We study a batch arrival MX/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular trans...We study a batch arrival MX/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtained, from which we obtain the stochastic decomposition structure of system length which indicates the relationship with that of the MX/M/1 queue without vacation. Some performance indices are derived by using the PGF of the stationary system length distribution. It is important that we obtain the Laplace Stieltjes transform (LST) of the stationary waiting time distribution. Further, we obtain the mean system length and the mean waiting time. Finally, numerical results for some special cases are presented to show the effects of system parameters.展开更多
In this paper, we study an M/M/1 queue with multiple working vacations under following Bernoulli control policy: at the instants of the completion of a service in vacation, the server will interrupt the vacation and e...In this paper, we study an M/M/1 queue with multiple working vacations under following Bernoulli control policy: at the instants of the completion of a service in vacation, the server will interrupt the vacation and enter regular busy period with probability 1 p (if there are customers in the queue) or continue the vacation with probability p. For this model, we drive the analytic expression of the stationary queue length and demonstrate stochastic decomposition structures of the stationary queue length and waiting time, also we obtain the additional queue length and the additional delay of this model. The results we got agree with the corresponding results for working vacation model with or without vacation interruption if we set p = 0 or p = 1, respectively.展开更多
In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on ...In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on the left real line and these results describe the point spectra of the operator. Then, we show that the essential growth bound of the C_0-semigroup generated by the operator is 0 and therefore it is not quasi compact, the essential spectral bound of the C_0-semigroup is equal to 1. Moreover, our results imply it is impossible that the time-dependent solution of the model exponentially converges to its steady-state solution.展开更多
In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M...In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/G/1 queue again. Through establishing and solving the density evolution equa tions, the busy-period distribution, and the stationary distributions of waitin g time and queue length were obtained. In addition, the stability condition of th is queue system was given by means of an imbedded renewal process.展开更多
Work zones present challenges to safety and mobility that require agencies to balance limited resources with vital traffic management activities. Extensive literature exists regarding the impact of congestion and reco...Work zones present challenges to safety and mobility that require agencies to balance limited resources with vital traffic management activities. Extensive literature exists regarding the impact of congestion and recommendations for work zone design to provide safe and efficient traffic operations. However, it is often infeasible or unsafe to inspect every work zone within an agency’s jurisdiction, so it is important to obtain operational feedback regarding congestion and crashes in work zones to prioritize inspection activities. This paper outlines the use of connected vehicle speed data and crash report data to identify operational performance problems in work zones. This is a way to provide feedback to queuing models used to design maintenance-of-traffic (MOT) plans. A weekly work zone report and dashboards were developed for use by the Indiana Department of Transportation (INDOT) for the purpose of assessing and improving both mobility and safety in work zones. The study has developed a mile-hours of congestion graph, frequency of speed delta heat map, congestion profile graph, and the Route Builder interactive application to comprehensively visualize work zone performance. This weekly report provides a mechanism for agency staff to maintain situational awareness of which work zones were most challenging for queues and during what periods those were likely to occur. In one case study, the reports were used to identify and mitigate operational performance problems in a work zone within 4 weeks, reducing congestion and crash rates. The integration of these data provided project managers with quantitative information about traffic mobility and performance of work zones for informed decision-making during the construction season.展开更多
This study investigates relationships between congestion and travel time performance metrics and crashes on road segments. The study focuses on work zone routes in Iowa, utilizing 2021 commercially-available probe veh...This study investigates relationships between congestion and travel time performance metrics and crashes on road segments. The study focuses on work zone routes in Iowa, utilizing 2021 commercially-available probe vehicle data and crash data. Travel time performance metrics were derived from the probe vehicle data, and crash counts were obtained from the crash data. Additional variables included road characteristics (traffic volume, road type, segment length) and a categorical variable for the presence of a work zone. A mixed effect linear regression model was employed to identify relationships between road segment crash counts and the selected performance metrics. This was accomplished for two sets of models that include congestion performance measures at different defining threshold values, along with travel time performance measures. The study results indicate that the congestion indicators, certain travel time performance measures, and traffic counts were statistically significant and positively correlated with crash counts. Indicator variables for rural interstate locations and non-active work zones have a stronger influence on crash count than those for municipal interstate locations and active work zones. These findings can inform decision-makers on work zone safety strategies and crash mitigation planning, especially in high traffic volume areas prone to congestion and queues.展开更多
考虑服务员在休假期间不是完全停止工作,而是以相对于正常服务期的低些的服务率服务顾客的GI/M/1工作休假排队模型.在此模型基础上,针对现实的GI/M/1排队模型中可能出现的外来干扰因素,提出了带RCE(removal of customers in the end)抵...考虑服务员在休假期间不是完全停止工作,而是以相对于正常服务期的低些的服务率服务顾客的GI/M/1工作休假排队模型.在此模型基础上,针对现实的GI/M/1排队模型中可能出现的外来干扰因素,提出了带RCE(removal of customers in the end)抵消策略的负顾客GI/M/1工作休假排队这一新的模型.服务规则为先到先服务.工作休假策略为空竭服务多重工作休假.抵消原则为负顾客一对一抵消队尾的正顾客,若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务.首先通过引进补充变量得到一个向量马氏过程,然后由矩阵几何解方法成功求得到达时刻和任意时刻系统队长的稳态分布.展开更多
文摘We study a batch arrival MX/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtained, from which we obtain the stochastic decomposition structure of system length which indicates the relationship with that of the MX/M/1 queue without vacation. Some performance indices are derived by using the PGF of the stationary system length distribution. It is important that we obtain the Laplace Stieltjes transform (LST) of the stationary waiting time distribution. Further, we obtain the mean system length and the mean waiting time. Finally, numerical results for some special cases are presented to show the effects of system parameters.
基金Foundation item： Supported by the National Science Foundation of China（60874083） Supported by the 2011 National Statistical Science Development Funds（2011LY014） Supported by the 2012 Soft Science Devel- opment Funds of Science and Technology Committee of Henan Province（122400450090）
文摘In this paper, we study an M/M/1 queue with multiple working vacations under following Bernoulli control policy: at the instants of the completion of a service in vacation, the server will interrupt the vacation and enter regular busy period with probability 1 p (if there are customers in the queue) or continue the vacation with probability p. For this model, we drive the analytic expression of the stationary queue length and demonstrate stochastic decomposition structures of the stationary queue length and waiting time, also we obtain the additional queue length and the additional delay of this model. The results we got agree with the corresponding results for working vacation model with or without vacation interruption if we set p = 0 or p = 1, respectively.
基金Supported by the National Natural Science Foundation of China(Grant No.11801485)
文摘In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on the left real line and these results describe the point spectra of the operator. Then, we show that the essential growth bound of the C_0-semigroup generated by the operator is 0 and therefore it is not quasi compact, the essential spectral bound of the C_0-semigroup is equal to 1. Moreover, our results imply it is impossible that the time-dependent solution of the model exponentially converges to its steady-state solution.
基金Project supported by the National Natural Science Foundation of China(Grant No.70171059)
文摘In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/G/1 queue again. Through establishing and solving the density evolution equa tions, the busy-period distribution, and the stationary distributions of waitin g time and queue length were obtained. In addition, the stability condition of th is queue system was given by means of an imbedded renewal process.
文摘Work zones present challenges to safety and mobility that require agencies to balance limited resources with vital traffic management activities. Extensive literature exists regarding the impact of congestion and recommendations for work zone design to provide safe and efficient traffic operations. However, it is often infeasible or unsafe to inspect every work zone within an agency’s jurisdiction, so it is important to obtain operational feedback regarding congestion and crashes in work zones to prioritize inspection activities. This paper outlines the use of connected vehicle speed data and crash report data to identify operational performance problems in work zones. This is a way to provide feedback to queuing models used to design maintenance-of-traffic (MOT) plans. A weekly work zone report and dashboards were developed for use by the Indiana Department of Transportation (INDOT) for the purpose of assessing and improving both mobility and safety in work zones. The study has developed a mile-hours of congestion graph, frequency of speed delta heat map, congestion profile graph, and the Route Builder interactive application to comprehensively visualize work zone performance. This weekly report provides a mechanism for agency staff to maintain situational awareness of which work zones were most challenging for queues and during what periods those were likely to occur. In one case study, the reports were used to identify and mitigate operational performance problems in a work zone within 4 weeks, reducing congestion and crash rates. The integration of these data provided project managers with quantitative information about traffic mobility and performance of work zones for informed decision-making during the construction season.
文摘This study investigates relationships between congestion and travel time performance metrics and crashes on road segments. The study focuses on work zone routes in Iowa, utilizing 2021 commercially-available probe vehicle data and crash data. Travel time performance metrics were derived from the probe vehicle data, and crash counts were obtained from the crash data. Additional variables included road characteristics (traffic volume, road type, segment length) and a categorical variable for the presence of a work zone. A mixed effect linear regression model was employed to identify relationships between road segment crash counts and the selected performance metrics. This was accomplished for two sets of models that include congestion performance measures at different defining threshold values, along with travel time performance measures. The study results indicate that the congestion indicators, certain travel time performance measures, and traffic counts were statistically significant and positively correlated with crash counts. Indicator variables for rural interstate locations and non-active work zones have a stronger influence on crash count than those for municipal interstate locations and active work zones. These findings can inform decision-makers on work zone safety strategies and crash mitigation planning, especially in high traffic volume areas prone to congestion and queues.
文摘考虑服务员在休假期间不是完全停止工作,而是以相对于正常服务期的低些的服务率服务顾客的GI/M/1工作休假排队模型.在此模型基础上,针对现实的GI/M/1排队模型中可能出现的外来干扰因素,提出了带RCE(removal of customers in the end)抵消策略的负顾客GI/M/1工作休假排队这一新的模型.服务规则为先到先服务.工作休假策略为空竭服务多重工作休假.抵消原则为负顾客一对一抵消队尾的正顾客,若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务.首先通过引进补充变量得到一个向量马氏过程,然后由矩阵几何解方法成功求得到达时刻和任意时刻系统队长的稳态分布.
