We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponen...We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.展开更多
Pooling,unpooling/specialization,and discretionary task completion are typical operational strategies in queueing systems that arise in healthcare,call centers,and online sales.These strategies may have advantages and...Pooling,unpooling/specialization,and discretionary task completion are typical operational strategies in queueing systems that arise in healthcare,call centers,and online sales.These strategies may have advantages and disadvantages in different operational environments.This paper uses the M/M/1 and M/M/2 queues to study the impact of pooling,specialization,and discretionary task completion on the average queue length.Closed-form solutions for the average M/M/2 queue length are derived.Computational examples illustrate how the average queue length changes with the strength of pooling,specialization,and discretionary task completion.Finally,several conjectures are made in the paper.展开更多
Mobile edge computing (MEC) has a vital role in various delay-sensitive applications. With the increasing popularity of low-computing-capability Internet of Things (IoT) devices in industry 4.0 technology, MEC also fa...Mobile edge computing (MEC) has a vital role in various delay-sensitive applications. With the increasing popularity of low-computing-capability Internet of Things (IoT) devices in industry 4.0 technology, MEC also facilitates wireless power transfer, enhancing efficiency and sustainability for these devices. The most related studies concerning the computation rate in MEC are based on the coordinate descent method, the alternating direction method of multipliers (ADMMs) and Lyapunov optimization. Nevertheless, these studies do not consider the buffer queue size. This research work concerns the computation rate maximization for wireless-powered and multiple-user MEC systems, specifically focusing on the computation rate of end devices and managing the task buffer queue before computation at the terminal devices. A deep reinforcement learning (RL)-based task offloading algorithm is proposed to maximize the computation rate of end devices and minimizes the buffer queue size at the terminal devices.Precisely, considering the channel gain, the buffer queue size and wireless power transfer, it further formalizes the task offloading problem. The mode selection for task offloading is based on the individual channel gain, the buffer queue size and wireless power transfer maximization in a particular time slot.The central idea of this work is to explore the best optimal mode selection for IoT devices connected to the MEC system. The proposed algorithm optimizes computation delay by maximizing the computation rate of end devices and minimizing the buffer queue size before computation at the terminal devices. Then, the current study presents a deep RL-based task offloading algorithm to solve such a mixed-integer and non-convex optimization problem, aiming to get a better trade-off between the buffer queue size and the computation rate. The extensive simulation results reveal that the presented algorithm is much more efficient than the existing work to maintain a small buffer queue for terminal devices while simultaneously achieving a high-level computation rate.展开更多
The quest to increase the performance of production systems that have become complex leads to the transfer to the maintenance function of the responsibility of guaranteeing the availability of such systems. Also, we w...The quest to increase the performance of production systems that have become complex leads to the transfer to the maintenance function of the responsibility of guaranteeing the availability of such systems. Also, we will never stop saying that maintenance must integrate into all of the company’s initiatives, to affirm its role, which is to ensure greater availability and sustainability of the means of production. The objective of this paper is to evaluate the reliability and availability of a system without knowing the distribution law of the operating times. Among the methods for evaluating dependability criteria (Fault Trees, Petri Nets, etc.), we are interested in queues that have the advantage of taking into account functional dependencies, thus allowing a quantified optimization of maintenance. Indeed, queues make it possible to model parallel or sequential processes, implementing operations taking place at the same time or one after the other, meeting the needs of modeling production systems. The main result of this paper is the study of the influence of availability on the reliability of a multi-state production system.展开更多
The high-performance computing paradigm needs high-speed switching fabrics to meet the heavy traffic generated by their applications.These switching fabrics are efficiently driven by the deployed scheduling algorithms...The high-performance computing paradigm needs high-speed switching fabrics to meet the heavy traffic generated by their applications.These switching fabrics are efficiently driven by the deployed scheduling algorithms.In this paper,we proposed two scheduling algorithms for input queued switches whose operations are based on ranking procedures.At first,we proposed a Simple 2-Bit(S2B)scheme which uses binary ranking procedure and queue size for scheduling the packets.Here,the Virtual Output Queue(VOQ)set with maximum number of empty queues receives higher rank than other VOQ’s.Through simulation,we showed S2B has better throughput performance than Highest Ranking First(HRF)arbitration under uniform,and non-uniform traffic patterns.To further improve the throughput-delay performance,an Enhanced 2-Bit(E2B)approach is proposed.This approach adopts an integer representation for rank,which is the number of empty queues in a VOQ set.The simulation result shows E2B outperforms S2B and HRF scheduling algorithms with maximum throughput-delay performance.Furthermore,the algorithms are simulated under hotspot traffic and E2B proves to be more efficient.展开更多
The multistage queue model was developed for a situation where parallel and unrelated queues exist at the first stage only. These queues merged into single queues at the remaining stages. The parallel queues offer ser...The multistage queue model was developed for a situation where parallel and unrelated queues exist at the first stage only. These queues merged into single queues at the remaining stages. The parallel queues offer services that are different from one another and customers arrive to join the queue that offer services that they need. The mathematical model was developed assuming an M/M/1 queue system and the measures of effectiveness were derived. The model was applied to solve the problem of customer congestion in a restaurant in the city of Ibadan, Nigeria that serves three different local delicacies. The three local delicacies constitute three different queues at the first stage. The second stage consists of only one queue which is for purchase of drinks and the third stage which is the last stage is for payment. Every customer in the restaurant passes through the three stages. Utilization factors for the five queues were determined and found to range from 70% to 97%. The average time spent by customers in the system was found to be 543.04 minutes. A simulation study using what-if scenario analysis was performed to determine the optimum service configuration for the system. The optimum configuration reduced average time for customers in the system from 543.04 minutes to 13.47 minutes without hiring new servers.展开更多
This paper presents the derivation of an analytical model for a multi-queue nodes network router, which is referred to as the multi-queue nodes （mQN） model. In this model, expressions are derived to calculate two pe...This paper presents the derivation of an analytical model for a multi-queue nodes network router, which is referred to as the multi-queue nodes （mQN） model. In this model, expressions are derived to calculate two performance metrics, namely, the queue node and system utilization factors. In order to demonstrate the flexibility and effectiveness of the mQN model in analyzing the performance of an mQN network router, two scenarios are performed. These scenarios investigated the variation of queue nodes and system utilization factors against queue nodes dropping probability for various system sizes and packets arrival routing probabilities. The performed scenarios demonstrated that the mQN analytical model is more flexible and effective when compared with experimental tests and computer simulations in assessing the performance of an mQN network router.展开更多
We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson stream...We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.展开更多
In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems the...In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems themselves—Queueing Systems. This article is dedicated to computer software modelling of processes taking place in the systems in question, Markov processes in particular. In this article, by means of Matlab environment, software realization of one of the typical models of queueing service theory-multichannel QS with unreliable recoverable servers and limited number of requirements in the system, is fulfilled. The results of this research are important because it gives the possibility to use received results to determine optimality degree of some real queueing systems that possess Markov property.展开更多
A new weighted fair queueing algorithm is proposed, which uses the novel flow-based service ratio parameters to schedule flows. This solves the main drawback of traditional weighted fair queneing algorithms- the packe...A new weighted fair queueing algorithm is proposed, which uses the novel flow-based service ratio parameters to schedule flows. This solves the main drawback of traditional weighted fair queneing algorithms- the packet-based calculation of the weight parameters. In addition, this paper proposes a novel service ratio calculation method and a queue mangement technology. The former adjusts the service ratio parameters adaptively based on the dynamics of the packet lengths and thee solves the unfairness problem induced by the variable packet length. The latter improves the utilization of the server＇s queue buffer and reduces the delay jitter through restricting the buffer length for each flow.展开更多
In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodol...In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodology for applying these theorems for the benefit of service systems. The limit theorems studied here are dominant in the literature. Our contribution is primarily on the analysis leading to the application of these theorems in various problem situations for better operations. Relevant Examples are included to aid the application of the results studied in this work.展开更多
In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the di...In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.展开更多
In this paper, we report research on how to design the tele-network. First of all, we defined the reliability of tele-network. According to the definition, we divide the whole reliability into two parts:the reliabilit...In this paper, we report research on how to design the tele-network. First of all, we defined the reliability of tele-network. According to the definition, we divide the whole reliability into two parts:the reliability of the mini-way and that of the whole system. Then we do algebra unintersection of the mini-way, deriving a function of reliability of tele-network. Also, we got a function of the cost of tele-network after analyzing the cost of arcs and points. Finally, we give a mathematical model to design a tele-network. For the algorithm, we define the distance of a network and adjacent area within certain boundaries . We present a new algorithm--Queue Competition Algorithm (QCA) based on the adjacent area . The QCA correlates sequence of fitnesses in their father-generations with hunting zone of mutation and the number of individuals generated by mutation, making the stronger fitness in a small zone converge at a local extreme value, but the weaker one takes the advantage of lots of individuals and a big zone to hunt a new local extreme value. In this way, we get the overall extreme value. Numerical simulation shows that we can get the efficient hunting and exact solution by using QCA. The QCA efficient hunting and exact solution.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11971486)。
文摘We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.
文摘Pooling,unpooling/specialization,and discretionary task completion are typical operational strategies in queueing systems that arise in healthcare,call centers,and online sales.These strategies may have advantages and disadvantages in different operational environments.This paper uses the M/M/1 and M/M/2 queues to study the impact of pooling,specialization,and discretionary task completion on the average queue length.Closed-form solutions for the average M/M/2 queue length are derived.Computational examples illustrate how the average queue length changes with the strength of pooling,specialization,and discretionary task completion.Finally,several conjectures are made in the paper.
基金National Natural Science Foundation of China(No.61902060)Shanghai Sailing Program,China(No.19YF1402100)+1 种基金Fundamental Research Funds for the Central Universities,China(No.2232019D3-51)Open Foundation of State Key Laboratory of Networking and Switching Technology(Beijing University of Posts and Telecommunications,China)(No.SKLNST-2021-1-06)。
文摘Mobile edge computing (MEC) has a vital role in various delay-sensitive applications. With the increasing popularity of low-computing-capability Internet of Things (IoT) devices in industry 4.0 technology, MEC also facilitates wireless power transfer, enhancing efficiency and sustainability for these devices. The most related studies concerning the computation rate in MEC are based on the coordinate descent method, the alternating direction method of multipliers (ADMMs) and Lyapunov optimization. Nevertheless, these studies do not consider the buffer queue size. This research work concerns the computation rate maximization for wireless-powered and multiple-user MEC systems, specifically focusing on the computation rate of end devices and managing the task buffer queue before computation at the terminal devices. A deep reinforcement learning (RL)-based task offloading algorithm is proposed to maximize the computation rate of end devices and minimizes the buffer queue size at the terminal devices.Precisely, considering the channel gain, the buffer queue size and wireless power transfer, it further formalizes the task offloading problem. The mode selection for task offloading is based on the individual channel gain, the buffer queue size and wireless power transfer maximization in a particular time slot.The central idea of this work is to explore the best optimal mode selection for IoT devices connected to the MEC system. The proposed algorithm optimizes computation delay by maximizing the computation rate of end devices and minimizing the buffer queue size before computation at the terminal devices. Then, the current study presents a deep RL-based task offloading algorithm to solve such a mixed-integer and non-convex optimization problem, aiming to get a better trade-off between the buffer queue size and the computation rate. The extensive simulation results reveal that the presented algorithm is much more efficient than the existing work to maintain a small buffer queue for terminal devices while simultaneously achieving a high-level computation rate.
文摘The quest to increase the performance of production systems that have become complex leads to the transfer to the maintenance function of the responsibility of guaranteeing the availability of such systems. Also, we will never stop saying that maintenance must integrate into all of the company’s initiatives, to affirm its role, which is to ensure greater availability and sustainability of the means of production. The objective of this paper is to evaluate the reliability and availability of a system without knowing the distribution law of the operating times. Among the methods for evaluating dependability criteria (Fault Trees, Petri Nets, etc.), we are interested in queues that have the advantage of taking into account functional dependencies, thus allowing a quantified optimization of maintenance. Indeed, queues make it possible to model parallel or sequential processes, implementing operations taking place at the same time or one after the other, meeting the needs of modeling production systems. The main result of this paper is the study of the influence of availability on the reliability of a multi-state production system.
文摘The high-performance computing paradigm needs high-speed switching fabrics to meet the heavy traffic generated by their applications.These switching fabrics are efficiently driven by the deployed scheduling algorithms.In this paper,we proposed two scheduling algorithms for input queued switches whose operations are based on ranking procedures.At first,we proposed a Simple 2-Bit(S2B)scheme which uses binary ranking procedure and queue size for scheduling the packets.Here,the Virtual Output Queue(VOQ)set with maximum number of empty queues receives higher rank than other VOQ’s.Through simulation,we showed S2B has better throughput performance than Highest Ranking First(HRF)arbitration under uniform,and non-uniform traffic patterns.To further improve the throughput-delay performance,an Enhanced 2-Bit(E2B)approach is proposed.This approach adopts an integer representation for rank,which is the number of empty queues in a VOQ set.The simulation result shows E2B outperforms S2B and HRF scheduling algorithms with maximum throughput-delay performance.Furthermore,the algorithms are simulated under hotspot traffic and E2B proves to be more efficient.
文摘The multistage queue model was developed for a situation where parallel and unrelated queues exist at the first stage only. These queues merged into single queues at the remaining stages. The parallel queues offer services that are different from one another and customers arrive to join the queue that offer services that they need. The mathematical model was developed assuming an M/M/1 queue system and the measures of effectiveness were derived. The model was applied to solve the problem of customer congestion in a restaurant in the city of Ibadan, Nigeria that serves three different local delicacies. The three local delicacies constitute three different queues at the first stage. The second stage consists of only one queue which is for purchase of drinks and the third stage which is the last stage is for payment. Every customer in the restaurant passes through the three stages. Utilization factors for the five queues were determined and found to range from 70% to 97%. The average time spent by customers in the system was found to be 543.04 minutes. A simulation study using what-if scenario analysis was performed to determine the optimum service configuration for the system. The optimum configuration reduced average time for customers in the system from 543.04 minutes to 13.47 minutes without hiring new servers.
文摘This paper presents the derivation of an analytical model for a multi-queue nodes network router, which is referred to as the multi-queue nodes （mQN） model. In this model, expressions are derived to calculate two performance metrics, namely, the queue node and system utilization factors. In order to demonstrate the flexibility and effectiveness of the mQN model in analyzing the performance of an mQN network router, two scenarios are performed. These scenarios investigated the variation of queue nodes and system utilization factors against queue nodes dropping probability for various system sizes and packets arrival routing probabilities. The performed scenarios demonstrated that the mQN analytical model is more flexible and effective when compared with experimental tests and computer simulations in assessing the performance of an mQN network router.
文摘We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.
文摘In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems themselves—Queueing Systems. This article is dedicated to computer software modelling of processes taking place in the systems in question, Markov processes in particular. In this article, by means of Matlab environment, software realization of one of the typical models of queueing service theory-multichannel QS with unreliable recoverable servers and limited number of requirements in the system, is fulfilled. The results of this research are important because it gives the possibility to use received results to determine optimality degree of some real queueing systems that possess Markov property.
基金National Natural Science Foundation of China ( No.60572157)Sharp Corporation of Japanthe Hi-Tech Research and Development Program(863) of China (No.2003AA123310)
文摘A new weighted fair queueing algorithm is proposed, which uses the novel flow-based service ratio parameters to schedule flows. This solves the main drawback of traditional weighted fair queneing algorithms- the packet-based calculation of the weight parameters. In addition, this paper proposes a novel service ratio calculation method and a queue mangement technology. The former adjusts the service ratio parameters adaptively based on the dynamics of the packet lengths and thee solves the unfairness problem induced by the variable packet length. The latter improves the utilization of the server＇s queue buffer and reduces the delay jitter through restricting the buffer length for each flow.
文摘In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodology for applying these theorems for the benefit of service systems. The limit theorems studied here are dominant in the literature. Our contribution is primarily on the analysis leading to the application of these theorems in various problem situations for better operations. Relevant Examples are included to aid the application of the results studied in this work.
文摘In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.
基金Supported by the National Natura1 Science Foundation of China(70071042,60073043,60133010)
文摘In this paper, we report research on how to design the tele-network. First of all, we defined the reliability of tele-network. According to the definition, we divide the whole reliability into two parts:the reliability of the mini-way and that of the whole system. Then we do algebra unintersection of the mini-way, deriving a function of reliability of tele-network. Also, we got a function of the cost of tele-network after analyzing the cost of arcs and points. Finally, we give a mathematical model to design a tele-network. For the algorithm, we define the distance of a network and adjacent area within certain boundaries . We present a new algorithm--Queue Competition Algorithm (QCA) based on the adjacent area . The QCA correlates sequence of fitnesses in their father-generations with hunting zone of mutation and the number of individuals generated by mutation, making the stronger fitness in a small zone converge at a local extreme value, but the weaker one takes the advantage of lots of individuals and a big zone to hunt a new local extreme value. In this way, we get the overall extreme value. Numerical simulation shows that we can get the efficient hunting and exact solution by using QCA. The QCA efficient hunting and exact solution.
