Objective： In our previous work, we incorporated complete blood count （CBC） into TNM stage to develop a new prognostic score model, which was validated to improve prediction efficiency of TNM stage for nasopharynge...Objective： In our previous work, we incorporated complete blood count （CBC） into TNM stage to develop a new prognostic score model, which was validated to improve prediction efficiency of TNM stage for nasopharyngeal carcinoma （NPC）. The purpose of this study was to revalidate the accuracy of the model, and its superiority to TNM stage, through data from a prospective study.Methods： CBC of 249 eligible patients from the 863 Program No. 2006AA02Z4B4 was evaluated. Prognostic index （PI） of each patient was calculated according to the score model. Then they were divided by the PI into three categories： the low-, intermediate-and high-risk patients. The 5-year disease-specific survival （DSS） of the three categories was compared by a log-rank test. The model and TNM stage （Tth edition） were compared on efficiency for predicting the 5-year DSS, through comparison of the area under curve （AUC） of their receiver-operating characteristic curves.Results： The 5-year DSS of the low-, intermediate- and high-risk patients were 96.0%, 79.1% and 62.2%, respectively. The low- and intermediate-risk patients had better DSS than the high-risk patients （P〈0.001 and P〈0.005, respectively）. And there was a trend of better DSS in the low-risk patients, compared with the intermediate-risk patients （P=0.049）. The AUC of the model was larger than that of TNM stage （0.726 vs. 0.661, P：0.023）. Conclusions： A CBC-based prognostic score model was revalidated to be accurate and superior to TNM stage on predicting 5-year DSS of NPC.展开更多
Several economists agree to say that the need for adjustment was essential for African countries over the decade of the 80’s. The econometric analysis of a sample of 28 sub-Saharan African countries, from variables r...Several economists agree to say that the need for adjustment was essential for African countries over the decade of the 80’s. The econometric analysis of a sample of 28 sub-Saharan African countries, from variables regarded as “representatives” for the adjustment objectives, proves that this assertion cannot be completely rejected.展开更多
Often the lifecycle data occur as count of the vital events and are recorded as integers.The purpose of this article is to model the fertility behavior based on religious,educational,economic,and occupational characte...Often the lifecycle data occur as count of the vital events and are recorded as integers.The purpose of this article is to model the fertility behavior based on religious,educational,economic,and occupational characteristics.The responses of classified groups according to these determinants are examined for significant influence on fertility using Poisson regression model(PRM) based on the National Family Health Survey-3 dataset.The observed and predicted probabilities under PRM indicate modal value of two children for the Poisson distribution modeled data.Presence of dominance of two child in the data motivates the authors to adopt multinomial regression model(MRM) in order to link fertility with various socioeconomic indicators responsible for fertility variation.Choice of the explanatory factors is limited to the availability of data.Trends and patterns of preference for birth counts suggest that religion,caste,wealth,female education,and occupation are the dominant factors shaping the observed birth process.Empirical analysis suggests that both the models used in the study perform similarly on the sample data.However,fitting of MRM by taking birth count of two as comparison category shows improved Akaike information criterion and consistent Akaike information criterion values.Current work contributes to the existing literature as it attempts to provide more insight into the determinants of Indian fertility using Poisson and MRM.展开更多
Different from the usual full counting statistics theoretical work that focuses on the higher order cumulants computation by using cumulant generating function in electrical structures, Monte Carlo simulation of singl...Different from the usual full counting statistics theoretical work that focuses on the higher order cumulants computation by using cumulant generating function in electrical structures, Monte Carlo simulation of single-barrier structure is performed to obtain time series for two types of widely applicable exclusion models, counter-flows model, and tunnel model. With high-order spectrum analysis of Matlab, the validation of Monte Carlo methods is shown through the extracted first four cumulants from the time series, which are in agreement with those from cumulant generating function. After the comparison between the counter-flows model and the tunnel model in a single barrier structure, it is found that the essential difference between them consists in the strictly holding of Pauli principle in the former and in the statistical consideration of Pauli principle in the latter.展开更多
Survival of HIV/AIDS patients is crucially dependent on comprehensive and targeted medical interventions such as supply of antiretroviral therapy and monitoring disease progression with CD4 T-cell counts. Statistical ...Survival of HIV/AIDS patients is crucially dependent on comprehensive and targeted medical interventions such as supply of antiretroviral therapy and monitoring disease progression with CD4 T-cell counts. Statistical modelling approaches are helpful towards this goal. This study aims at developing Bayesian joint models with assumed generalized error distribution (GED) for the longitudinal CD4 data and two accelerated failure time distributions, Lognormal and loglogistic, for the survival time of HIV/AIDS patients. Data are obtained from patients under antiretroviral therapy follow-up at Shashemene referral hospital during January 2006-January 2012 and at Bale Robe general hospital during January 2008-March 2015. The Bayesian joint models are defined through latent variables and association parameters and with specified non-informative prior distributions for the model parameters. Simulations are conducted using Gibbs sampler algorithm implemented in the WinBUGS software. The results of the analyses of the two different data sets show that distributions of measurement errors of the longitudinal CD4 variable follow the generalized error distribution with fatter tails than the normal distribution. The Bayesian joint GED loglogistic models fit better to the data sets compared to the lognormal cases. Findings reveal that patients’ health can be improved over time. Compared to the males, female patients gain more CD4 counts. Survival time of a patient is negatively affected by TB infection. Moreover, increase in number of opportunistic infection implies decline of CD4 counts. Patients’ age negatively affects the disease marker with no effects on survival time. Improving weight may improve survival time of patients. Bayesian joint models with GED and AFT distributions are found to be useful in modelling the longitudinal and survival processes. Thus we recommend the generalized error distributions for measurement errors of the longitudinal data under the Bayesian joint modelling. Further studies may investigate the models with various types of shared random effects and more covariates with predictions.展开更多
This paper proposes some additional moment conditions for the linear feedback model with explanatory variables being predetermined, which is proposed by [1] for the purpose of dealing with count panel data. The newly ...This paper proposes some additional moment conditions for the linear feedback model with explanatory variables being predetermined, which is proposed by [1] for the purpose of dealing with count panel data. The newly proposed moment conditions include those associated with the equidispersion, the Negbin I-type model and the stationarity. The GMM estimators are constructed incorporating the additional moment conditions. Some Monte Carlo experiments indicate that the GMM estimators incorporating the additional moment conditions perform well, compared to that using only the conventional moment conditions proposed by [2,3].展开更多
Count data that exhibit over dispersion (variance of counts is larger than its mean) are commonly analyzed using discrete distributions such as negative binomial, Poisson inverse Gaussian and other models. The Poisson...Count data that exhibit over dispersion (variance of counts is larger than its mean) are commonly analyzed using discrete distributions such as negative binomial, Poisson inverse Gaussian and other models. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial and the Poisson inverse Gaussian have variance larger than the mean and therefore are more appropriate to model over-dispersed count data. As an alternative to these two models, we shall use the generalized Poisson distribution for group comparisons in the presence of multiple covariates. This problem is known as the ANCOVA and is solved for continuous data. Our objectives were to develop ANCOVA using the generalized Poisson distribution, and compare its goodness of fit to that of the nonparametric Generalized Additive Models. We used real life data to show that the model performs quite satisfactorily when compared to the nonparametric Generalized Additive Models.展开更多
Background: Daily paediatric asthma readmissions within 28 days are a good example of a low count time series and not easily amenable to common time series methods used in studies of asthma seasonality and time trends...Background: Daily paediatric asthma readmissions within 28 days are a good example of a low count time series and not easily amenable to common time series methods used in studies of asthma seasonality and time trends. We sought to model and predict daily trends of childhood asthma readmissions over time inVictoria,Australia. Methods: We used a database of 75,000 childhood asthma admissions from the Department ofHealth,Victoria,Australiain 1997-2009. Daily admissions over time were modeled using a semi parametric Generalized Additive Model (GAM) and by sex and age group. Predictions were also estimated by using these models. Results: N = 2401 asthma readmissions within 28 days occurred during study period. Of these, n = 1358 (57%) were boys. Overall, seasonal peaks occurred in winter (30.5%) followed by autumn (28.6%) and then spring (24.6%) (p展开更多
母猪乳头数量是生猪选育中重要参考指标之一,也是生猪繁殖表型数据的组成部分。成年母猪其腹部视频较难获取,且容易受污渍干扰,乳头自动点数实现难度较大,人工计数母猪乳头数工作量大、强度高、效率低、容易产生人为误差。鉴于猪仔从出...母猪乳头数量是生猪选育中重要参考指标之一,也是生猪繁殖表型数据的组成部分。成年母猪其腹部视频较难获取,且容易受污渍干扰,乳头自动点数实现难度较大,人工计数母猪乳头数工作量大、强度高、效率低、容易产生人为误差。鉴于猪仔从出生到成年乳头数量保持一致性,该研究提出了一种基于仔猪腹部视频的深度学习乳头计数及乳房形态评估方法。通过架设在仔猪初生护理平台上的相机拍摄仔猪腹部视频,根据清晰度筛选出细节清晰的帧序列图像集,经过数据预处理再使用改进Pignip-YOLOv5s目标检测网络对仔猪乳头进行自动计数。为提高计数准确率,帧序列图像集的乳头计数使用滑动窗口取众数得到最终计数结果。试验结果表明,改进的Pignip-YOLOv5s平均精度值(mean average precision, mAP)高达0.97,较YOLOv5原模型具备更高的鲁棒性。该研究方案在113段仔猪腹部视频数据集上测试得到仔猪乳头计数方法准确率达90.26%。同时该研究提出仔猪乳房形态评估参数乳头成对数、乳头间距,从而量化仔猪乳头形态表型特征,构建了母猪乳房外在形态指标,可为母猪选育和繁殖工作提供重要的参考依据。展开更多
Clinicians need to predict the number of involved nodes in breast cancer patients in order to ascertain severity, prognosis, and design subsequent treatment. The distribution of involved nodes often displays over-disp...Clinicians need to predict the number of involved nodes in breast cancer patients in order to ascertain severity, prognosis, and design subsequent treatment. The distribution of involved nodes often displays over-dispersion—a larger variability than expected. Until now, the negative binomial model has been used to describe this distribution assuming that over-dispersion is only due to unobserved heterogeneity. The distribution of involved nodes contains a large proportion of excess zeros (negative nodes), which can lead to over-dispersion. In this situation, alternative models may better account for over-dispersion due to excess zeros. This study examines data from 1152 patients who underwent axillary dissections in a tertiary hospital in India during January 1993-January 2005. We fit and compare various count models to test model abilities to predict the number of involved nodes. We also argue for using zero inflated models in such populations where all the excess zeros come from those who have at some risk of the outcome of interest. The negative binomial regression model fits the data better than the Poisson, zero hurdle/inflated Poisson regression models. However, zero hurdle/inflated negative binomial regression models predicted the number of involved nodes much more accurately than the negative binomial model. This suggests that the number of involved nodes displays excess variability not only due to unobserved heterogeneity but also due to excess negative nodes in the data set. In this analysis, only skin changes and primary site were associated with negative nodes whereas parity, skin changes, primary site and size of tumor were associated with a greater number of involved nodes. In case of near equal performances, the zero inflated negative binomial model should be preferred over the hurdle model in describing the nodal frequency because it provides an estimate of negative nodes that are at “high-risk” of nodal involvement.展开更多
Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be depende...Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.展开更多
The issue of document management has been raised for a long time, especially with the appearance of office automation in the 1980s, which led to dematerialization and Electronic Document Management (EDM). In the same ...The issue of document management has been raised for a long time, especially with the appearance of office automation in the 1980s, which led to dematerialization and Electronic Document Management (EDM). In the same period, workflow management has experienced significant development, but has become more focused on the industry. However, it seems to us that document workflows have not had the same interest for the scientific community. But nowadays, the emergence and supremacy of the Internet in electronic exchanges are leading to a massive dematerialization of documents;which requires a conceptual reconsideration of the organizational framework for the processing of said documents in both public and private administrations. This problem seems open to us and deserves the interest of the scientific community. Indeed, EDM has mainly focused on the storage (referencing) and circulation of documents (traceability). It paid little attention to the overall behavior of the system in processing documents. The purpose of our researches is to model document processing systems. In the previous works, we proposed a general model and its specialization in the case of small documents (any document processed by a single person at a time during its processing life cycle), which represent 70% of documents processed by administrations, according to our study. In this contribution, we extend the model for processing small documents to the case where they are managed in a system comprising document classes organized in subclasses;which is the case for most administrations. We have thus observed that this model is a Markovian <i>M<sup>L×K</sup>/M<sup>L×K</sup>/</i>1 queues network. We have analyzed the constraints of this model and deduced certain characteristics and metrics. <span style="white-space:normal;"><i></i></span><i>In fine<span style="white-space:normal;"></span></i>, the ultimate objective of our work is to design a document workflow management system, integrating a component of global behavior prediction.展开更多
基金supported by Hi-Tech Research and Development Program of China (863 Program) (No.2006AA02Z4B4)
文摘Objective： In our previous work, we incorporated complete blood count （CBC） into TNM stage to develop a new prognostic score model, which was validated to improve prediction efficiency of TNM stage for nasopharyngeal carcinoma （NPC）. The purpose of this study was to revalidate the accuracy of the model, and its superiority to TNM stage, through data from a prospective study.Methods： CBC of 249 eligible patients from the 863 Program No. 2006AA02Z4B4 was evaluated. Prognostic index （PI） of each patient was calculated according to the score model. Then they were divided by the PI into three categories： the low-, intermediate-and high-risk patients. The 5-year disease-specific survival （DSS） of the three categories was compared by a log-rank test. The model and TNM stage （Tth edition） were compared on efficiency for predicting the 5-year DSS, through comparison of the area under curve （AUC） of their receiver-operating characteristic curves.Results： The 5-year DSS of the low-, intermediate- and high-risk patients were 96.0%, 79.1% and 62.2%, respectively. The low- and intermediate-risk patients had better DSS than the high-risk patients （P〈0.001 and P〈0.005, respectively）. And there was a trend of better DSS in the low-risk patients, compared with the intermediate-risk patients （P=0.049）. The AUC of the model was larger than that of TNM stage （0.726 vs. 0.661, P：0.023）. Conclusions： A CBC-based prognostic score model was revalidated to be accurate and superior to TNM stage on predicting 5-year DSS of NPC.
文摘Several economists agree to say that the need for adjustment was essential for African countries over the decade of the 80’s. The econometric analysis of a sample of 28 sub-Saharan African countries, from variables regarded as “representatives” for the adjustment objectives, proves that this assertion cannot be completely rejected.
基金supported by R&D Grant from University of DelhiDU-DST PURSE GrantICMR Grant No.3/1/3/JRF-2010/HRD-122(35831)
文摘Often the lifecycle data occur as count of the vital events and are recorded as integers.The purpose of this article is to model the fertility behavior based on religious,educational,economic,and occupational characteristics.The responses of classified groups according to these determinants are examined for significant influence on fertility using Poisson regression model(PRM) based on the National Family Health Survey-3 dataset.The observed and predicted probabilities under PRM indicate modal value of two children for the Poisson distribution modeled data.Presence of dominance of two child in the data motivates the authors to adopt multinomial regression model(MRM) in order to link fertility with various socioeconomic indicators responsible for fertility variation.Choice of the explanatory factors is limited to the availability of data.Trends and patterns of preference for birth counts suggest that religion,caste,wealth,female education,and occupation are the dominant factors shaping the observed birth process.Empirical analysis suggests that both the models used in the study perform similarly on the sample data.However,fitting of MRM by taking birth count of two as comparison category shows improved Akaike information criterion and consistent Akaike information criterion values.Current work contributes to the existing literature as it attempts to provide more insight into the determinants of Indian fertility using Poisson and MRM.
基金Project supported by the National Natural Science Foundation of China(Grant No.60676053)Applied Material in Xi'an Innovation Funds(Grant No.XA-AM-200603)
文摘Different from the usual full counting statistics theoretical work that focuses on the higher order cumulants computation by using cumulant generating function in electrical structures, Monte Carlo simulation of single-barrier structure is performed to obtain time series for two types of widely applicable exclusion models, counter-flows model, and tunnel model. With high-order spectrum analysis of Matlab, the validation of Monte Carlo methods is shown through the extracted first four cumulants from the time series, which are in agreement with those from cumulant generating function. After the comparison between the counter-flows model and the tunnel model in a single barrier structure, it is found that the essential difference between them consists in the strictly holding of Pauli principle in the former and in the statistical consideration of Pauli principle in the latter.
文摘Survival of HIV/AIDS patients is crucially dependent on comprehensive and targeted medical interventions such as supply of antiretroviral therapy and monitoring disease progression with CD4 T-cell counts. Statistical modelling approaches are helpful towards this goal. This study aims at developing Bayesian joint models with assumed generalized error distribution (GED) for the longitudinal CD4 data and two accelerated failure time distributions, Lognormal and loglogistic, for the survival time of HIV/AIDS patients. Data are obtained from patients under antiretroviral therapy follow-up at Shashemene referral hospital during January 2006-January 2012 and at Bale Robe general hospital during January 2008-March 2015. The Bayesian joint models are defined through latent variables and association parameters and with specified non-informative prior distributions for the model parameters. Simulations are conducted using Gibbs sampler algorithm implemented in the WinBUGS software. The results of the analyses of the two different data sets show that distributions of measurement errors of the longitudinal CD4 variable follow the generalized error distribution with fatter tails than the normal distribution. The Bayesian joint GED loglogistic models fit better to the data sets compared to the lognormal cases. Findings reveal that patients’ health can be improved over time. Compared to the males, female patients gain more CD4 counts. Survival time of a patient is negatively affected by TB infection. Moreover, increase in number of opportunistic infection implies decline of CD4 counts. Patients’ age negatively affects the disease marker with no effects on survival time. Improving weight may improve survival time of patients. Bayesian joint models with GED and AFT distributions are found to be useful in modelling the longitudinal and survival processes. Thus we recommend the generalized error distributions for measurement errors of the longitudinal data under the Bayesian joint modelling. Further studies may investigate the models with various types of shared random effects and more covariates with predictions.
文摘This paper proposes some additional moment conditions for the linear feedback model with explanatory variables being predetermined, which is proposed by [1] for the purpose of dealing with count panel data. The newly proposed moment conditions include those associated with the equidispersion, the Negbin I-type model and the stationarity. The GMM estimators are constructed incorporating the additional moment conditions. Some Monte Carlo experiments indicate that the GMM estimators incorporating the additional moment conditions perform well, compared to that using only the conventional moment conditions proposed by [2,3].
文摘Count data that exhibit over dispersion (variance of counts is larger than its mean) are commonly analyzed using discrete distributions such as negative binomial, Poisson inverse Gaussian and other models. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial and the Poisson inverse Gaussian have variance larger than the mean and therefore are more appropriate to model over-dispersed count data. As an alternative to these two models, we shall use the generalized Poisson distribution for group comparisons in the presence of multiple covariates. This problem is known as the ANCOVA and is solved for continuous data. Our objectives were to develop ANCOVA using the generalized Poisson distribution, and compare its goodness of fit to that of the nonparametric Generalized Additive Models. We used real life data to show that the model performs quite satisfactorily when compared to the nonparametric Generalized Additive Models.
文摘Background: Daily paediatric asthma readmissions within 28 days are a good example of a low count time series and not easily amenable to common time series methods used in studies of asthma seasonality and time trends. We sought to model and predict daily trends of childhood asthma readmissions over time inVictoria,Australia. Methods: We used a database of 75,000 childhood asthma admissions from the Department ofHealth,Victoria,Australiain 1997-2009. Daily admissions over time were modeled using a semi parametric Generalized Additive Model (GAM) and by sex and age group. Predictions were also estimated by using these models. Results: N = 2401 asthma readmissions within 28 days occurred during study period. Of these, n = 1358 (57%) were boys. Overall, seasonal peaks occurred in winter (30.5%) followed by autumn (28.6%) and then spring (24.6%) (p
文摘母猪乳头数量是生猪选育中重要参考指标之一,也是生猪繁殖表型数据的组成部分。成年母猪其腹部视频较难获取,且容易受污渍干扰,乳头自动点数实现难度较大,人工计数母猪乳头数工作量大、强度高、效率低、容易产生人为误差。鉴于猪仔从出生到成年乳头数量保持一致性,该研究提出了一种基于仔猪腹部视频的深度学习乳头计数及乳房形态评估方法。通过架设在仔猪初生护理平台上的相机拍摄仔猪腹部视频,根据清晰度筛选出细节清晰的帧序列图像集,经过数据预处理再使用改进Pignip-YOLOv5s目标检测网络对仔猪乳头进行自动计数。为提高计数准确率,帧序列图像集的乳头计数使用滑动窗口取众数得到最终计数结果。试验结果表明,改进的Pignip-YOLOv5s平均精度值(mean average precision, mAP)高达0.97,较YOLOv5原模型具备更高的鲁棒性。该研究方案在113段仔猪腹部视频数据集上测试得到仔猪乳头计数方法准确率达90.26%。同时该研究提出仔猪乳房形态评估参数乳头成对数、乳头间距,从而量化仔猪乳头形态表型特征,构建了母猪乳房外在形态指标,可为母猪选育和繁殖工作提供重要的参考依据。
文摘Clinicians need to predict the number of involved nodes in breast cancer patients in order to ascertain severity, prognosis, and design subsequent treatment. The distribution of involved nodes often displays over-dispersion—a larger variability than expected. Until now, the negative binomial model has been used to describe this distribution assuming that over-dispersion is only due to unobserved heterogeneity. The distribution of involved nodes contains a large proportion of excess zeros (negative nodes), which can lead to over-dispersion. In this situation, alternative models may better account for over-dispersion due to excess zeros. This study examines data from 1152 patients who underwent axillary dissections in a tertiary hospital in India during January 1993-January 2005. We fit and compare various count models to test model abilities to predict the number of involved nodes. We also argue for using zero inflated models in such populations where all the excess zeros come from those who have at some risk of the outcome of interest. The negative binomial regression model fits the data better than the Poisson, zero hurdle/inflated Poisson regression models. However, zero hurdle/inflated negative binomial regression models predicted the number of involved nodes much more accurately than the negative binomial model. This suggests that the number of involved nodes displays excess variability not only due to unobserved heterogeneity but also due to excess negative nodes in the data set. In this analysis, only skin changes and primary site were associated with negative nodes whereas parity, skin changes, primary site and size of tumor were associated with a greater number of involved nodes. In case of near equal performances, the zero inflated negative binomial model should be preferred over the hurdle model in describing the nodal frequency because it provides an estimate of negative nodes that are at “high-risk” of nodal involvement.
基金Supported by the National Natural Science Foundation of China(Nos.11571058&11301481)Humanities and Social Science Foundation of the Ministry of Education of China(No.17YJC910007)+1 种基金Zhejiang Provincial Natural Science Foundation of China(No.LY17A010004)Fundamental Research Funds for the Central Universities(No.DUT17LK31)
文摘Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.
文摘The issue of document management has been raised for a long time, especially with the appearance of office automation in the 1980s, which led to dematerialization and Electronic Document Management (EDM). In the same period, workflow management has experienced significant development, but has become more focused on the industry. However, it seems to us that document workflows have not had the same interest for the scientific community. But nowadays, the emergence and supremacy of the Internet in electronic exchanges are leading to a massive dematerialization of documents;which requires a conceptual reconsideration of the organizational framework for the processing of said documents in both public and private administrations. This problem seems open to us and deserves the interest of the scientific community. Indeed, EDM has mainly focused on the storage (referencing) and circulation of documents (traceability). It paid little attention to the overall behavior of the system in processing documents. The purpose of our researches is to model document processing systems. In the previous works, we proposed a general model and its specialization in the case of small documents (any document processed by a single person at a time during its processing life cycle), which represent 70% of documents processed by administrations, according to our study. In this contribution, we extend the model for processing small documents to the case where they are managed in a system comprising document classes organized in subclasses;which is the case for most administrations. We have thus observed that this model is a Markovian <i>M<sup>L×K</sup>/M<sup>L×K</sup>/</i>1 queues network. We have analyzed the constraints of this model and deduced certain characteristics and metrics. <span style="white-space:normal;"><i></i></span><i>In fine<span style="white-space:normal;"></span></i>, the ultimate objective of our work is to design a document workflow management system, integrating a component of global behavior prediction.
