Hazard Rate

One of the most popular approaches to analyze failure time data in the presence of influential covariates is proportional hazards model. In this paper, the multiplicity-cause economic design of X-control charts are extended by employing this family as the shock model of the process. For illustration, the Weibull and the Chen lifetime distributions

The author proposes some simple diagnostics for the assessment of the necessity of selected model terms in smoothing spline ANOVA models; the elimination of practically insignificant terms generally enhances the interpretability of the estimates, and sometimes may also have inferential implications. The diagnostics are derived from Kullback-Leibler geometry, and are illustrated in the settings of regression, probability density estimation, and hazard rate estimation. Résumé : The author proposes some simple diagnostics for the assessment of the necessity of selected model terms in smoothing spline ANOVA models; the elimination of practically insignificant terms generally enhances the interpretability of the estimates, and sometimes may also have inferential implications. The diagnostics are derived from Kullback-Leibler geometry, and are illustrated in the settings of regression, probability density estimation, and hazard rate estimation.

The glycemic effects of diets high in refined grains and starchy foods might increase stomach cancer risk by affecting circulating glucose, insulin and insulin-like growth factor-I levels. No prospective data on the role of high glycemic load and glycemic index diets on stomach cancer risk have been reported. We therefore prospectively investigated dietary glycemic load, overall glycemic index and carbohydrate intake in relation to the incidence of stomach cancer among 61,433 women in the population-based Swedish Mammography Cohort. Diet was assessed at baseline (1987-1990) and again in 1997. During 903,586 person-years of follow-up, a total of 156 incident cases of stomach cancer were ascertained. We observed no material associations of dietary glycemic load, overall glycemic index and total carbohydrate intake with the risk of stomach cancer. The multivariate hazard ratios for the highest versus the lowest quintile were 0.76 (95% CI 5 0.46-1.25) for glycemic load, 0.77 (95% CI 5 0.46-1.30) for overall glycemic index and 0.85 (95% CI 5 0.50-1.43) for carbohydrate intake. The associations did not vary according to body mass index. Lack of information on Helicobacter pylori infection status did not allow stratification by this potential effect modifier. Findings from this population-based prospective cohort of middle-aged and elderly women did not provide evidence of a positive association between glycemic load, glycemic index and carbohydrate intake with risk of stomach cancer.

This paper uses data drawn from the English Football League to model separate hazard rates for club managers for the 2001/2, 2002/3 and 2003/4 seasons. On average over the three seasons, approximately one-third of managers involuntarily exited employment status with their club. We model the hazard using a standard logistic model exploiting information on the spell at risk rather than the individual. The role of neglected heterogeneity is also examined using random and fixed effects logistic models within a discrete-time setting. League position at the start of the spell at risk is found to be the most important determinant of a manager's involuntary exit. A variety of individual specific human capital and other covariates are found to be unimportant in determining the hazard and no role for unobservable heterogeneity as captured by random effects is detected.

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Hazard rates play an important role in various areas, e.g., reliability theory, survival analysis, biostatistics, queueing theory and actuarial studies. Mixtures of distributions are also of a great preeminence in such areas as most populations of components are indeed heterogeneous. In this study we present a sufficient condition for mixtures of two elements of the same natural exponential family (NEF) to have an increasing hazard rate. We then apply this condition to some classical NEF's having either quadratic, or cubic variance functions (VF) and others as well. A particular attention is devoted to the hyperbolic cosine NEF having a quadratic VF, the Ressel NEF having a cubic VF and to the Kummer distributions of type 2 NEF. The application of such a sufficient condition is quite intricate and cumbersome, in particular when applied to the latter three NEF's. Various lemmas and propositions are needed then to verify this condition for these NEF's.

Alliances are recognized as an indispensable tool for managers operating in a global business environment, and as a fundamental stage of the internationalization process of the firm. Drawing on a co-evolutionary framework, this article investigates the mimetic and experiential effects in international alliance formation. We focus on a critical unresolved issue in the literature: what is the role of mimetic behavior and previous alliance experience in mitigating the uncertainty associated with engaging in cross-border operations? An event history analysis of 792 international marketing alliance formations initiated by 317 firms in the US pharmaceutical industry is employed to test the hypotheses. The findings of two different hazard rate models reveal significant complex effects of density and cross-border alliance experience on the propensity to engage in new international marketing alliances.

Many organisations have scheduling, assignment, supply chain and other problems that could be solved with a constraint programming toolkit. Although the solution of these problems is of vital importance, constraint programming toolkits are not widely used because there is insufficient expertise available to model problems as constraint programs. This so-called modelling bottleneck could be reduced by the development of a general, principled understanding of modelling that in the future could guide the manual or automatic formulation of models and the choice among alternative models. Researchers and practitioners have developed effective models for a wide range of problems. The time has come to form generalisations from these case studies that can be used to guide modelling in the future. These generalisations could then be systematised for use by a non-expert and be codified in textbooks in much the same way that data structuring expertise is. Ultimately this modelling expertise could be embedded in automated modelling tools. Progress on any of these fronts would bring the proven power of constraint programming to a wider user base. This "Fifth International Workshop on Constraint Modelling and Reformulation" was convened to provide a forum for researchers who share these goals. This volume contains eight contributed papers. We wish to thank all the authors who submitted papers to the workshop, the members of the programme committee and reviewers, and the CP 2006 Workshop Chair, Barry O'Sullivan.

In this paper, we consider the problem of the optimal flow control for a production system with one machine which is subject to failures and produces one part type. In most previous work, it has been assumed that the machine has exponential up and down times, i.e., its state process is a Markov process. The system considered in our study has general machine up and down times. Our main result is establishing monotone properties for the optimal control policy.

Abstract. We describe configuration systems using constraint problem solving formalisms where feasible products are computed by constraint problem solvers. A feasible product is a configuration of constituent components that violates none of the configuration constraints and meets users' preferences as much as possible. To help users find desirable products, a system must possess and understand users' preference model as well as value functions. A constraint-based multi-attribute optimization problem (MOP) assigns utility functions to the ...

Objective To investigate whether angiotensin receptor blockers protect against Alzheimer's disease and dementia or reduce the progression of both diseases. Design Prospective cohort analysis. Setting Administrative database of the US Veteran Affairs, 2002-6. Population 819 491 predominantly male participants (98%) aged 65 or more with cardiovascular disease. Main outcome measures Time to incident Alzheimer's disease or dementia in three cohorts (angiotensin receptor blockers, lisinopril, and other cardiovascular drugs, the "cardiovascular comparator") over a four year period (fiscal years 2003-6) using Cox proportional hazard models with adjustments for age, diabetes, stroke, and cardiovascular disease. Disease progression was the time to admission to a nursing home or death among participants with pre-existing Alzheimer's disease or dementia. Results Hazard rates for incident dementia in the angiotensin receptor blocker group were 0.76 (95% confidence interval 0.69 to 0.84) compared with the cardiovascular comparator and 0.81 (0.73 to 0.90) compared with the lisinopril group. Compared with the cardiovascular comparator, angiotensin receptor blockers in patients with pre-existing Alzheimer's disease were associated with a significantly lower risk of admission to a nursing home (0.51, 0.36 to 0.72) and death (0.83, 0.71 to 0.97). Angiotensin receptor blockers exhibited a dose-response as well as additive effects in combination with angiotensin converting enzyme inhibitors. This combination compared with angiotensin converting enzyme inhibitors alone was associated with a reduced risk of incident dementia (0.54, 0.51 to 0.57) and admission to a nursing home (0.33, 0.22 to 0.49). Minor differences were shown in mean systolic and diastolic blood pressures between the groups. Similar results were observed for Alzheimer's disease. Conclusions Angiotensin receptor blockers are associated with a significant reduction in the incidence and progression of Alzheimer's disease and dementia compared with angiotensin converting enzyme inhibitors or other cardiovascular drugs in a predominantly male population.

This paper analyses with a multi-period logistic model corporate bankruptcy in the manufacturing industry over the period 1980 to 2007. The contribution of this paper to the bankruptcy prediction literature is the concentration on one of the most important industries in the U.S.; the manufacturing industry. In addition, this research includes the effect of the Gross Domestic Product on bankruptcy filings, which turns out to be a powerful predictor. The results show that accounting variables lose predicting power when market driven variables are added. Only one accounting variable (a liquidity ratio) turns out to be statistically significant once market variables are accounted for. This study finds; liquidity of the company, excess return and volatility of the publicly traded shares and macroeconomic growth are significant in predicting bankruptcy in the whole manufacturing industry. In the analysis of the manufacturing sub-industries the excess return of company shares over the S&P500 return is a significant bankruptcy predictor in 7 of the 8 manufacturing sub-industries. GDP is significant in the industrial machinery industry and liquidity is significant in the textile and chemicals industry.

This paper analyses with a multi-period logistic model corporate bankruptcy in the manufacturing industry over the period 1980 to 2007. The contribution of this paper to the bankruptcy prediction literature is the concentration on one of the most important industries in the U.S.; the manufacturing industry. In addition, this research includes the effect of the Gross Domestic Product on bankruptcy filings, which turns out to be a powerful predictor. The results show that accounting variables lose predicting power when market driven variables are added. Only one accounting variable (a liquidity ratio) turns out to be statistically significant once market variables are accounted for. This study finds; liquidity of the company, excess return and volatility of the publicly traded shares and macroeconomic growth are significant in predicting bankruptcy in the whole manufacturing industry. In the analysis of the manufacturing sub-industries the excess return of company shares over the S&P500 return is a significant bankruptcy predictor in 7 of the 8 manufacturing sub-industries. GDP is significant in the industrial machinery industry and liquidity is significant in the textile and chemicals industry.

Discrete survival models have been extended in several ways. More flexible models are obtained by including time-varying coefficients and covariates which determine the hazard rate in an additive but not further specified form. In this paper a general model is considered which comprises both types of covariate effects. An additional extension is the incorporation of smooth interaction between time and covariates. Thus in the linear predictor smooth effects of covariates which may vary across time are allowed. It is shown how simple duration models produce artefacts which may be avoided by flexible models. For the general model which includes parametric terms, time-varying coefficients in parametric terms and time-varying smooth effects estimation procedures are derived which are based on the regularized expansion of smooth effects in basis functions.

Social characteristics that differ by place of residence are consequential for health. To study implications of this among older adults in rural vs. urban China, this study employs data from the Beijing municipality, a region that has witnessed growth and gaps in development. Life and active life expectancy is assessed using a multistate life table technique that estimates hazard rates and subsequent expected years in various health states. Hazards are estimated for a model that adjusts regional differences for age and sex and for a series of other models including additional covariates. Results indicate urban residents have an advantage. Specific factors show socio-economic status and access to health service account for a large part, social support and health behaviors for little, while disease is a suppressor.

We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation spectrum as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews.

We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation surface as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews. The characteristic dependence of the correlation skew on term to maturity and portfolio hazard rate in these models has a significant impact on both relative value analysis and risk management of CDO tranches.

In this paper, we develop a simple test procedure for comparing the cause-specific hazard rates of a competing risks model based on a right censored (competing risks) data. Asymptotic distributions of the test statistic under both the null and alternative hypotheses are shown to be normal by expressing the statistic in terms of counting processes and using martingale central limit theory. These results enable us to assess the power of the test analytically rather than through simulations. The power comparison of the test with some existing tests shows that the proposed test performs better in the presence of censoring. An application of the test for comparing the risks of two types of cancer mortality (thymic lymphoma and reticulum cell carcinoma) in a strain of laboratory mice is illustrated.

For the competing risk setting where the lifetime data are due to one of several distinct and exclusive causes, comparison of cause-specific hazard rates is of interest to researchers. In this paper we survey existing methods for related tests and provide a new test for a common overall rate for all causes and groups. Tests given in the literature for checking for a common rate for causes and a common rate for the groups are shown to be in the same framework as the proposed test for common overall rate. Asymptotics are shown to follow a common theme for each test. An extensive numerical and graphical investigation and an example are presented to substantiate the proposed methods.

Unemployment during and after the Great Recession has been persistently high. One concern is that the housing bust reduced geographical mobility and prevented workers from moving for jobs. We characterize flows out of unemployment that are related to geographical mobility to construct an upper bound on the effect of mobility on unemployment between 2007 and 2012. The effect of geographical mobility is always small: Using pre-recession mobility rates, decreased mobility can account for only an 11 basis points increase in the unemployment rate over the period. Using dynamics of renter geographical mobility in this period to calculate homeowner counterfactual mobility, delivers similar results. Using the highest mobility rate observed in the data, reduced mobility accounts for only a 33 basis points increase in the unemployment rate.

This paper considers dynamic games in which multiple principals contract sequentially and noncooperatively with the same agent. We first show that when contracting is private, i.e. when downstream principals do not observe the mechanisms offered upstream and the decisions taken in these mechanisms, all PBE outcomes can be characterized through pure-strategy profiles in which the principals offer menus of contracts and delegate to the agent the choice of the contractual terms. We then show that, in most cases of interest for applications, the characterization of the equilibrium outcomes is further facilitated by the fact that the principals can be restricted to offer incentive-compatible extended direct mechanisms in which the agent reports the endogenous payoff-relevant decisions contracted upstream in addition to his exogenous private information. Finally we show how the aforementioned results must be adjusted to accommodate alternative assumptions about the observability of upstream histories and/or the timing of contracting examined in the literature.

Alliances are recognized as an indispensable tool for managers operating in a global business environment, and as a fundamental stage of the internationalization process of the firm. Drawing on a co-evolutionary framework, this article investigates the mimetic and experiential effects in international alliance formation. We focus on a critical unresolved issue in the literature: what is the role of mimetic behavior and previous alliance experience in mitigating the uncertainty associated with engaging in cross-border operations? An event history analysis of 792 international marketing alliance formations initiated by 317 firms in the US pharmaceutical industry is employed to test the hypotheses. The findings of two different hazard rate models reveal significant complex effects of density and cross-border alliance experience on the propensity to engage in new international marketing alliances.

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In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical...

This paper deals with the impact of structure of dependency and the choice of procedures for rareevent simulation on the pricing of multi-name credit derivatives such as n th to default swap and Collateralized Debt Obligations (CDO). The correlation between names defaulting has an effect on the value of the basket credit derivatives. We present a copula based simulation procedure for pricing basket default swaps and CDO under different structure of dependency and assessing the influence of different price drivers (correlation, hazard rates and recovery rates) on modelling portfolio losses. Gaussian copulas and Monte Carlo simulation is widely used to measure the default risk in basket credit derivatives. Default risk is often considered as a rare-event and then, many studies have shown that many distributions have fatter tails than those captured by the normal distribution. Subsequently, the choice of copula and the choice of procedures for rare-event simulation govern the pricing of basket credit derivatives. An alternative to the Gaussian copula is Clayton copula and tstudent copula under importance sampling procedures for simulation which captures the dependence structure between the underlying variables at extreme values and certain values of the input random variables in a simulation have more impact on the parameter being estimated than others .

We use administrative micro-data to investigate exits from unemployment of benefit recipients in Spain. Because the data allow us to distinguish between transitions to a new job and recall to the same employer, we apply a competing risks model with observed and unobserved heterogeneity. We are also able to control for the type of benefit received by the worker: insurance benefit or assistance benefit. We find significant differences between the new job hazard and the recall hazard. Both hazard rates increase around the time that insurance benefit elapses. We also find that when larger firms recall unemployed workers they tend to do so faster than smaller firms. In general, our results are consistent with predictions derived from search and implicit contract models. They highlight the importance of taking into account the possibility of recall in the analysis of unemployment duration among unemployment benefit recipients.

Compliance with drug therapy is of major concern to clinicians as well as policy makers since uncontrolled symptoms due to noncompliance present health risks for patients and may lead to social costs. Noncompliance comes in the form of skipped dosages as well as discontinuation well before a clinician deems it appropriate. The problem is especially severe in behavioral disorders among children where the symptoms can last well beyond adolescence. We use pharmacy dispensing and clinical diagnosis data on children diagnosed with attention-deficit hyperactivity disorder (ADHD) and who are on ADHD-related medications. The paper shows how the pharmacy refill data fit naturally into a discrete time hazard rate framework, and then compares estimates from alternative definitions of discontinuation. We use a long follow-up period (up to six years), allow for a flexible duration dependence and account for unobserved heterogeneity. The expected duration is about 18 months with significant differences across race, gender, copays, medication switching, and seasonality. We find that African-American, Hispanic and, Asian children are about 39% more likely, on average, to quit therapy in a given month than white children. Similarly, compared to a child that initiates drug therapy at age nine, a child that starts therapy at age ten is 26.4% more likely to discontinue at any given time. Earlier literature using the hazard approach reports smaller associations between these covariates and durations. We show that this could be because of ignored unobserved heterogeneity, use of a relatively short follow-up study design and monotonic duration dependence. Finally, our results are of particular relevance to clinicians as well as to policy makers given recent changes in federal and state policies that may make early detection and diagnosis of ADHD among children less likely.

Le NDYP (The New Deal for Young People) est le principal programme d’aide sociale au travail au Royaume-Uni destiné aux chômeurs âgés de 18 à 24 ans recevant une allocation de demandeur d’emploi (JSA) pendant au moins six mois.
L’objectif naturel du programme est d’améliorer l’employabilité à la fois extensive (trouver un emploi) et intensive (emploi durable de haute qualité), tout en acquérant des compétences et de la motivation.
Les principales questions auxquelles répond ce document sont les suivantes : « La politique améliore-t-elle réellement les perspectives d’emploi des jeunes ? » et « Les effets de la politique perdurent-ils sur différentes cohortes ? ».

Background: The efficacy of preventive zinc supplementation against diarrhea and respiratory illness may depend on simultaneous supplementation with other micronutrients. We aimed to assess the effect of supplementation with zinc and multiple micronutrients on diarrhea and other causes of non-malarial morbidity. Methods and Findings: Rural Tanzanian children (n = 612) aged 6-60 months and with height-forage z-score ,-1.5 SD were randomized to daily supplementation with zinc (10 mg) alone, multi-nutrients without zinc, multi-nutrients with zinc, or placebo. Children were followed for an average of 45 weeks. During follow-up, we recorded morbidity episodes. We found no evidence that concurrent supplementation with multi-nutrients influenced the magnitude of the effect of zinc on rates of diarrhea, respiratory illness, fever without localizing signs, or other illness (guardian-reported illness with symptoms involving skin, ears, eyes and abscesses, but excluding trauma or burns). Zinc supplementation reduced the hazard rate of diarrhea by 24% (4%-40%). By contrast, multi-nutrients seemed to increase this rate (HR; 95% CI: 1.19; 0.94-1.50), particularly in children with asymptomatic Giardia infection at baseline (2.03; 1.24-3.32). Zinc also protected against episodes of fever without localizing signs (0.75; 0.57-0.96), but we found no evidence that it reduced the overall number of clinic visits. Conclusions: We found no evidence that the efficacy of zinc supplements in reducing diarrhea rates is enhanced by concurrent supplementation with other micronutrients. By reducing rates of fever without localizing signs, supplementation with zinc may reduce inappropriate drug use with anti-malarial medications and antibiotics.

The exponential, Rayleigh, linear failure rate and Weibull distributions are the most commonly used distributions for analyzing lifetime data. These distributions have several desirable properties and nice physical interpretations. This paper introduces a new distribution named modified Weibull distribution. This distribution generalizes the following distributions: (1) exponential, (2) Rayleigh, (3) linear failure rate, and (4) Weibull. The properties of the modified Weibull distribution are discussed. The maximum likelihood estimates of its unknown parameters are obtained. A real data set is analyzed and it observed that the present distribution can provide a better fit than some other known distributions.

The general hazard rate model is a relevant model to specify the life time distributions in reliability theory and life testing. In this paper, we use masked data to obtain estimations of the unknown parameters included in life time distributions of the individual components belonging to a series system consists of J independent and nonidentical components. It is assumed here that the failure rate of component j is general with the form h j ðtÞ ¼ a j þ b j t c j À1 , j ¼ 1; 2;. .. ; J , where a j , b j , c j are non-negative parameters. Maximum likelihood and Bayes estimates of the parameters a j , b j are obtained while c j are known. Symmetrical triangular prior distributions are assumed for the unknown parameters to be estimated in obtaining the Bayes estimators for these parameters. A large simulation study is done in order to (i) explain how one can utilize the theoretical results obtained and (ii) compare the two procedures used. The problem of estimating the unknown parameters included in increasing linear failure rate model can be obtained as special case by setting c j ¼ 2 for all j ¼ 1; 2;. .. ; J .

This paper presents a robust and practical CDO valuation framework based on the application of multi-factor credit models in conjunction with weighted Monte Carlo techniques used in options pricing. The framework produces arbitrage-free prices and can be seen as an extension to the implied copula methodology of Hull and White (2006). We demonstrate the practical advantages of working through multi-factor models, rather than directly on a common hazard rate (or a set of them), to value consistently CDOs of bespoke portfolios, CDO-squared and cash CDOs.

The best known methods for estimating hazard rate functions in survival analysis models are either purely parametric or purely nonparametric. The parametric ones are sometimes too biased while the nonparametric ones are sometimes too variable. In the present paper a certain semiparametric approach to hazard rate estimation, proposed in Hjort (1991), is developed further, aiming to combine parametric and nonparametric features. It uses a dynamic local likelihood approach to fit the locally most suitable member in a given parametric class of hazard rates, and amounts to a version of non parametric parameter smoothing within the parametric class. Thus the parametric hazard rate estimate at time 8 inserts a parameter estimate that also depends on 8. We study bias and variance properties of the resulting estimator and methods for choosing the local smoothing parameter. It is shown that dynamic likelihood estimation often leads to better performance than the purely nonparametric methods, while also having capacity for not losing much to the parametric methods in cases where the model being smoothed is adequate.

We study a single-server queue, operating under the first-in-first-out (FIFO) service discipline, in which each customer independently abandons the queue if his service has not begun within a generally distributed amount of time. Under some mild conditions on the abandonment distribution, we identify a limiting heavy-traffic regime in which the resulting diffusion approximation for both the offered waiting time process (the process that tracks the amount of time an infinitely patient arriving customer would wait for service) and the queue-length process contain the entire abandonment distribution. To use a continuous mapping approach to establish our weak convergence results, we additionally develop existence, uniqueness, and continuity results for nonlinear generalized regulator mappings that are of independent interest. We further perform a simulation study to evaluate the quality of the proposed approximations for the steady-state mean queue length and the steady-state probability of abandonment suggested by the limiting diffusion process.

We obtain a heavy traffic limit for the GI/M/n + GI queue, which includes the entire patience time distribution. Our main approach is to scale the hazard rate function of the patience time distribution in such a way that our resulting diffusion approximation contains the entire hazard rate function. We then show through numerical studies that for various performance measures, our approximations tend to outperform those commonly used in practice. The robustness of our results is also demonstrated by applying them to solving constraint satisfaction problems arising in the context of telephone call centers.

We study a single-server queue, operating under the first-in-first-out (FIFO) service discipline, in which each customer independently abandons the queue if his service has not begun within a generally distributed amount of time. Under some mild conditions on the abandonment distribution, we identify a limiting heavy-traffic regime in which the resulting diffusion approximation for both the offered waiting time process (the process that tracks the amount of time an infinitely patient arriving customer would wait for service) and the queue-length process contain the entire abandonment distribution. To use a continuous mapping approach to establish our weak convergence results, we additionally develop existence, uniqueness, and continuity results for nonlinear generalized regulator mappings that are of independent interest. We further perform a simulation study to evaluate the quality of the proposed approximations for the steady-state mean queue length and the steady-state probabilit...

We obtain a heavy-traffic limit for the GI/M/n + GI queue which includes the entire aban-donment distribution. Our main approach is to scale the hazard rate function in an appropriate way such that our resulting diffusion approximation contains the entire hazard rate function. We ...