization of agricultural waste products and residue in construction work is an excellent alternative solution in reducing the solid waste disposal problem of the environment. In this research, the application of maize cob ash (MCA) in asphalt concrete production is investigated as filler material in hot mix asphalt for binder course. Physical and chemical tests were investigated for MCA. Asphalt specimen prepared using crushed stone dust (CSD) as filler without maize cob ash used as a control material. The content of CSD filler was replaced with MCA at a rate of 0%, 25%, 50%, 75%, and 100% by weight of CSD. A total of thirty (30) mix specimens were prepared, fifteen asphalt concrete samples were prepared by a 6% of CSD as filler by weight of aggregate with bitumen content between 4.5 and 6.5% at varying increments of 0.5% by total weight of the mix to determine the optimum bitumen content (OBC). The remaining specimen was prepared at 5.30% OBC to find out the optimum replacement rate of MCA. The values of Marshall stability, flow, unit weight, air voids, and voids in mineral aggregate and voids filled with asphalt at 75% replacement of CSD with MCA were, 11.7 KN, 3.13 mm, 2.360 g/cm3, 4.0%, 14.58%, and 72.56%, respectively. Research findings indicated an optimum value of MCA could be replaced the CSD is 75% by weight of CSD filler or 4.5% (by weight of aggregate in the production of hot mix asphalt binder course for heavy-trafficked roads. Results also indicated that agriculture waste materials used in this investigation can be constructively used as partial replacement of CSD fillers in the hot mix asphalt binder course. Overall, it is established that MCA is a viable agriculture waste product that can be used as filler materials at a specified percentage in the production of asphaltic binder courses for heavy-trafficked roads. [ABSTRACT FROM AUTHOR]

One of the important causes of air pollution is automobile emissions Automobile exhausts can be toxic and harmful to plants. In light of this, this study aimed to examine the anatomical and micromorphological effects of auto exhaust pollution on Pistacia vera L. (Pistachio), an important agricultural plant. Pistachio leaflet samples taken from heavy traffic areas and rural areas were compared anatomically and micromorphologically. Also, the data were statistically evaluated. As a result of the study, it was seen that there are anatomical and micromorphological differences between the plant in the rural area and the plant in the heavy traffic area in the city center where air pollution and the number of cars are high. In particular, significant differences were detected in the epidermis surface and cuticle structure, trichome cover, stomatal characteristics, as well as mesophyll width, and epidermis anticlinal outer wall width. As a result, the study revealed that the agriculturally important P. vera is affected by pollution anatomically and micromorphologically. [ABSTRACT FROM AUTHOR]

We derive a general spherical coordinate formula for a quantum state of n-qubit register and study n-qubit operation rules on (n + 1) -sphere with the target to help developing a (photon or other technique)-based programmable quantum computer. The newly developed angle-based n-qubit operation rules are simple and efficient, which reduce the complicated quantum multiplication and division operations to simple addition and subtraction operations just like those used in a conventional computer. The rules for n-qubit operations are realized through measurement-based feedback controls and quantum entanglements. In the meanwhile, we derive the scaling limits (called reflecting Gaussian random fields on a (n + 1) -sphere) for n-qubit quantum computer-based queueing systems under two different heavy traffic regimes. The queueing systems are with multiple classes of users and batch quantum random walks over the (n + 1) -sphere as arrival inputs. In the first regime, the qubit number n is fixed and the scaling is in terms of both time and space. Under this regime, performance modeling during deriving the scaling limit in terms of balancing the arrival and service rates under first-in first-out and work-conserving service policy is conducted. In the second regime, besides the time and space scaling parameters, the qubit number n itself is also considered as a varying scaling parameter with the additional aim to find a suitable number of qubits for the design of a quantum computer. This regime is in contrast to the well-known Halfin–Whitt regime. [ABSTRACT FROM AUTHOR]

Setting traffic light signals is a classical topic in traffic engineering, and important in heavy-traffic conditions when green times become scarce and longer queues are inevitably formed. For the fixed-cycle traffic-light queue, an elementary queueing model for one traffic light with cyclic signaling, we obtain heavy-traffic limits that capture the long-term queue behavior. We leverage the limit theorems to obtain sharp performance approximations for one queue in heavy traffic. We also consider optimization problems that aim for optimal division of green times among multiple conflicting traffic streams. We show that inserting heavy-traffic approximations leads to tractable optimization problems and close-to-optimal signal prescriptions. • Heavy-traffic analysis of long-term queueing behavior of fixed-cycle traffic lights. • Special limiting regime with high load and non-zero delay probability. • Sharp performance approximations for one traffic queue in heavy traffic. • Easy prescription of close-to-optimal green times for conflicting traffic flows. [ABSTRACT FROM AUTHOR]

Haphazard and noisy traffic in congested and densely populated old cities has become a challenge for the environmental and transportation engineers to provide better means of transportation with raised quality of life and environment. Faisalabad is an old and major industrial city of Pakistan, which has huge influx of population due to its industrial significance. It has been facing severe traffic issues, which result in a noisy and irritating environment all around. This research work was planned to find out the health impact of noisy traffic on the residents and their social life, determining noise level variation trends with the changing density of traffic at different time intervals in a day and how variations occur during different weekdays. This study was focused to enquire the severity of noise levels due to road traffic with reference to significant selected locations throughout the city. It was aimed to develop a framework for a sustainable transportation system for Faisalabad city to cope with severe health impacts. Peak and average values were measured at significant locations, and GIS maps were also drawn spatially to demonstrate clusters of dense traffic at specific time. Furthermore, GS+ and Geostatistical module of Arc GIS 9.3 were used for evaluating sound level data. First, the data were analyzed in GS+, after doing calculation, the best possible model with the highest coefficient of determination (R2) and the minimum error of estimation (RSS) was selected, and the performance of each model was tested using cross-validation and the model which gives best result was used. Spatial prediction maps of noise level data for all the four towns of Faisalabad city were prepared by using the kriging method. Alarmingly high noise levels were observed during peak hours at specific locations. Such findings lead to the development of a framework for a sustainable transportation system to reduce the negative impact on the residents.

Concrete paving block (CPB) has become a popular construction material for pavements subjected to passive loads (parking, toll plazas, gas stations, and street pavements). Due to the short time in the production of CPB, the concrete block industry has experienced tremendous growth over the past decade. In this scenario, the environmental distress cannot be ignored due to the increased extraction of raw materials (fossil fuels, limestone, river sand, and crushed aggregates) in the manufacturing of CPB. The sustainability issues demand the utilization of eco-friendly materials instead of natural ones to minimize the abiotic depletion caused by the construction industry. This study investigates the technical and environmental performance of CPB production incorporating an eco-friendly mineral admixture, i.e., ground granulated blast furnace slag (GGBS), as a cement replacement material. The optimum level of GGBS was decided based on the required engineering performance and minimal environmental impact. For the determination of the engineering performance of CPB, several parameters were considered such as compressive strength (CS), impact toughness (IT), and water absorption (WA). The environmental impact of Global Warming Potential (GWP) was assessed based on a cradle-to-gate LCA analysis. The results suggested that maximum mechanical performance and minimum GWP can be simultaneously achieved at 5–10% replacement of cement with GGBS, while to satisfy the minimum strength requirement, CPB can be prepared using 25% GGBS as a replacement for cement that accounts for 17% lower GWP than that of the conventional CPB manufacturing. [ABSTRACT FROM AUTHOR]

In Braverman et al. [3], the authors justify the steady-state diffusion approximation of a multiclass queueing network under static buffer priority policy in heavy traffic. A major assumption in [3] is the moment state space collapse (moment-SSC) property of the steady-state queue length. In this paper, we prove that moment-SSC holds under a corresponding state space collapse condition on the fluid model. Our approach is inspired by Dai and Meyn [8], which was later adopted by Budhiraja and Lee [4] to justify the diffusion approximation for generalized Jackson networks. We will verify that the fluid state space collapse holds for various networks. [ABSTRACT FROM AUTHOR]

Multiserver queueing systems are found at the core of a wide variety of practical systems. Many important multiserver models have a previously-unexplained similarity: identical mean response time behavior is empirically observed in the heavy traffic limit. We explain this similarity for the first time. We do so by introducing the work-conserving finite-skip (WCFS) framework, which encompasses a broad class of important models. This class includes the heterogeneous M/G/k, the Limited Processor Sharing policy for the M/G/1, the Threshold Parallelism model and the Multiserver-Job model under a novel scheduling algorithm. We prove that for all WCFS models, scaled mean response time E [ T ] (1 - ρ) converges to the same value, E [ S 2 ] / (2 E [ S ]) , in the heavy-traffic limit, which is also the heavy traffic limit for the M/G/1/FCFS. Moreover, we prove additively tight bounds on mean response time for the WCFS class, which hold for all load ρ . For each of the four models mentioned above, our bounds are the first known bounds on mean response time. [ABSTRACT FROM AUTHOR]

Copyright of Guangdong Architecture Civil Engineering is the property of Guangdong Architecture Civil Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Owing to high density, concrete paving blocks (CPB) are highly brittle when subjected to occasional impact loads. Fractures in CPB create riding discomfort and increase maintenance costs. This issue demands the engineering design of CPB suitable for occasional dynamic loadings. Therefore, this study explores the effect of eco-friendly and cheap fiber recycled from scrape tire steel on the performance of paving blocks. For this purpose, several CPB batches were prepared and studied with the varying contents of recycled tire steel fiber (RTSF). The studied properties included density, water absorption, ultrasonic pulse velocity (UPV), compressive strength, flexural strength, and impact toughness. It was shown that RTSF caused nominal changes in the compressive strength of CPB. However, it was highly useful in enhancing the flexural strength and impact toughness of CPB. At 0.5% volume fraction RTSF, flexural strength and impact toughness of plain CPB were increased by 42% and 271%, respectively. RTSF incorporation can prolong the life of CPB pavements and can help in preserving riding comfort.

The paper is devoted to the analysis of queueing systems in the context of the network and communication theory (called a multi-server multi-core open queueing network). The ob ject of this research on the queueing theory is theorems about the Functional Strong Laws of Large Numbers (FSLLN) in multi-server multi-core open queueing networks, working under overload heavy traffic conditions. FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for extreme values of important probabilistic characteristics of the multi-server multicore open queueing network, investigated as well as the virtual waiting time of a job and the queue length of jobs. As applications of the proved theorems Little's laws in a multi-server multi-core open queueing network are presented. [ABSTRACT FROM AUTHOR]

In this paper, we study an N server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as N → ∞. This fluid limit depends on the initial number of tasks. In order to prove these results, we develop extreme value theory and diffusion approximations for the queue lengths. [ABSTRACT FROM AUTHOR]

Extending the results of Kruk (Queueing theory and network applications. QTNA 2019. Lecture notes in computer science, vol 11688. Springer, Cham, pp 263–275, 2019), we derive heavy traffic limit theorems for a single server, single customer class queue in which the server uses the Shortest Remaining Processing Time (SRPT) policy from heavy traffic limits for the corresponding Earliest Deadline First queueing systems. Our analysis allows for correlated customer inter-arrival and service times and heavy-tailed inter-arrival and service time distributions, as long as the corresponding stochastic primitive processes converge weakly to continuous limits under heavy traffic scaling. Our approach yields simple, concise justifications and new insights for SRPT heavy traffic limit theorems of Gromoll et al. (Stoch Syst 1(1):1–16, 2011). Corresponding results for the longest remaining processing time policy are also provided. [ABSTRACT FROM AUTHOR]

Opening of the Blanka Tunnel Complex (BTC) in Prague, Czech Republic, the longest city tunnel in Europe, significantly increased traffic on a connected main road, the V Holešovičkách street (VHS). To study environmental changes in VHS connected with BTC opening, sampling of road dust and airborne particulate matter in the VHS vicinity started 3 years before BTC opening and continued until BTC pilot operation. The enrichment factors calculated for the collected samples from elemental compositions determined by instrumental neutron activation analysis (INAA) have shown significant enrichment for Se, Sb, Hg, Br, Mo, Zn, As, W, Cr, Ba, and Fe, but not their increase after starting BTC operation. The Principal Component Analysis allowed distinguishing between detrital and anthropogenic, probably traffic related, origin of the elements determined in samples. The study demonstrated a potential of INAA for multielement trace analysis of minute samples (28 elements determined in samples down to 20 μg, with detection limits down to sub-ng level) and its application in urban geochemistry studies. [ABSTRACT FROM AUTHOR]

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We study the relationship between capacity and performance for a service firm with spatial operations, in the sense that requests arrive with origin-destination pairs. An example of such a system is a ride-hailing platform in which each customer arrives in the system with the need to travel from an origin to a destination. We propose a parsimonious representation of a spatial multiserver system through a state-dependent queueing model that captures spatial frictions as well as spatial economies of scale through the service rate. In a classical M / M / n queueing model, the square root safety (SRS) staffing rule is known to balance server utilization and customer wait times. By contrast, we find that the SRS rule does not lead to such a balance in spatial systems. In a spatial environment, pick-up times increase the load in the system; furthermore, they are an endogenous source of extra workload that leads the system to only operate efficiently if there is sufficient imbalance between supply and demand. In heavy traffic, we derive the mapping from load to operating regimes and establish implications on various metrics of interest. In particular, to obtain a balance of utilization and wait times, the service firm should use a higher safety factor, proportional to the offered load to the power of 2 / 3. We also discuss implications of these results for general systems. [ABSTRACT FROM AUTHOR]

A"scheduled" arrival process is one in which the nth arrival is scheduled for time n, but instead occurs at n + ξ n , where the ξ j 's are i.i.d. We describe here the behavior of a single server queue fed by such traffic in which the processing times are deterministic. A particular focus is on perturbations with Pareto-like tails but with finite mean. We obtain tail approximations for the steady-state workload in both cases where the queue is critically loaded and under a heavy-traffic regime. A key to our approach is our analysis of the tail behavior of a sum of independent Bernoulli random variables with parameters of the form p n ∼ c n - α as n → ∞ , for c > 0 and α > 1 . [ABSTRACT FROM AUTHOR]

We develop a robust queueing network analyzer algorithm to approximate the steady‐state performance of a single‐class open queueing network of single‐server queues with Markovian routing. The algorithm allows nonrenewal external arrival processes, general service‐time distributions and customer feedback. The algorithm is based on a decomposition approximation, where each flow is partially characterized by its rate and a continuous function that measures the stochastic variability over time. This function is a scaled version of the variance‐time curve, called the index of dispersion for counts (IDC). The required IDC functions for the external arrival processes can be calculated from the model primitives or estimated from data. Approximations for the IDC functions of the internal flows are calculated by solving a set of linear equations. The theoretical basis is provided by heavy‐traffic limits for the flows established in our previous papers. A robust queueing technique is used to generate approximations of the mean steady‐state performance at each queue from the IDC of the total arrival flow and the service specification at that queue. The algorithm's effectiveness is supported by extensive simulation studies. [ABSTRACT FROM AUTHOR]

With the increase in bridge operation life and the effect of vehicle load, the property of bridge especially the reciprocating effect of heavy-load traffic, which endangers the safety of bridge operation, will be degraded. To further clarify the relationship between the stiffness and fatigue damage under heavy traffic, six prestressed concrete fatigue test beams were designed and manufactured. The equivalent fatigue load was determined by the statistics of traffic flow data. On the basis of the fatigue damage principle, the fatigue failure form and crack development of test beams under equivalent fatigue load were analysed. The constant-amplitude fatigue test method was employed to analyze the section stiffness degradation law and the member stiffness degradation law under equivalent fatigue load. Results demonstrate that the final failure mode of the test beam is the bending failure, which starts from the fatigue fracture of the longitudinal tensile steel bars at the bottom of the beam. With increased fatigue loading times, the stiffness of the test beams exhibits a threestage decay trend of "fast-gentle-fast". The equivalent fatigue load accelerates the initial stiffness degradation of the prestressed beam, and the bridge design by the normal operating load is conservative. The section stiffness, which is characterized by the prestressed reinforcement strain, correlates best with the member stiffness of the beam. The proposed method provides a certain reference for the design, detection, and early warning of damage of bridge structures. [ABSTRACT FROM AUTHOR]

Natural recovery of acidic soils following heavy traffic is assumed to take several decades. The aim of this study was to monitor the recovery of soil penetration resistance (PR) after soil compaction by heavy traffic at two forest sites. The sites, located in northeast France, have soils that differ slightly in pH and silt content. The impact on soil PR following heavy traffic was dependent on the soil water content (WC) at the time of measurement, and, therefore, the entire WC range and corresponding PR values were measured. For the most acidic and silty soil, no difference in PR among treatments was observed when the soils were near saturation; however, the difference in PR values was high when soils were close to wilting point. For the least acidic and silty soil, the impact of heavy traffic on PR could be detected whatever the soil moisture, with the magnitude of the effect dependent on the soil water content and depth considered. Standardized PR values with regard to WC allowed an analysis of the evolution of the effect of heavy traffic with time. Ten years after being subjected to heavy traffic, the PR values in the 0‐ to 40‐cm layer recovered to undisturbed values at the least acidic and silty site, but not WC dynamic. The most acidic and silty soil site did not show any recovery of PR or WC dynamic ten years following traffic, although liming at this site was able to increase the regeneration of PR to undisturbed levels. [ABSTRACT FROM AUTHOR]

We study a sequence of single server queues with customer abandonment ( G I / G I / 1 + G I ) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known Lee and Weerasinghe (Stochastic Process Appl 121(11):2507–2552, 2011) and Reed and Ward (Math Oper Res 33(3):606–644, 2008) that the sequence of scaled offered waiting time processes converges weakly to a reflecting diffusion process with nonlinear drift, as the traffic intensity approaches one. In this paper, we further show that the sequence of stationary distributions and moments of the offered waiting times, with diffusion scaling, converge to those of the limit diffusion process. This justifies the stationary performance of the diffusion limit as a valid approximation for the stationary performance of the G I / G I / 1 + G I queue. Consequently, we also derive the approximation for the abandonment probability for the G I / G I / 1 + G I queue in the stationary state. [ABSTRACT FROM AUTHOR]

The object of this research on queueing theory is to analyze the behaviour of open queueing network, working under overload heavy traffic conditions. We have proved probability limit theorem for the global values of virtual waiting time of a customer in open queueing networks. Finally, we present application of the recurrent method in the further analysis of open queuing networks. [ABSTRACT FROM AUTHOR]

We consider a dynamic storage allocation model with a finite number of storage spaces. There are m primary spaces and R secondary spaces. Items arrive according to a Poisson process and an arriving item takes the lowest ranked available space. Each item occupies a storage space for an exponentially distributed amount of time. Letting N1and N2denote the numbers of occupied primary and secondary spaces, we examine the steady-state marginal distribution of N2and derive various conditional limit laws for Prob[N1=k∣N2=r]. The joint process (N1,N2)behaves as a random walk in a lattice rectangle. We scale the storage capacities m and R to be large and study the problem asymptotically as the Poisson arrival rate λ becomes large. We previously derived detailed asymptotic results for the joint distribution Prob[N1=k,N2=r]and we use these results here to study the marginal and conditional distributions.

The Adaptive MaxWeight policy achieves optimal throughput for switches with nonzero reconfiguration delay and has been shown to have good delay performance in simulation. In this paper, we analyze the queue length behavior of a switch with nonzero reconfiguration delay operating under the Adaptive MaxWeight. We first show that the Adaptive MaxWeight policy exhibits a weak state space collapse behavior in steady state, which can be viewed as an inheritance of a similar property of the MaxWeight policy in a switch with zero reconfiguration delay. The weak state space collapse result is then utilized to obtain an asymptotically tight bound on an expression involving the steady-state queue length and the probability of reconfiguration for the Adaptive MaxWeight policy in the heavy traffic regime. We then derive the relation between the expected schedule duration and the steady-state queue length through Lyapunov drift analysis and characterize bounds for the expected steady-state queue length. While the resulting queue length bounds are not asymptotically tight, they suggest an approximate queue length scaling behavior, which approaches the optimal scaling with respect to the traffic load and the reconfiguration delay when the hysteresis function of the Adaptive MaxWeight policy approaches a linear function. [ABSTRACT FROM AUTHOR]

In this paper, we analyze weekdays' speed data from heavy traffic locations in Mexico City. The objective is to determine the “common denominator” speed from the weeks under study. For a specific location and time, speed data is compared between the same day for different weeks. Both a method and an algorithm are proposed to achieve this goal. The method conducts the following tasks: 1) organizes speed data of vehicles into “cell arrays”, 2) estimates “usual traffic” values from the raw data through a heuristic technique, and 3) detects unusual speed values by a comparison of raw speed values against estimated usual traffic values. The algorithm is employed to determine the expected speed, and a metric score compares the expected and the observed values, which in turn returns the locations and times that present anomalous results. The twelve top locations with the worst traffic conditions in Mexico City during 2016 were chosen. Measurements were realized in 2018. Results show that it is possible to detect the locations, days and times when the vehicles' speed was unusual. This indicates that it is desirable to conduct further investigations to determine the causes inducing significant deviation, higher or lower, from the expected speed.

Increasing in urban traffic brings heavy burden on metro transportations, especially for metro hubs which are crossing metro stations with railways. It calls for special scheduling optimization for such metro hubs by taking consideration of train arrivals. First, a detailed procedure is proposed on how to predict the traffic in such metro hubs under influence of train arrivals, including metros train and metro stations. Moreover, a service-oriented metro scheduling optimization procedure is proposed. Further analysis is then conducted when there is heavy traffic such as special holidays. A practical case on a major metro hub is studies for validation, the Chongqingbei (Chongqing North) metro hub in the city of Chongqing, China. The Chongqingbei metro hub is with four metro lines (Lines 3/4/10/Loop), three metro stations (Longtousi, Chongqingbei North Square, Chongqingbei South Square), and two non-connected railway stations (Chongqingbei North and Chongqingbei South). Passengers on three metro stations over four lines are calculated. Case study results show that: (1) when there is normal traffic, a hybrid schedule is more effective in comparison with regular shifts for Line 3 while Lines 4/10/Loop require no additional shifts, (2) when there is heavy traffic, an optimized metro schedule with a smaller interval (original 6-minute interval is reduced to 4-minute) is more effective for Line 3 whereas hybrid shifts and Line 10 requires hybrid shifts and Line 4 and the Loop Line require no additional shifts.

A brief overview of the practical use of the new construction material of MONICA is given. An experimental study was performed for the first time on the analysis of the influence of the microstructural state on fatigue resistance. It is established that the fatigue limit of this material, based on 108 cycles, is not lower than 243 MPa. The role of the stress concentration in the vicinity of nonmetallic (graphite) inclusions on the formation of the fatigue resistance of MONICA is discussed. The ways of possible increase of the fatigue limit of this material up to ∼300 MPa and more are indicated.

This paper addresses the analysis of the queue-length process of single-server queues under overdispersion, i.e., queues fed by an arrival process for which the variance of the number of arrivals in a given time window exceeds the corresponding mean. Several variants are considered, using concepts as mixing and Markov modulation, resulting in different models with either endogenously triggered or exogenously triggered random environments. Only in special cases explicit expressions can be obtained, e.g., when the random arrival and/or service rate can attain just finitely many values. While for more general model variants exact analysis is challenging, one can derive limit theorems in the heavy-traffic regime. In some of our derivations we rely on evaluating the relevant Laplace transform in the heavy-traffic scaling using Taylor expansions, whereas other results are obtained by applying the continuous mapping theorem. [ABSTRACT FROM AUTHOR]

In order to cope with the recent dramatic growth in mobile traffic, it is important to understand and exploit its unique features in wireless communications. For example, the fact that a relatively small number of popular contents accounts for most of the traffic is considered one of the most promising factors to explore. This paper proposes a multicast system with user caching in a heavy traffic model. Through the efficient combination of caching and multicasting, the proposed system reduces the redundant communication resource consumptions for the duplicated requests of the same content from different users. The performance of the proposed system is analyzed in closed-form expressions in terms of outage probability and average network throughput by means of the asymptotic analysis. The derived expressions provide insight into the impact of system parameters on performance and can be used to capture the gains in performance obtained from user caching and multicasting in the proposed system. Furthermore, the simulation results confirm the convergence of the asymptotic analysis results in the heavy traffic model and provide additional information on the average network throughput in general cases.

We consider resource sharing networks of the form introduced in work of Massoulié and Roberts as models for Internet flows. The goal is to study the open problem, formulated in Harrison et al. (2014) [Harrison JM, Mandayam C, Shah D, Yang Y (2014) Resource sharing networks: Overview and an open problem. Stochastic Systems 4(2):524–555.], of constructing simple form rate-allocation policies for broad families of resource sharing networks with associated costs converging to the hierarchical greedy ideal performance in the heavy traffic limit. We consider two types of cost criteria: an infinite horizon discounted cost and a long-time average cost per unit time. We introduce a sequence of rate-allocation control policies that are determined in terms of certain thresholds for the scaled queue-length processes and prove that, under conditions, both type of costs associated with these policies converge in the heavy traffic limit to the corresponding hierarchical greedy ideal (HGI) performance. The conditions needed for these results are satisfied by all the examples considered in the above cited paper of Harrison et al. [ABSTRACT FROM AUTHOR]

This paper studies stationary customer flows in an open queueing network. The flows are the processes counting customers flowing from one queue to another or out of the network. We establish the existence of unique stationary flows in generalized Jackson networks and convergence to the stationary flows as time increases. We establish heavy-traffic limits for the stationary flows, allowing an arbitrary subset of the queues to be critically loaded. The heavy-traffic limit with a single bottleneck queue is especially tractable because it yields limit processes involving one-dimensional reflected Brownian motion. That limit plays an important role in our new nonparametric decomposition approximation of the steady-state performance using indices of dispersion and robust optimization. [ABSTRACT FROM AUTHOR]