Geographic information system （GIS） is increasingly managing very large sets of data, hence a centralized data index may not always provide the most scalable solution. Recently, the peer to peer （P2P） networks hav...Geographic information system （GIS） is increasingly managing very large sets of data, hence a centralized data index may not always provide the most scalable solution. Recently, the peer to peer （P2P） networks have become very popular for sharing information in a totally decentralized manner. In this paper, a new hybrid P2P spatial indexing network （HPSIN） is proposed, which combines distributed quad-tree with distributed Hash table （DHT） based Chord network to maintain both query efficiency and system load balance. In addition, a simple theoretical model based on opened queueing network for HPSIN is established. Assuming each peer as M/M/1 queueing processor in the model, fundamental characteristics of the system is captured, and expression of average query delay is obtained in close form. The theoretical analysis and numerical computing results show that there exists an optimum point of tradeoff between efficiency and load balance. By setting a proper value of start index level ls for different network scale and query rate, HPSIN will achieve the minimum overall query delay, therefore, can adapt to different P2P application environments.展开更多
In this paper, we give a reliability anlysis of some queueing modesl with reparable service station. By using the method of supplementary variable,we obtained some system characters and reliability indices of the ser...In this paper, we give a reliability anlysis of some queueing modesl with reparable service station. By using the method of supplementary variable,we obtained some system characters and reliability indices of the service station.展开更多
In order to improve the scalability and reliability of Software Defined Networking(SDN),many studies use multiple controllers to constitute logically centralized control plane to provide load balancing and fail over.I...In order to improve the scalability and reliability of Software Defined Networking(SDN),many studies use multiple controllers to constitute logically centralized control plane to provide load balancing and fail over.In this paper,we develop a flexible dormant multi-controller model based on the centralized multi-controller architecture.The dormant multi-controller model allows part of controllers to enter the dormant state under light traffic condition for saving system cost.Meanwhile,through queueing analysis,various performance measures of the system can be obtained.Moreover,we analyze the real traffic of China Education Network and use the results as the parameters of computer simulation and verify the effects of parameters on the system characteristics.Finally,a total expected cost function is established,and genetic algorithm is employed to find the optimal values of various parameters to minimize system cost for the deployment decision making.展开更多
In this paper, we apply the backward equations of Markov skeleton processes to qucueing systems. The transient distribution of the waiting time of a GI/G/1 queueing system, the transient distribution of the length of... In this paper, we apply the backward equations of Markov skeleton processes to qucueing systems. The transient distribution of the waiting time of a GI/G/1 queueing system, the transient distribution of the length of a GI/G/N queueing system and the transient distribution of the length of queueing networks are obtained.展开更多
This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed...This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed： 1） The probability that the server is in a ＂generalized busy period＂ at time n; 2） The probability that the service station is in failure at time n, i.e., the transient unavailability of the service station, and the steady state unavailability of the service station; 3） The expected number of service station failures during the time interval （0, hi, and the steady state failure frequency of the service station; 4） The expected number of service station breakdowns in a server＇s ＂generalized busy period＂. Finally, the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.展开更多
During epidemics,controlling the patients’congestion is a way to reduce disease spreading.Raising medical demands converts hospitals into one of the sources of disease outbreaks.The long patient waiting time in queue...During epidemics,controlling the patients’congestion is a way to reduce disease spreading.Raising medical demands converts hospitals into one of the sources of disease outbreaks.The long patient waiting time in queues to receive medical services leads to more casualties.The rise of patients increases their waste,which is another source of disease outbreak.In this study,a mathematical model is developed to control patients’congestion in a medical center and manage their waste,considering environmental issues.Besides a queueing system controlling the patients’congestion in the treatment center,another queue is considered for vehicles.An inventory model is employed to prevent waste accumulation.The developed model is solved and reaches an exact solution in small size,and obtains an acceptable solution in large size using the Grasshopper algorithm.A case study is considered to demonstrate the model’s applicability.Also,Sensitivity analysis and valuable managerial insights are presented.展开更多
This paper studies a single server discrete-time Erlang loss system with Bernoulli arrival process and no waiting space. The server in the system is assumed to provide two different types of services, namely essential...This paper studies a single server discrete-time Erlang loss system with Bernoulli arrival process and no waiting space. The server in the system is assumed to provide two different types of services, namely essential and optional services, to the customer. During the operation of the system, the arrival of the catastrophe will break the system down and simultaneously induce customer to leave the system immediately. Using a new type discrete supplementary variable technique, the authors obtain some performance characteristics of the queueing system, including the steady-state availability and failure frequency of the system, the steady-state probabilities for the server being idle, busy, breakdown and the loss probability of the system etc. Finally, by the numerical examples, the authors study the influence of the system parameters on several performance measures.展开更多
The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arri...The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arrival processes modulated by queues comprise the external system,all others are belong to the internal system.It is well known that the exogenous arrival has a great influence on the asymptotic variability of performance measures in queues.For the considered queueing network in heavy traffic,we get all the LILs for the queue length,workload,busy time,idle time and departure processes,and present them by some simple functions of the primitive data.The LILs tell us some interesting insights,such as,the LILs of busy and idle times are zero and they reflect a small variability around their fluid approximations,the LIL of departure has nothing to do with the arrival process,both of the two phenomena well explain the service station’s situation of being busy all the time.The external system shows us a distinguishing effect on the performance measures:an underloaded(overloaded,critically loaded)external system affects the internal system through its arrival(departure,arrival and departure together).In addition,we also get the strong approximation of the network as an auxiliary result.展开更多
For a 2-station and 3-class reentrant line under first-buffer first-served(FBFS)service discipline in light traffic,we firstly construct the strong approximations for performance measures including the queue length,wo...For a 2-station and 3-class reentrant line under first-buffer first-served(FBFS)service discipline in light traffic,we firstly construct the strong approximations for performance measures including the queue length,workload,busy time and idle time processes.Based on the obtained strong approximations,we use a strong approximation method to find all the law of the iterated logarithms(LILs)for the above four performance measures,which are expressed as some functions of system parameters:means and variances of interarrival and service times,and characterize the fluctuations around their fluid approximations.展开更多
In the Internet of Things（IoT）, various battery-powered wireless devices are connected to collect and exchange data, and typical traffic is periodic and heterogeneous. Polling with power management is a very promisi...In the Internet of Things（IoT）, various battery-powered wireless devices are connected to collect and exchange data, and typical traffic is periodic and heterogeneous. Polling with power management is a very promising technique that can be used for communication among these devices in the IoT. In this paper, we propose a novel and scalable model to study the delay and the power consumption performance for polling schemes with power management under heterogeneous settings（particularly the heterogeneous sleeping interval）. In our model,by introducing the concept of virtual polling interval, we successfully convert the considered energy-efficient polling scheme into an equivalent purely-limited vacation system. Thus, we can easily evaluate the mean and variance of the delay and the power consumption by applying existing queueing formulae, without developing a new theoretical model as required in previous works. Extensive simulations show that our analytical results are very accurate for both homogeneous and heterogeneous settings.展开更多
The M/G/1 queueing system with multiclass customer arrivals, fixed feedback, and first come first served policy is considered, where different classes of customers have different arrival rates, service-time distributi...The M/G/1 queueing system with multiclass customer arrivals, fixed feedback, and first come first served policy is considered, where different classes of customers have different arrival rates, service-time distributions, and feedback numbers. The joint probabifity generation function of queue size of each class and the Laplace-Stieltjes transform of the total sojourn time of a customer in each class are presented, which extended the results obtained by Choi B D. The mean queue size of each class and mean total sojourn time of a customer in each class are obtained with this result. The results can be used in computer and communication networks for their performance analysis.展开更多
By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its s...By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point.展开更多
This paper develops a QKD （quantum key distribution）-based queueing model to investigate the data delay on QKD link and network, especially that based on trusted relays. It shows the mean packet delay performance of...This paper develops a QKD （quantum key distribution）-based queueing model to investigate the data delay on QKD link and network, especially that based on trusted relays. It shows the mean packet delay performance of the QKD system. Furthermore, it proposes a key buffering policy which could effectively improve the delay performance in practice. The results will be helpful for quality of service in practical QKD systems.展开更多
In this paper, we prove strong approximations for the open queueing network in heavytraffic. Strong approximations are given for the queueing length, the virtual waiting timeand the sojourn time processes, and for the...In this paper, we prove strong approximations for the open queueing network in heavytraffic. Strong approximations are given for the queueing length, the virtual waiting timeand the sojourn time processes, and for the embedded sequences associated with the queueinglength processes.展开更多
We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the...We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the server commences service and serves exhaustively before taking another vacation. If the server finds the system empty, it waits a fixed time c. At the expiration of this time, the server commences another vacation if no customer has arrived;otherwise, it serves exhaustively before commencing another vacation. Analytical results are derived for the mean waiting time in the system. The timeout scheme is shown to be a generalized scheme of which both the single vacation and multiple vacations schemes are special cases, with c=∞and c=0, respectively. The model is extended to the N-policy vacation queueing system.展开更多
Bottlenecks, the key ingredients for improving the performances of the production networks, have been profoundly studied during the last decade. Yet, because of the complexity of the research results, there is still a...Bottlenecks, the key ingredients for improving the performances of the production networks, have been profoundly studied during the last decade. Yet, because of the complexity of the research results, there is still a significant gap between theory and practice. In this paper, we review various bottleneck definitions, detection methods and the asymptotic results and provide a practical guidance for recognizing and utilizing the bottlenecks in production networks. Queueing theory works as the mathematical foundation in our study. Various definitions of the bottlenecks are classified as either Performance in Processing （PIP） based or sensitivity based definitions, which reflect the preferences of the managers. Detection methods are surveyed closely based on the definitions. These methods are used to recognize the bottlenecks and to provide diagnosis results to managers. Comparisons show that different detection methods may lead to vastly different conclusions. The recognition of the bottlenecks has another advantage： the ultimate phenomena of the bottlenecks can greatly reduce the computation complexity in calculating the system performances. Bottlenecks based approximation and asymptotic results are studied to exhibit the contribution of bottlenecks in performance estimation and theoretical analysis.展开更多
The unforeseen mobile data explosion as well as the scarce of spectrum resource pose a major challenge to the performance of today＇s cellular networks which are in urgent need of novel solutions to handle such volumi...The unforeseen mobile data explosion as well as the scarce of spectrum resource pose a major challenge to the performance of today＇s cellular networks which are in urgent need of novel solutions to handle such voluminous mobile data. Long term evolution-unlicensed （LTE-U）, which extends the LTE standard operating on the unlicensed band, has been proposed to improve system throughput. In LTE-U system, arriving users will contend the unlicensed spectrum resource with wireless fidelity （WiFi） users to transmit data information. Nevertheless, there is no clear consensus as to the benefits of transmission using unlicensed bands for LTE users. To this end, in this paper an analytical model is presented based on a queue system to understand the performance achieved by unlicensed based LTE system taking quality of services （QoS） and LTE-U users＇ behaviors into account. To obtain the stead-state solutions of the queue system, a matrix geometric method is used to solve it. Then, the average delay and utilization of unlicensed band for the LTE-U users is derived by using the queuing model. The performance of LTE-U coexistence is evaluated with WiFi using the proposed model and provide some initial insights as to the advantage of LTE-U in practice.展开更多
基金supported by the Hi-Tech Research and Development Program of China (2009AA12Z219)the National Natural Science Foundation of China (40801149)+1 种基金the Jiangsu Province Bureau of Surveying and Mappings Research Fund (JSCHKY200810)Visiting Scholar Foundation of Key Lab. In University, the NJUPT Research Fund (NY206009)
文摘Geographic information system （GIS） is increasingly managing very large sets of data, hence a centralized data index may not always provide the most scalable solution. Recently, the peer to peer （P2P） networks have become very popular for sharing information in a totally decentralized manner. In this paper, a new hybrid P2P spatial indexing network （HPSIN） is proposed, which combines distributed quad-tree with distributed Hash table （DHT） based Chord network to maintain both query efficiency and system load balance. In addition, a simple theoretical model based on opened queueing network for HPSIN is established. Assuming each peer as M/M/1 queueing processor in the model, fundamental characteristics of the system is captured, and expression of average query delay is obtained in close form. The theoretical analysis and numerical computing results show that there exists an optimum point of tradeoff between efficiency and load balance. By setting a proper value of start index level ls for different network scale and query rate, HPSIN will achieve the minimum overall query delay, therefore, can adapt to different P2P application environments.
文摘In this paper, we give a reliability anlysis of some queueing modesl with reparable service station. By using the method of supplementary variable,we obtained some system characters and reliability indices of the service station.
基金the National High-tech R&D Program ("863" Program) of China，the National Science Foundation of China，National Science & Technology Pillar Program of China，the National Science Foundation of China，the Post-Doctoral Funding of China，Tsinghua-Huawei joint research project
文摘In order to improve the scalability and reliability of Software Defined Networking(SDN),many studies use multiple controllers to constitute logically centralized control plane to provide load balancing and fail over.In this paper,we develop a flexible dormant multi-controller model based on the centralized multi-controller architecture.The dormant multi-controller model allows part of controllers to enter the dormant state under light traffic condition for saving system cost.Meanwhile,through queueing analysis,various performance measures of the system can be obtained.Moreover,we analyze the real traffic of China Education Network and use the results as the parameters of computer simulation and verify the effects of parameters on the system characteristics.Finally,a total expected cost function is established,and genetic algorithm is employed to find the optimal values of various parameters to minimize system cost for the deployment decision making.
基金the National Natural Sciences Foundation of China (No.10171009) "211 Project"+1 种基金"985 Project"Research Fund for Ph.D Programs of MOE of China (No.20010533001).
文摘 In this paper, we apply the backward equations of Markov skeleton processes to qucueing systems. The transient distribution of the waiting time of a GI/G/1 queueing system, the transient distribution of the length of a GI/G/N queueing system and the transient distribution of the length of queueing networks are obtained.
基金supported in part by the National Natural Science Foundation of China under Grant Nos. 71171138,70871084the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.200806360001
文摘This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed： 1） The probability that the server is in a ＂generalized busy period＂ at time n; 2） The probability that the service station is in failure at time n, i.e., the transient unavailability of the service station, and the steady state unavailability of the service station; 3） The expected number of service station failures during the time interval （0, hi, and the steady state failure frequency of the service station; 4） The expected number of service station breakdowns in a server＇s ＂generalized busy period＂. Finally, the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.
文摘During epidemics,controlling the patients’congestion is a way to reduce disease spreading.Raising medical demands converts hospitals into one of the sources of disease outbreaks.The long patient waiting time in queues to receive medical services leads to more casualties.The rise of patients increases their waste,which is another source of disease outbreak.In this study,a mathematical model is developed to control patients’congestion in a medical center and manage their waste,considering environmental issues.Besides a queueing system controlling the patients’congestion in the treatment center,another queue is considered for vehicles.An inventory model is employed to prevent waste accumulation.The developed model is solved and reaches an exact solution in small size,and obtains an acceptable solution in large size using the Grasshopper algorithm.A case study is considered to demonstrate the model’s applicability.Also,Sensitivity analysis and valuable managerial insights are presented.
基金supported by the National Natural Science Foundation of China under Grant No.70871084Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 200806360001the Scientific Research Fund of Sichuan Provincial Education Department under Grant No.10ZA136
文摘This paper studies a single server discrete-time Erlang loss system with Bernoulli arrival process and no waiting space. The server in the system is assumed to provide two different types of services, namely essential and optional services, to the customer. During the operation of the system, the arrival of the catastrophe will break the system down and simultaneously induce customer to leave the system immediately. Using a new type discrete supplementary variable technique, the authors obtain some performance characteristics of the queueing system, including the steady-state availability and failure frequency of the system, the steady-state probabilities for the server being idle, busy, breakdown and the loss probability of the system etc. Finally, by the numerical examples, the authors study the influence of the system parameters on several performance measures.
基金supported by the National Natural Science Foundation of China(No.11871116 and No.11971074).
文摘The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arrival processes modulated by queues comprise the external system,all others are belong to the internal system.It is well known that the exogenous arrival has a great influence on the asymptotic variability of performance measures in queues.For the considered queueing network in heavy traffic,we get all the LILs for the queue length,workload,busy time,idle time and departure processes,and present them by some simple functions of the primitive data.The LILs tell us some interesting insights,such as,the LILs of busy and idle times are zero and they reflect a small variability around their fluid approximations,the LIL of departure has nothing to do with the arrival process,both of the two phenomena well explain the service station’s situation of being busy all the time.The external system shows us a distinguishing effect on the performance measures:an underloaded(overloaded,critically loaded)external system affects the internal system through its arrival(departure,arrival and departure together).In addition,we also get the strong approximation of the network as an auxiliary result.
基金supported by the National Natural Science Foundation of China(No.11871116 and No.11971074)by the Fundamental Research Funds for the Central Universities(No.2023ZCJH02)。
文摘For a 2-station and 3-class reentrant line under first-buffer first-served(FBFS)service discipline in light traffic,we firstly construct the strong approximations for performance measures including the queue length,workload,busy time and idle time processes.Based on the obtained strong approximations,we use a strong approximation method to find all the law of the iterated logarithms(LILs)for the above four performance measures,which are expressed as some functions of system parameters:means and variances of interarrival and service times,and characterize the fluctuations around their fluid approximations.
基金supported by Macao FDCT-MOST grant 001/2015/AMJ, Macao FDCT grants 013/2014/A1 and 005/2016/A1the National Natural Science Foundation of China (Nos. 61373027 and 61672321)the Natural Science Foundation of Shandong Province (No. ZR2012FM023)
文摘In the Internet of Things（IoT）, various battery-powered wireless devices are connected to collect and exchange data, and typical traffic is periodic and heterogeneous. Polling with power management is a very promising technique that can be used for communication among these devices in the IoT. In this paper, we propose a novel and scalable model to study the delay and the power consumption performance for polling schemes with power management under heterogeneous settings（particularly the heterogeneous sleeping interval）. In our model,by introducing the concept of virtual polling interval, we successfully convert the considered energy-efficient polling scheme into an equivalent purely-limited vacation system. Thus, we can easily evaluate the mean and variance of the delay and the power consumption by applying existing queueing formulae, without developing a new theoretical model as required in previous works. Extensive simulations show that our analytical results are very accurate for both homogeneous and heterogeneous settings.
基金the National Natural Science Foundation of China (60703094)Mathematical Tianyuan Foundation of China (10626021)
文摘The M/G/1 queueing system with multiclass customer arrivals, fixed feedback, and first come first served policy is considered, where different classes of customers have different arrival rates, service-time distributions, and feedback numbers. The joint probabifity generation function of queue size of each class and the Laplace-Stieltjes transform of the total sojourn time of a customer in each class are presented, which extended the results obtained by Choi B D. The mean queue size of each class and mean total sojourn time of a customer in each class are obtained with this result. The results can be used in computer and communication networks for their performance analysis.
基金supported by the National Natural Science Foundation of China(11371303)Natural Science Foundation of Xinjiang(2012211A023)Science Foundation of Xinjiang University(XY110101)
文摘By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point.
基金Project supported by National Fundamental Research Program of China (Grant No 2006CB921900)National Natural Science Foundation of China (Grant Nos 60537020 and 60621064)Knowledge Innovation Project of Chinese Academy of Sciences
文摘This paper develops a QKD （quantum key distribution）-based queueing model to investigate the data delay on QKD link and network, especially that based on trusted relays. It shows the mean packet delay performance of the QKD system. Furthermore, it proposes a key buffering policy which could effectively improve the delay performance in practice. The results will be helpful for quality of service in practical QKD systems.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, we prove strong approximations for the open queueing network in heavytraffic. Strong approximations are given for the queueing length, the virtual waiting timeand the sojourn time processes, and for the embedded sequences associated with the queueinglength processes.
文摘We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the server commences service and serves exhaustively before taking another vacation. If the server finds the system empty, it waits a fixed time c. At the expiration of this time, the server commences another vacation if no customer has arrived;otherwise, it serves exhaustively before commencing another vacation. Analytical results are derived for the mean waiting time in the system. The timeout scheme is shown to be a generalized scheme of which both the single vacation and multiple vacations schemes are special cases, with c=∞and c=0, respectively. The model is extended to the N-policy vacation queueing system.
基金This work was supported by NSFC Grant. No. (60074012,60274011) and NCET-04-0094 program.
文摘Bottlenecks, the key ingredients for improving the performances of the production networks, have been profoundly studied during the last decade. Yet, because of the complexity of the research results, there is still a significant gap between theory and practice. In this paper, we review various bottleneck definitions, detection methods and the asymptotic results and provide a practical guidance for recognizing and utilizing the bottlenecks in production networks. Queueing theory works as the mathematical foundation in our study. Various definitions of the bottlenecks are classified as either Performance in Processing （PIP） based or sensitivity based definitions, which reflect the preferences of the managers. Detection methods are surveyed closely based on the definitions. These methods are used to recognize the bottlenecks and to provide diagnosis results to managers. Comparisons show that different detection methods may lead to vastly different conclusions. The recognition of the bottlenecks has another advantage： the ultimate phenomena of the bottlenecks can greatly reduce the computation complexity in calculating the system performances. Bottlenecks based approximation and asymptotic results are studied to exhibit the contribution of bottlenecks in performance estimation and theoretical analysis.
基金supported by Beijing Municipal Commission of Education (201501001)Beijing Municipal Science and Technology Commission (Z16111000500000)+1 种基金the National Natural Science Foundation of China (61671073)supported by Beijing Laboratory of Advanced Information Network
文摘The unforeseen mobile data explosion as well as the scarce of spectrum resource pose a major challenge to the performance of today＇s cellular networks which are in urgent need of novel solutions to handle such voluminous mobile data. Long term evolution-unlicensed （LTE-U）, which extends the LTE standard operating on the unlicensed band, has been proposed to improve system throughput. In LTE-U system, arriving users will contend the unlicensed spectrum resource with wireless fidelity （WiFi） users to transmit data information. Nevertheless, there is no clear consensus as to the benefits of transmission using unlicensed bands for LTE users. To this end, in this paper an analytical model is presented based on a queue system to understand the performance achieved by unlicensed based LTE system taking quality of services （QoS） and LTE-U users＇ behaviors into account. To obtain the stead-state solutions of the queue system, a matrix geometric method is used to solve it. Then, the average delay and utilization of unlicensed band for the LTE-U users is derived by using the queuing model. The performance of LTE-U coexistence is evaluated with WiFi using the proposed model and provide some initial insights as to the advantage of LTE-U in practice.
