Interpolation approximations for queues in series

Due to the analytical intractability of general tandem queues, we develop methods to quantify the dependence among servers through simulation. Dependence is defined by the contribution queue time at each server, and contribution factors are developed based on the insight from Friedman's reduction method and Jackson networks. In a tandem queue, the dependence among stations can be either diffusion or blocking, and their impact depends on the positions relative to the bottlenecks.

Dependence among servers is the root cause of the analytic intractability of general queueing networks. A tandem queue is the smallest unit possessing the dependence. Understand its behavior is the key to understand the behavior of general queueing networks. Based on observed properties, such as intrinsic gap and intrinsic ratio, a new approximation approach for tandem queues is proposed. Across a broad range of examined cases, this new approach outperforms prior methods based on stochastic independence or diffusion approximations.

New bounds for expected cycle times in tandem queues with blocking

This paper considers a queueing system consisting of two single-server queues in series, in which the service times of an arbitrary customer at both queues are identical. Customers arrive at the first queue according to a Poisson process. Of this model, which is of importance in modern network design, a rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity of the tandem system, expressions for the joint stationary distributions of the actual waiting times at both queues and of the virtual waiting times at both queues, and explicit expressions (i.e., not in transform form) for the stationary distributions of the sojourn times and of the actual and virtual waiting times at the second queue. In Part II (pp. 644–659) these results will be used to obtain asymptotic and numerical results, which will provide more insight into the general phenomenon of tandem queueing with correlated service times at the consecutive queues.

Using a definition of partial ordering of distribution functions, it is proven that for a tandem queueing system with many stations in series, where each station can have either one server with an arbitrary service distribution or a number of constant servers in parallel, the expected total waiting time in system of every customer decreases as the interarrival and service distributions becomes smaller with respect to that ordering. Some stronger conclusions are also given under stronger order relations. Using these results, bounds for the expected total waiting time in system are then readily obtained for wide classes of tandem queues.

The queueing analysis of store and forward data communication networks is complicated by the fact that messages preserve their length as they traverse the system: in the queueing model service times of a message at successive queues (channels) are dependent. The present study considers the case of two communication channels in series with identical capacities and with a finite intermediate buffer. That part of a message for which there is no room in the buffer is lost. The resulting queueing model of two queues in series with identical service requirements at both queues is extensively analysed. Results include the distribution of the response time in the second queue (time in buffer plus transmission time in second channel) and of the total amount of work in the second queue. A comparison is made with the analogous queueing model with independent service requirements.

Due to the analytical intractability of general tandem queues, we develop innovative methods to quantify the dependence among stations through simulation. Dependence is defined by the contribution queue time at each station, and contribution factors are developed based on the insight from Friedman's reduction method and Jackson networks. In a tandem queue, the dependence among stations can be either diffusion or blocking, and their impact depends on the positions relative to the bottlenecks. Based on these results, we show that improving the performance of the system bottleneck may not be the most effective place to reduce system cycle time. Rather than making independence assumptions, the proposed method points out a promising direction and sheds light on the insights of the dependence in practical systems.

This paper evaluated the feasibility of using the horizontal radial plume mapping (HRPM) technique to locate multiple emission sources via computational simulation. Seventy-two test maps, each having two Gaussian distributions, were generated in a two-dimensional domain. The HRPM technique with the non-negative least square (NNLS) algorithm was then applied to reconstruct the plumes, assuming a nine-beam scanning beam geometry. The NNLS algorithm successfully reconstructed the source locations of 68 of the 72 test maps. However, when one of the plumes was near the origin, the NNLS did not always identify the peak locations correctly. Furthermore, when the two plumes were spaced closely, the NNLS tended to reconstruct a wide plume covering both plumes instead of separating them due to the resolution limitation of the current nine-beam geometry. In the sensitivity analysis, five sets of random error (1%, 5%, 10%, 20%, and 30%) were added in the path-integrated concentration (PIC) from the 72 test maps, and thus, an additional 360 reconstructions were implemented. Robust results were obtained when the noise added was less than 20%. The results generally support the implementation of the NNLS algorithm in the HRPM technique as described in the U.S. Environmental Agency (EPA) Other Test Method 10 (OTM-10). Implications: The methodology evaluated in this paper provides near-real-time estimates about the locations of multiple emission sources. The involved optical remote sensing instruments can monitor large spatial areas (e.g., landfills) in a cost-effective way. Supplementary Materials: Supplementary materials are available for this paper. Go to the publisher's online edition of the Journal of the Air & Waste Management Association for three failed cases of narrow plumes and examples of the translated grids.

From 1995 to 2004, in Genoa, Italy, daily concentrations of twelve polycyclic aromatic hydrocarbons (PAHs) were measured in particulate phase (PM10), around a coke oven plant in operation from the 1950s and closed in 2002. The study permitted to identify the coke oven as the main PAH source in Genoa, causing constant exceeding of benzo(a)pyrene (BaP) air quality target (1.0 ng/m3) in the urban area till 1,900 meters distance downwind the plant. For this reason the plant was closed. Distance and daily hours downwind the coke plant were the main sources of variability of toxic BaP equivalent (BaPeq) concentrations and equations that best fitted these variables were experimentally obtained. During full plant activity, annual average BaPeq concentrations, measured in the three sampling sites aligned downwind to the summer prevalent winds, were: 85 ng/m3 at 40 m (site 2, industrial area), 13.2 ng/m3 at 300 m (site 3, residential area) and 5.6 ng/m3 at 575 m (site 4, residential area). Soon after the coke oven's closure (February 2002) BaPeq concentrations (annual average) measured in residential area, decreased drastically: 0.2 ng/m3 at site 3, 0.4 ng/m3 at site 4. Comparing 1998 and 2003 data, BaPeq concentrations decreased 97.6% in site 3 and 92.8% in site 4. Samples collected at site 3, during the longest downwind conditions, provided a reliable PAH profile of fugitive coke oven emissions. This profile was significantly different from the PAH profile, contemporary found at site 5, near the traffic flow. This study demonstrates that risk assessment based only on distance of residences from a coke plant can be heavily inaccurate and confirmed that seasonal variability of BaPeq concentrations and high variability of fugitive emissions of PAHs during coke oven activities require at least one year of frequent and constant monitoring (10-15 samples each month). Implications: Around a coking plant, polycyclic aromatic hydrocarbons (PAHs), concentrations depend mainly on downwind hours and distance. Equations that best fit these variables were experimentally calculated. Fugitive emissions of an old coke oven did not comply with the threshold BAP air concentration proposed by the World Health Organization (WHO), up to 1,900 m distance. The study identified the PAH profile of fugitive emissions of a coke oven, statistically different from the profile of traffic emissions. During its activity, in the Genoa residential area, 575 m away from the plant, 92.8% of found PAHs was due to coke oven emission only. Supplemental Materials: Supplemental materials are available for this article. Go to the publisher's online edition of the Journal of the Air & Waste Management Association for information about samples analyses, statistical analyses and regression models figure.

A combination of multiplatform satellite observations and statistical data analysis are used to improve the correlation between estimates of PM2.5 (particulate mass with aerodynamic diameter less that 2.5 µm) retrieved from satellite observations and ground-level measured PM2.5. Accurate measurements of PM2.5 can be used to assess the impact of air pollution levels on human health and the environment and to validate air pollution models. The area under study is California's San Joaquin Valley (SJV) that has a history of poor particulate air quality. Attempts to use simple linear regressions to estimate PM2.5 from satellite-derived aerosol optical depth (AOD) have not yielded good results. The period of study for this project was from October 2004 to July 2008 for six sites in the SJV. A simple linear regression between surface-measured PM2.5 and satellite-observed AOD (from MODIS [Moderate Resolution Imaging Spectroradiometer]) yields a correlation coefficient of about 0.17 in this region. The correlation coefficient between the measured PM2.5 and that retrieved combining satellite observations in a generalized additive model (GAM) resulted in an improved correlation coefficient of 0.77. The model used combinations of MODIS AOD, OMI (Ozone Monitoring Instrument) AOD, NO2 concentration, and a seasonal variable as parameters. Particularly noteworthy is the fact that the PM2.5 retrieved using the GAM captures many of the PM2.5 exceedances that were not seen in the simple linear regression model. Implications: Particulate Mass (PM) in the air is a concern because of its effect on climate and human health. PM concentrations retrieved from satellite observations of aerosol optical depth can provide broad regional coverage that is not attained by surface sites. The techniques developed in this paper have resulted in greatly improved correlations between PM retrieved from satellite observations and PM from surface measurements in areas where the correlation is typically low. These improved retrievals can be used to fill in the gaps between surface sites and validate air quality models that are used for air quality forecasts and epidemiological studies. Supplemental Materials: Supplemental materials are available for this paper. Go to the publisher's online edition of the Journal of the Air & Waste Management Association for information on the effects of grid size and MODIS data quality flags on the GAM results. The coefficients for the GAMs used in this study are also listed.

As part of an ongoing study of soil vapor intrusion (SVI), concentration data for approximately 2000 air and vapor samples were assembled from remedial site investigations and stand-alone assessments conducted at New York State Manufactured Gas Plant (MGP) sites. Vapor samples were collected from ambient outdoor air, indoor air, beneath building slabs, and from outside of buildings. Despite the large sample size, the considerable variability in compound and sample-specific censoring limits inhibited the use of conventional tools for statistical interpretation. This paper describes the development and application of improved statistical tools to address an unusually high degree of data censoring and possible artifacts related to uneven distributions of samples across sites and buildings. In addition to methods for calculating population percentiles and associated confidence intervals, methods for comparing the population of MGP-SVI data with a reference population were also developed and evaluated via illustrative comparisons with the published 2001 EPA Building Assessment Survey and Evaluation (BASE) study of industrial buildings. The focus of this work is on the development and evaluation of new statistical methods; a more complete summary and evaluation of the full NYS MGP-SVI data set will be presented in a companion paper. Implications: Data from vapor intrusion and other environmental studies are often stratified and/or censored, which complicates comparisons with background data or reference populations. In some cases, statistical methods for censored data can be modified to support population-based inference and reduce biases associated with the presence of repeated measurements from multiple sources. Such modifications are particularly appropriate for retrospective data mining studies that are not guided by a formal experimental design. Supplemental Materials: Supplemental materials are available for this paper. Go to the publisher's online edition of the Journal of the Air & Waste Management Association.

Speciated PM2.5 (particulate matter with an aerodynamic diameter ≤2.5 μm) data has been collected for about 20 yr (1990–present) at a rural location in the Lake Tahoe Basin (Bliss State Park) and about 15 yr (1989–2004) at an urban site in South Lake Tahoe. The Bliss State Park site is representative of the Desolation Wilderness, a Class I air quality area with visibility protection under the Clean Air Act. Carbonaceous aerosol dominated reconstructed fine mass at both sites, with 58% at Bliss State Park (BLIS) and 68% at South Lake Tahoe (SOLA). Fine mass at SOLA is 2.5 times that at BLIS, mainly due to enhanced organic and elemental carbon (OC and EC). SOLA experiences a winter peak in PM2.5 mainly due to OC and EC from residential wood combustion, whereas BLIS experiences a summer peak in PM2.5 mainly due to OC and EC from wildfires. Carbonaceous aerosol dominates visibility impairment, causing about ½ the reconstructed aerosol light extinction at BLIS and 70% at SOLA. Trend analysis (1990–2009) showed statistically significant decreases in aerosol extinction at BLIS on 20% best and 60% middle visibility days and statistically insignificant upward trends on 20% worst days. SOLA (1990–2003) showed statistically significant decreases in aerosol extinction for all day categories, driven by decreasing OC and EC. From the regional haze rule baseline period of 2000–2004 until 2005–2009, BLIS saw 20% best days improving and 20% worst days getting worse due to increased wildfire effects. Receptor modeling was performed using positive matrix factorization (PMF) and chemical mass balance (CMB). It confirmed that (1) biomass burning dominanted PM2.5 sources at both sites with increasing importance over time; (2) low combustion efficiency burning accounts for most of the biomass burning contribution; (3) road dust and traffic contributions were much higher at SOLA than at BLIS; and (4) industrial combustion and salting were minor sources. Implications: Visibility on the 20% worst visibility days decreased at Bliss State Park, which represents the Desolation and Mokelumne Wilderness Class I areas. This decrease in visibility, contrary to Regional Haze Rule requirements, was mainly due to increased wildfire activity. Increased sulfate-caused light extinction on worst visibility days may be due to long-range transport from Asia. These factors may make it difficult to achieve reasonable progress toward the national visibility goal. Methods need to be developed to account for the effect of wildfires and intercontinental transport when evaluating progress toward the national goal. Supplemental Materials: Supplemental materials are available for this article. Go to the publisher's online edition of the Journal of the Air & Waste Management Association for details of the receptor modeling, including the average and signal-to-noise ratio (SNR) of PM2.5 mass and chemical concentrations for the 3 PMF modeling groups, PMF factor profiles, and sensitivity test results for the EV-CMP modeling.

The assignment of extra servers to stations in Tandem Queueing systems with small or no buffers

Problem definition: Classical models of queueing systems with rational and strategic customers assume queues to be either fully visible or invisible, while service parameters are known with certainty. In practice, however, people only have “partial information” on the service environment, in the sense that they are not able to fully discern prevalent uncertainties. This is because assessing possible delays and rewards is costly, as it requires time, attention, and cognitive capacity, which are all limited. On the other hand, people are also adaptive and endogenously respond to information frictions. Methodology: We develop an equilibrium model for a single-server queueing system with customers having limited attention. Following the theory of rational inattention, we assume that customers optimize their learning strategies by deciding the type and amount of information to acquire and act accordingly while internalizing the associated costs. Results: We establish the existence and uniqueness of a customer equilibrium when customers allocate their attention to learn uncertain queue lengths and delineate the impact of service characteristics. We provide a complete spectrum of the impact of information costs on throughput and show numerically that throughput might be nonmonotone. This is also reflected in social welfare if the firm’s profit margin is high enough, although customer welfare always suffers from information costs. Managerial implications: We identify service settings where service firms and social planners should be most cautious for customers’ limited attention and translate our results to advisable strategies for information provision and service design. For example, we recommend firms to avoid partial hindrance of queue-length information when a low-demand service is not highly valued by customers. For a popular service that customers value reasonably highly, however, partial hindrance of information is particularly advisable. Academic/practical relevance: We propose a microfounded framework for strategic customer behavior in queues that links beliefs, rewards, and information costs. It offers a holistic perspective on the impact of information prevalence (and information frictions) on operational performance and can be extended to analyze richer customer behavior and complex queue structures, rendering it a valuable tool for service design. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.1032 .

The introduction of two types of organic carboxylate ligands into the Cu(II)/phen system leads to the formation of two new complexes, namely [Cu(L1)(phen)(H2O)2·NO3] (1) and [Cu(L2)(phen)2(H2O)·2H2O] (2) (HL1 = 2-ethoxynicotinic acid and H2L2 = 4,5-dihydroxybenzene-1,3-disulfonic acid). In 1 and 2, both of them are mononuclear structures, which could be linked by the hydrogen-bonded interactions into 3D motifs. However, the types of the hydrogen interactions and resulting motifs are different. The difference of final structures can be attributed to the effect of carboxylate ligands. Supplementary materials are available for this article. Go to the publisher's online edition of Synthesis and Reactivity in Inorganic, Metal-Organic, and Nano-Metal Chemistry to view the supplemental figure.