The M/M/r/r＋d retrial queuing system with unreliable server is considered. The customers arrive according to a Poisson process and the service time distribution is negative exponential. The life time of the server an...The M/M/r/r＋d retrial queuing system with unreliable server is considered. The customers arrive according to a Poisson process and the service time distribution is negative exponential. The life time of the server and repair times are also negative exponential. If the system is full at the time of arrival of a customer, the customer enters into an orbit. From the orbit the customer tries his luck. The time between two successive retrial follows negative exponential distribution. The model is analyzed using Matrix Geometric Method. The joint distribution of system size and orbit size in steady state is studied. Some system performance measures are obtained. We also provide numerical examples by taking particular values to the parameters.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
Recently, there has been a rapid growing interest in new applications requiring quality of service (QoS) guarantees through wireless local area networks (WLAN). These demands have led to the introduction of new 802.11...Recently, there has been a rapid growing interest in new applications requiring quality of service (QoS) guarantees through wireless local area networks (WLAN). These demands have led to the introduction of new 802.11 standard series to enhance access medium supporting QoS for multimedia applications. However, some applications such as variable bit rate (VBR) traffic address some challenges in the hybrid coordination function (HCF) nominated to provide QoS. This paper presents a novel priority queuing model to analyze a medium access in the HCF controlled channel access (HCCA) mode. This model makes use of a MAP (Markovian Arrival Process)/PH (Phase Type)/1 queue with two types of jobs which are suitable to support VBR traffic. Using a MAP for traffic arrival process and PH distribution for service process, the inclusion of vacation period makes our analysis very general and comprehensive to support various types of practical traffic streams. The proposed priority queuing model is very useful to evaluate and enhance the performance of the scheduler and the admission controller in the HCCA mechanism.展开更多
In this paper, we study the M/M/1 queue with working vacations and vacation interruptions. The working vacation is introduced recently, during which the server can still provide service on the original ongoing work at...In this paper, we study the M/M/1 queue with working vacations and vacation interruptions. The working vacation is introduced recently, during which the server can still provide service on the original ongoing work at a lower rate. Meanwhile, we introduce a new policy：, the server can come back from the vacation to the normal working level once some indices of the system, such as the number of customers, achieve a certain value in the vacation period. The server may come back from the vacation without completing the vacation. Such policy is called vacation interruption. We connect the above mentioned two policies and assume that if there are customers in the system after a service completion during the vacation period, the server will come back to the normal working level. In terms of the quasi birth and death process and matrix-geometric solution method, we obtain the distributions and the stochastic decomposition structures for the number of customers and the waiting time and provide some indices of systems.展开更多
In this paper,we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting.We first describe a more ...In this paper,we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting.We first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive mechanism.Then we establish a pyramid Markov process and show that it is irreducible and positive recurrent,and its stationary probability vector is matrix-geometric with an explicitly representable rate matrix.Also,we use the stationary probability vector to study the influence of orphan blocks on the waste of computing resource.Next,we set up a pyramid Markov reward process to investigate the long-run average mining profits of the honest and dishonest mining pools,respectively.As a by-product,we build one-dimensional Markov reward processes and provide some new interesting interpretation on the Markov chain and the revenue analysis reported in the seminal work by Eyal and Sirer(2014).Note that the pyramid Markov(reward)processes can open up a new avenue in the study of blockchain selfish mining.Thus we hope that the methodology and results developed in this paper shed light on the blockchain selfish mining such that a series of promising research can be developed potentially.展开更多
In this paper, a steady-state Markovian multi-server retrial queueing system with Bernoulli vacation scheduling service is studied. Using matrix-geometric approach, various interesting and important system performance...In this paper, a steady-state Markovian multi-server retrial queueing system with Bernoulli vacation scheduling service is studied. Using matrix-geometric approach, various interesting and important system performance measures are obtained. Further, the probability descriptors like ideal retrial and vain retrial are provided. Finally, extensive numerical illustrations are presented to indicate the quantifying nature of the approach to obtain solutions to this queueing system.展开更多
We study an M/PH/1 queue with phase type working vacation and vacation interruption where the vacation time follows a phase type distribution. The server serves the customers at a lower rate in a vacation period. The ...We study an M/PH/1 queue with phase type working vacation and vacation interruption where the vacation time follows a phase type distribution. The server serves the customers at a lower rate in a vacation period. The server comes back to the regular busy period at a service completion without completing the vacation. Such policy is called vacation interruption. In terms of quasi birth and death process and matrix-geometric solution method, we obtain the stationary queue length distribution. Moreover we obtain the conditional stochastic decomposition structures of queue length and waiting time when the service time distribution in the regular busy period is exponential.展开更多
The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of wai...The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of waiting time of a customer in the system. Furthermore, the conditional stochastic decomposition results of queue length and waiting time are given.展开更多
文摘The M/M/r/r＋d retrial queuing system with unreliable server is considered. The customers arrive according to a Poisson process and the service time distribution is negative exponential. The life time of the server and repair times are also negative exponential. If the system is full at the time of arrival of a customer, the customer enters into an orbit. From the orbit the customer tries his luck. The time between two successive retrial follows negative exponential distribution. The model is analyzed using Matrix Geometric Method. The joint distribution of system size and orbit size in steady state is studied. Some system performance measures are obtained. We also provide numerical examples by taking particular values to the parameters.
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.
文摘Recently, there has been a rapid growing interest in new applications requiring quality of service (QoS) guarantees through wireless local area networks (WLAN). These demands have led to the introduction of new 802.11 standard series to enhance access medium supporting QoS for multimedia applications. However, some applications such as variable bit rate (VBR) traffic address some challenges in the hybrid coordination function (HCF) nominated to provide QoS. This paper presents a novel priority queuing model to analyze a medium access in the HCF controlled channel access (HCCA) mode. This model makes use of a MAP (Markovian Arrival Process)/PH (Phase Type)/1 queue with two types of jobs which are suitable to support VBR traffic. Using a MAP for traffic arrival process and PH distribution for service process, the inclusion of vacation period makes our analysis very general and comprehensive to support various types of practical traffic streams. The proposed priority queuing model is very useful to evaluate and enhance the performance of the scheduler and the admission controller in the HCCA mechanism.
基金This work was supported in part by National Natural Science Foundation of China under Grant No. 10671170.5. Acknowledgment The authors thank to the anonymous referees for their insightful comments and suggestions, which are very helpful to improve the presentations of the paper.
文摘In this paper, we study the M/M/1 queue with working vacations and vacation interruptions. The working vacation is introduced recently, during which the server can still provide service on the original ongoing work at a lower rate. Meanwhile, we introduce a new policy：, the server can come back from the vacation to the normal working level once some indices of the system, such as the number of customers, achieve a certain value in the vacation period. The server may come back from the vacation without completing the vacation. Such policy is called vacation interruption. We connect the above mentioned two policies and assume that if there are customers in the system after a service completion during the vacation period, the server will come back to the normal working level. In terms of the quasi birth and death process and matrix-geometric solution method, we obtain the distributions and the stochastic decomposition structures for the number of customers and the waiting time and provide some indices of systems.
基金This work is supported by the National Key R&D Program of China under Grant No.2020AAA0103801Quanlin Li is supported by the National Natural Science Foundation of China under Grant Nos.71671158 and 71932002+1 种基金the Beijing Social Science Foundation Research Base Project under Grant No.19JDGLA004Xiaole Wu is supported by the National Natural Science Foundation of China under Grant No.72025102.
文摘In this paper,we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting.We first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive mechanism.Then we establish a pyramid Markov process and show that it is irreducible and positive recurrent,and its stationary probability vector is matrix-geometric with an explicitly representable rate matrix.Also,we use the stationary probability vector to study the influence of orphan blocks on the waste of computing resource.Next,we set up a pyramid Markov reward process to investigate the long-run average mining profits of the honest and dishonest mining pools,respectively.As a by-product,we build one-dimensional Markov reward processes and provide some new interesting interpretation on the Markov chain and the revenue analysis reported in the seminal work by Eyal and Sirer(2014).Note that the pyramid Markov(reward)processes can open up a new avenue in the study of blockchain selfish mining.Thus we hope that the methodology and results developed in this paper shed light on the blockchain selfish mining such that a series of promising research can be developed potentially.
文摘In this paper, a steady-state Markovian multi-server retrial queueing system with Bernoulli vacation scheduling service is studied. Using matrix-geometric approach, various interesting and important system performance measures are obtained. Further, the probability descriptors like ideal retrial and vain retrial are provided. Finally, extensive numerical illustrations are presented to indicate the quantifying nature of the approach to obtain solutions to this queueing system.
文摘We study an M/PH/1 queue with phase type working vacation and vacation interruption where the vacation time follows a phase type distribution. The server serves the customers at a lower rate in a vacation period. The server comes back to the regular busy period at a service completion without completing the vacation. Such policy is called vacation interruption. In terms of quasi birth and death process and matrix-geometric solution method, we obtain the stationary queue length distribution. Moreover we obtain the conditional stochastic decomposition structures of queue length and waiting time when the service time distribution in the regular busy period is exponential.
基金the National Natural Science Foundation of China under Grant No.10671170the Doctorial Foundation of Yanshan University under Grant No.B228.
文摘The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of waiting time of a customer in the system. Furthermore, the conditional stochastic decomposition results of queue length and waiting time are given.
