We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digita...We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.展开更多
Querétaro-Celaya highway is the obligatory road to the center of Mexico;the establishment of new companies in the area has generated the need to study the dynamics of the vehicular flow that transits this route.G...Querétaro-Celaya highway is the obligatory road to the center of Mexico;the establishment of new companies in the area has generated the need to study the dynamics of the vehicular flow that transits this route.Given that the flow of traffic on a highway is a stochastic phenomenon,it is necessary to apply tools that take into account the randomness of the system to measure performance.Queueing theory models capture the random nature of the phenomenon and provide direct information about the relationship between the variables of the system.In this work,the flow of vehicles on the Querétaro-Celaya highway is analyzed with a macroscopic approach and using analytical models of queueing theory;it is concluded that currently the flow on this road is non-congested.The method is an alternative for institutions that do not have specialized packages to carry out studies of this nature.展开更多
In cognitive radio networks, the spectrum utilization can be improved by cognitive users opportunistically using the idle channels licensed to the primary users. However, the new arrived cognitive users may not be abl...In cognitive radio networks, the spectrum utilization can be improved by cognitive users opportunistically using the idle channels licensed to the primary users. However, the new arrived cognitive users may not be able to use the channel immediately since the channel usage state is random. This will impose additional time delay for the cognitive users. Excessive waiting delay can make cognitive users miss the spectrum access chances. In this paper, a discrete-time Markov queuing model from a macro point of view is provided. Through the matrix-geometric solution theory, the average sojourn time for cognitive users in the steady state before accessing the spectrum is obtained. Given the tolerant delay of cognitive users, the macro-based throughput is derived and an access control mechanism is proposed. The numerical results show the effects of service completion probability on average sojourn time and throughput. It is confirmed that the throughput can be obviously improved by using the proposed access control mechanism. Finally, the performance evaluations based on users are compared to that based on data packets.展开更多
This paper proposes a new discrete-time Geo/G/1 queueing model under the control of bi-level randomized(p,N1,N2)-policy.That is,the server is closed down immediately when the system is empty.If N1(≥1)customers are ac...This paper proposes a new discrete-time Geo/G/1 queueing model under the control of bi-level randomized(p,N1,N2)-policy.That is,the server is closed down immediately when the system is empty.If N1(≥1)customers are accumulated in the queue,the server is activated for service with probability p(0≤p≤1)or still left off with probability(1−p).When the number of customers in the system becomes N_(2)(≥N1),the server begins serving the waiting customers until the system becomes empty again.For the model,firstly,we obtain the transient solution of the queue size distribution and the explicit recursive formulas of the stationary queue length distribution by employing the total probability decomposition technique.Then,the expressions of its probability generating function of the steady-state queue size and the expected steady-state queue size are presented.Additionally,numerical examples are conducted to discuss the effect of the system parameters on some performance indices.Furthermore,the steady-state distribution of queue length at epochs n−,n and outside observer’s observation epoch are explored,respectively.Finally,we establish a cost function to investigate the cost optimization problem under the constraint of the average waiting time.And the presented model provides a less expected cost as compared to the traditional N-policy.展开更多
In order to estimate vehicular queue length at signalized intersections accurately and overcome the shortcomings and restrictions of existing studies especially those based on shockwave theory,a new methodology is pre...In order to estimate vehicular queue length at signalized intersections accurately and overcome the shortcomings and restrictions of existing studies especially those based on shockwave theory,a new methodology is presented for estimating vehicular queue length using data from both point detectors and probe vehicles. The methodology applies the shockwave theory to model queue evolution over time and space. Using probe vehicle locations and times as well as point detector measured traffic states,analytical formulations for calculating the maximum and minimum( residual) queue length are developed. The proposed methodology is verified using ground truth data collected from numerical experiments conducted in Shanghai,China. It is found that the methodology has a mean absolute percentage error of 17. 09%,which is reasonably effective in estimating the queue length at traffic signalized intersections. Limitations of the proposed models and algorithms are also discussed in the paper.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
The close-in weapon system(CIWS)is a combat system that faces a complex environment full of dynamic and unknown challenges,whose construction and planning require a systematic design method.Multiliving agent(MLA)theor...The close-in weapon system(CIWS)is a combat system that faces a complex environment full of dynamic and unknown challenges,whose construction and planning require a systematic design method.Multiliving agent(MLA)theory is a methodology for the combat system design,which uses the livelihood degree to evaluate the multi-dimensional long-term operational effectiveness of the system;whereas,there is still no uniform quantization framework for the livelihood degree,and the adjustment methods of livelihood degree need to be further improved.In this paper,we propose the uniform quantization framework for the livelihood degree and detailed discuss the methods of livelihood adjustment.Based on the MLA theory,the multi-dimensional operational effectiveness of the missile-gun integrated weapon system(MGIWS)is analyzed,and the long-term combat effectiveness against the saturation attack is assessed.Furthermore,the planning problem of the equipment deployment and configuration is investigated.Two objectives,including the overall livelihood degree and cost-effectiveness(CE),are proposed,and the optimization method based on genetic algorithm(GA)is studied for the planning problem.展开更多
One of the more challenging and unresolved issues in ATM networks is the congestion control of available bit rate （ABR）. The dynamic controller is designed based on the control theory and the feedback mechanism of e...One of the more challenging and unresolved issues in ATM networks is the congestion control of available bit rate （ABR）. The dynamic controller is designed based on the control theory and the feedback mechanism of explicit rates With the given method of a chosen parameter, it can guarantee the stability of the controller and closed loop system with propagation delay and bandwidth oscillation. It needs less parameters（only one） to be designed. The queue length can converge to the given value in the least steps. The fairness of different connections is considered further. The simulations show better performance and good quality of service（QoS） is achieved.展开更多
Congestion is one of the well-studied problems in computer networks,which occurs when the request for network resources exceeds the buffer capacity.Many active queue management techniques such as BLUE and RED have bee...Congestion is one of the well-studied problems in computer networks,which occurs when the request for network resources exceeds the buffer capacity.Many active queue management techniques such as BLUE and RED have been proposed in the literature to control congestions in early stages.In this paper,we propose two discrete-time queueing network analytical models to drop the arrival packets in preliminary stages when the network becomes congested.The first model is based on Lambda Decreasing and it drops packets from a probability value to another higher value according to the buffer length.Whereas the second proposed model drops packets linearly based on the current queue length.We compare the performance of both our models with the original BLUE in order to decide which of these methods offers better quality of service.The comparison is done in terms of packet dropping probability,average queue length,throughput ratio,average queueing delay,and packet loss rate.展开更多
This paper considers a Geo/Geo/1 queueing system with infinite capacity, in which the service rate changes depending on the workload. Initially, when the number of customers in the system is less than a certain thresh...This paper considers a Geo/Geo/1 queueing system with infinite capacity, in which the service rate changes depending on the workload. Initially, when the number of customers in the system is less than a certain threshold L, low service rate is provided for cost saving. On the other hand, the high service rate is activated as soon as L customers accumulate in the system and such service rate is preserved until the system becomes completely empty even if the number of customers falls below L. The steady-state probability distribution and the expected number of customers in the system are derived. Through the first-step argument, a recursive algorithm for computing the first moment of the conditional sojourn time is obtained. Furthermore, employing the results of regeneration cycle analysis, the direct search method is also implemented to determine the optimal value of L for minimizing the long-run average cost rate function.展开更多
The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[1...The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[10].In this paper,we shall give the su？cient and necessary conditions of l-ergodicity,geometric ergodicity,and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.展开更多
This paper considers the departure process and the optimal control strategy for a discretetime Geo/G/1 queueing model in which the system operates under the control of multiple server vacations and Min(N, V)-policy. U...This paper considers the departure process and the optimal control strategy for a discretetime Geo/G/1 queueing model in which the system operates under the control of multiple server vacations and Min(N, V)-policy. Using the law of total probability decomposition, the renewal theory and the probability generating function technique, the transient and the steady-state probabilities that the server is busy at any epoch n^+ are derived. The authors also obtain the explicit expression of the probability generating function for the expected number of departures occurring in the time interval (0^+, n^+] from any initial state. Meanwhile, the relationship among departure process, server's state process and service renewal process in server busy period is found, which shows the special structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by our results. Furthermore, the approximate expansion for calculating the expected number of departures is presented. In addition, some other important performance measures,including the expected length of server busy period, server's actual vacation period and busy cycle period etc., are analyzed. Finally, some numerical results are provided to determine the optimum value N*for minimizing the system cost under a given cost structure.展开更多
This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service co...This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service completion, begins a process of search in order to find the following customer to be served with a certain probability, or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or on vacation. Finally, the author gives two stochastic decomposition laws, and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.展开更多
The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times.As soon as the orbit is empty,the server takes a vacation.However,the server is allowed to take a maximum numb...The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times.As soon as the orbit is empty,the server takes a vacation.However,the server is allowed to take a maximum number J of vacations,if the system remains empty after the end of a vacation.If there is at least one customer in the orbit at the end of a vacation,the server begins to serve the new arrivals or the arriving customers from the orbit.For this model,the authors focus on the steady-state analysis for the considered queueing system.Firstly,the authors obtain the generating functions of the number of customers in the orbit and in the system.Then,the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size.Besides,the relationship between this discrete-time model and the corresponding continuous-time model is also investigated.Finally,some numerical results are provided.展开更多
This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer ...This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the parameters on several performance characteristics of the system.展开更多
In this paper, we consider a discrete-time preemptive priority queue with different service com- pletion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model c...In this paper, we consider a discrete-time preemptive priority queue with different service com- pletion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers＇ arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated than the continuous- time model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the low-priority queue, as well as along the direction of the high-priority queue.展开更多
This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject ...This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject to breakdowns at random when it is in operation. As soon as the server fails, a repair process immediately begins. During the repair period, the defective server still provides service for the waiting customers at a lower service rate rather than completely stopping service.We analyze the stability condition for the considered system. Using the probability generating function technique, we obtain the probability generating function of the steady-state queue size distribution.Also, various important performance measures are derived explicitly. Furthermore, some numerical results are provided to carry out the sensitivity analysis so as to illustrate the effect of different parameters on the system performance measures. Finally, an operating cost function is formulated to model a computer system and the parabolic method is employed to numerically find the optimum service rate in working breakdown period.展开更多
文摘We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.
文摘Querétaro-Celaya highway is the obligatory road to the center of Mexico;the establishment of new companies in the area has generated the need to study the dynamics of the vehicular flow that transits this route.Given that the flow of traffic on a highway is a stochastic phenomenon,it is necessary to apply tools that take into account the randomness of the system to measure performance.Queueing theory models capture the random nature of the phenomenon and provide direct information about the relationship between the variables of the system.In this work,the flow of vehicles on the Querétaro-Celaya highway is analyzed with a macroscopic approach and using analytical models of queueing theory;it is concluded that currently the flow on this road is non-congested.The method is an alternative for institutions that do not have specialized packages to carry out studies of this nature.
文摘In cognitive radio networks, the spectrum utilization can be improved by cognitive users opportunistically using the idle channels licensed to the primary users. However, the new arrived cognitive users may not be able to use the channel immediately since the channel usage state is random. This will impose additional time delay for the cognitive users. Excessive waiting delay can make cognitive users miss the spectrum access chances. In this paper, a discrete-time Markov queuing model from a macro point of view is provided. Through the matrix-geometric solution theory, the average sojourn time for cognitive users in the steady state before accessing the spectrum is obtained. Given the tolerant delay of cognitive users, the macro-based throughput is derived and an access control mechanism is proposed. The numerical results show the effects of service completion probability on average sojourn time and throughput. It is confirmed that the throughput can be obviously improved by using the proposed access control mechanism. Finally, the performance evaluations based on users are compared to that based on data packets.
基金Supported by the National Natural Science Foundation of China(71571127)the Opening Fund of Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things(2023WZJ02)。
文摘This paper proposes a new discrete-time Geo/G/1 queueing model under the control of bi-level randomized(p,N1,N2)-policy.That is,the server is closed down immediately when the system is empty.If N1(≥1)customers are accumulated in the queue,the server is activated for service with probability p(0≤p≤1)or still left off with probability(1−p).When the number of customers in the system becomes N_(2)(≥N1),the server begins serving the waiting customers until the system becomes empty again.For the model,firstly,we obtain the transient solution of the queue size distribution and the explicit recursive formulas of the stationary queue length distribution by employing the total probability decomposition technique.Then,the expressions of its probability generating function of the steady-state queue size and the expected steady-state queue size are presented.Additionally,numerical examples are conducted to discuss the effect of the system parameters on some performance indices.Furthermore,the steady-state distribution of queue length at epochs n−,n and outside observer’s observation epoch are explored,respectively.Finally,we establish a cost function to investigate the cost optimization problem under the constraint of the average waiting time.And the presented model provides a less expected cost as compared to the traditional N-policy.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51138003)
文摘In order to estimate vehicular queue length at signalized intersections accurately and overcome the shortcomings and restrictions of existing studies especially those based on shockwave theory,a new methodology is presented for estimating vehicular queue length using data from both point detectors and probe vehicles. The methodology applies the shockwave theory to model queue evolution over time and space. Using probe vehicle locations and times as well as point detector measured traffic states,analytical formulations for calculating the maximum and minimum( residual) queue length are developed. The proposed methodology is verified using ground truth data collected from numerical experiments conducted in Shanghai,China. It is found that the methodology has a mean absolute percentage error of 17. 09%,which is reasonably effective in estimating the queue length at traffic signalized intersections. Limitations of the proposed models and algorithms are also discussed in the paper.
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.
基金the Beijing Natural Science Foundation under contract number L191004the National Natural Science Foundation of China under contract number U1833203.
文摘The close-in weapon system(CIWS)is a combat system that faces a complex environment full of dynamic and unknown challenges,whose construction and planning require a systematic design method.Multiliving agent(MLA)theory is a methodology for the combat system design,which uses the livelihood degree to evaluate the multi-dimensional long-term operational effectiveness of the system;whereas,there is still no uniform quantization framework for the livelihood degree,and the adjustment methods of livelihood degree need to be further improved.In this paper,we propose the uniform quantization framework for the livelihood degree and detailed discuss the methods of livelihood adjustment.Based on the MLA theory,the multi-dimensional operational effectiveness of the missile-gun integrated weapon system(MGIWS)is analyzed,and the long-term combat effectiveness against the saturation attack is assessed.Furthermore,the planning problem of the equipment deployment and configuration is investigated.Two objectives,including the overall livelihood degree and cost-effectiveness(CE),are proposed,and the optimization method based on genetic algorithm(GA)is studied for the planning problem.
基金This project was supported partly by the Outstanding Youth Scientific Foundation of China(60525303)the National Natural Science Foundation of China(60404022, 60604012)the Natural Science Foundation of Hebei Province of China(F2005000390).
文摘One of the more challenging and unresolved issues in ATM networks is the congestion control of available bit rate （ABR）. The dynamic controller is designed based on the control theory and the feedback mechanism of explicit rates With the given method of a chosen parameter, it can guarantee the stability of the controller and closed loop system with propagation delay and bandwidth oscillation. It needs less parameters（only one） to be designed. The queue length can converge to the given value in the least steps. The fairness of different connections is considered further. The simulations show better performance and good quality of service（QoS） is achieved.
文摘Congestion is one of the well-studied problems in computer networks,which occurs when the request for network resources exceeds the buffer capacity.Many active queue management techniques such as BLUE and RED have been proposed in the literature to control congestions in early stages.In this paper,we propose two discrete-time queueing network analytical models to drop the arrival packets in preliminary stages when the network becomes congested.The first model is based on Lambda Decreasing and it drops packets from a probability value to another higher value according to the buffer length.Whereas the second proposed model drops packets linearly based on the current queue length.We compare the performance of both our models with the original BLUE in order to decide which of these methods offers better quality of service.The comparison is done in terms of packet dropping probability,average queue length,throughput ratio,average queueing delay,and packet loss rate.
文摘This paper considers a Geo/Geo/1 queueing system with infinite capacity, in which the service rate changes depending on the workload. Initially, when the number of customers in the system is less than a certain threshold L, low service rate is provided for cost saving. On the other hand, the high service rate is activated as soon as L customers accumulate in the system and such service rate is preserved until the system becomes completely empty even if the number of customers falls below L. The steady-state probability distribution and the expected number of customers in the system are derived. Through the first-step argument, a recursive algorithm for computing the first moment of the conditional sojourn time is obtained. Furthermore, employing the results of regeneration cycle analysis, the direct search method is also implemented to determine the optimal value of L for minimizing the long-run average cost rate function.
基金Supported by the Chinese Universities Scientific Fund(BUPT2009RC0707,BUPT2011RC0703)
文摘The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[10].In this paper,we shall give the su？cient and necessary conditions of l-ergodicity,geometric ergodicity,and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.
基金supported by the National Natural Science Foundation of China under Grant Nos.71571127and 71171138
文摘This paper considers the departure process and the optimal control strategy for a discretetime Geo/G/1 queueing model in which the system operates under the control of multiple server vacations and Min(N, V)-policy. Using the law of total probability decomposition, the renewal theory and the probability generating function technique, the transient and the steady-state probabilities that the server is busy at any epoch n^+ are derived. The authors also obtain the explicit expression of the probability generating function for the expected number of departures occurring in the time interval (0^+, n^+] from any initial state. Meanwhile, the relationship among departure process, server's state process and service renewal process in server busy period is found, which shows the special structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by our results. Furthermore, the approximate expansion for calculating the expected number of departures is presented. In addition, some other important performance measures,including the expected length of server busy period, server's actual vacation period and busy cycle period etc., are analyzed. Finally, some numerical results are provided to determine the optimum value N*for minimizing the system cost under a given cost structure.
基金supported by the National Natural Science Foundation of China under Grant No.11171019the Fundamental Research Funds for the Central Universities under Grant No.2011JBZ012the Program for New Century Excellent Talents in University under Grant No.NCET-11-0568
文摘This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service completion, begins a process of search in order to find the following customer to be served with a certain probability, or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or on vacation. Finally, the author gives two stochastic decomposition laws, and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.
基金supported by the National Natural Science Foundation of China under Grant No.71071133
文摘The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times.As soon as the orbit is empty,the server takes a vacation.However,the server is allowed to take a maximum number J of vacations,if the system remains empty after the end of a vacation.If there is at least one customer in the orbit at the end of a vacation,the server begins to serve the new arrivals or the arriving customers from the orbit.For this model,the authors focus on the steady-state analysis for the considered queueing system.Firstly,the authors obtain the generating functions of the number of customers in the orbit and in the system.Then,the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size.Besides,the relationship between this discrete-time model and the corresponding continuous-time model is also investigated.Finally,some numerical results are provided.
基金Supported by the National Natural Science Foundation of China(No.10871020)
文摘This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the parameters on several performance characteristics of the system.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11271373 and 11361007the Guangxi Natural Science Foundation under Grant No.2014GXNSFCA118001 and 2012GXNSFBA053010
文摘In this paper, we consider a discrete-time preemptive priority queue with different service com- pletion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers＇ arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated than the continuous- time model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the low-priority queue, as well as along the direction of the high-priority queue.
基金Supported by the National Natural Science Foundation of China(71571127)the Training Fund Program of Excellent Paper of Sichuan Normal University([2016]4-1)
文摘This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject to breakdowns at random when it is in operation. As soon as the server fails, a repair process immediately begins. During the repair period, the defective server still provides service for the waiting customers at a lower service rate rather than completely stopping service.We analyze the stability condition for the considered system. Using the probability generating function technique, we obtain the probability generating function of the steady-state queue size distribution.Also, various important performance measures are derived explicitly. Furthermore, some numerical results are provided to carry out the sensitivity analysis so as to illustrate the effect of different parameters on the system performance measures. Finally, an operating cost function is formulated to model a computer system and the parabolic method is employed to numerically find the optimum service rate in working breakdown period.
