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
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
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
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
This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating mo...This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability generating functions of the steady state probabilities of several states of the system including the steady state queue size distribution. Further, we discuss some particular cases of the proposed queueing model. We present numerical examples in order to demonstrate the effects of server vacation and reneging on the various states of the system. The study revealed that an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, the probability of server vacation, the probability of system is under repair and the probabilities that the server provides service in three fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates.展开更多
We prove a heavy traffic limit theorem to justify diffusion approximations for multiclass queueing networks under preemptive priority service discipline and provide effective stochastic dynamical models for the system...We prove a heavy traffic limit theorem to justify diffusion approximations for multiclass queueing networks under preemptive priority service discipline and provide effective stochastic dynamical models for the systems. Such queueing networks appear typically in high-speed integrated services packet networks about telecommunication system. In the network, there is a number of packet traffic types. Each type needs a number of job classes （stages） of processing and each type of jobs is assigned the same priority rank at every station where it possibly receives service. Moreover, there is no inter-routing among different traffic types throughout the entire network.展开更多
In recent years, the transportation system has been faced by increasing challenge in congestion and inefficiency, and research in traffic network has become a significant area of interest. In this paper, we introduce ...In recent years, the transportation system has been faced by increasing challenge in congestion and inefficiency, and research in traffic network has become a significant area of interest. In this paper, we introduce a dynamic-information-based （DIB） queueing strategy into network traffic model under the efficient routing strategy. DIB makes a packet with higher priority to be delivered if there are less packets travelling along its path from the current node to the destination. It is found that, compared with the traditional first-in-first-out （FIFO） queueing strategy, DIB can effectively bMance the traffic load of the system via delaying packets to be delivered to congested nodes. Although the network capacity has no obvious changes, some other indexes which reflect transportation efficiency are efficiently improved in the congestion state. Besides, extensive simulation results and discussions are provided to explain the phenomena. The results may provide novel insights for research on traffic systems.展开更多
The impaction of aggregated network traffic on queueing system is studied in this paper. It shows that the network traffic stayed in buffer has different impaction on queueing performance when it is aggregated at diff...The impaction of aggregated network traffic on queueing system is studied in this paper. It shows that the network traffic stayed in buffer has different impaction on queueing performance when it is aggregated at different scales. And its influence is related not only to traffic parameters but also to system parameter, such as buffer size. The increased buffer size can absorb the effect of short-range dependence （SRD） in network traffic and only the effect of long-range dependence （LRD） is expressed. The queueing length is asymptotic Weibull distribution with increasing buffer size, which is irrespective with the effect of short-range dependence character. Monte-Carlo based simulation confirmed the validity of these results.展开更多
In this paper,the concept of the infinitesimal realization factor is extended to the parameter dependent performance functions in closed queueing networks.Then the concepts of realization matrix (its elements are cal...In this paper,the concept of the infinitesimal realization factor is extended to the parameter dependent performance functions in closed queueing networks.Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced,and the relations between infinitesimal realization factors and these two quantities are discussed.This provides a united framework for both IPA and non IPA approaches.Finally,another physical meaning of the service rate is given.展开更多
This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.U...This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.Upon each arrival, an admission/routing decision is made, and the accepted job is routed to one of the two servers with each being associated with a queue.After each service completion, the servers have an option of serving a job from its own queue, serving a jockeying job from another queue, or staying idle.The system performance is inclusive of the revenues from accepted jobs, the costs of holding jobs in queues, the service costs and the job jockeying costs.To maximize the total expected discounted return, we formulate a Markov decision process(MDP) model for this system.The value iteration method is employed to characterize the optimal policy as a hedging point policy.Numerical studies verify the structure of the hedging point policy which is convenient for implementing control actions in practice.展开更多
In this paper, the open queueing network model is proposed for solving the problem of public transportation in cities. The vertices of the networks(i.e., the bus stops) are determined by means of the fuzzy clusteri...In this paper, the open queueing network model is proposed for solving the problem of public transportation in cities. The vertices of the networks(i.e., the bus stops) are determined by means of the fuzzy clustering method. The arcs (i.e., the paths of the public transportation) can be set up by using the shortest path model in the time sense or the 0 1 integer programming method.Applying the statistics method, we can calculate the parameters(such as the passenger flow's distribution, passenger flow's transition probability, mean waiting time for the bus etc. ) of the public transportation network. In this paper, we suggest to divide the network into two or three stages to implement the public transportation system in the form of ``frog jumping' fast transfer and ``permeation' fast dispersion.Combining the computer simulation and the evaluation of the achievement and effect of public transportation system, we modify the model so as to solve the public transportation problem better.展开更多
In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on ...In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on the left real line and these results describe the point spectra of the operator. Then, we show that the essential growth bound of the C_0-semigroup generated by the operator is 0 and therefore it is not quasi compact, the essential spectral bound of the C_0-semigroup is equal to 1. Moreover, our results imply it is impossible that the time-dependent solution of the model exponentially converges to its steady-state solution.展开更多
The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of t...The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of the service distribution,but not on the interarrival distribution.We shall also give explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases（Case 1：the rate function r（n）=exp（sn1/1＋α）,α〉0,s〉0;Case 2：polynomial rate function r（n）=nα,α〉0;Case 3：logarithmic rate function r（n）=logαn,α〉0）.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
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
Weighted priority queueing is a modification of priority queueing that eliminates the possibility of blocking lower priority traffic. The weights assigned to priority classes determine the fractions of the bandwith th...Weighted priority queueing is a modification of priority queueing that eliminates the possibility of blocking lower priority traffic. The weights assigned to priority classes determine the fractions of the bandwith that are guaranteed for individual traffic classes, similarly as in weighted fair queueing. The paper describes a timed Petri net model of weighted priority queueing and uses discrete-event simulation of this model to obtain performance characteristics of simple queueing systems. The model is also used to analyze the effects of finite queue capacity on the performance of queueing systems.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
Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rate...Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.展开更多
The Distributed Queuing (DQ) algorithm is predicted as one of the solutions to the issues currently found in IoT networks over the use of Aloha based algorithms. Since recently, the algorithm has been of interest to m...The Distributed Queuing (DQ) algorithm is predicted as one of the solutions to the issues currently found in IoT networks over the use of Aloha based algorithms. Since recently, the algorithm has been of interest to many IoT researchers as a replacement of those Aloha variants for channel access. However, previous works analyzed and evaluated the DQ algorithm without any consideration of the stability of its queues, assuming it is stable for any given number of nodes in the network. In this paper, we define the DQ stability condition in a single-channel M2M environment considering a traffic model of periodic and urgent frames from each node in the network. Besides, a steady-state evaluation of the algorithm’s performance metrics is also presented. In general, the DQ algorithm, when it is stable, was observed not to efficiently use the contention slots for the collision resolution. In a single-channel environment, the DQ algorithm is found to outperform the Aloha based algorithms only in an idle-to-saturation scenario.展开更多
In this paper, we present an approach for model transformation from Queueing Network Models (QNMs) into Queueing Petri Nets (QPNs). The performance of QPNs can be analyzed using a powerful simulation engine, SimQPN, d...In this paper, we present an approach for model transformation from Queueing Network Models (QNMs) into Queueing Petri Nets (QPNs). The performance of QPNs can be analyzed using a powerful simulation engine, SimQPN, designed to exploit the knowledge and behavior of QPNs to improve the efficiency of simulation. When QNMs are transformed into QPNs, their performance can be analyzed efficiently using SimQPN. To validate our approach, we apply it to analyze the performance of several queueing network models including a model of a database system. The evaluation results show that the performance analysis of the transformed QNMs has high accuracy and low overhead. In this context, model transformation enables the performance analysis of queueing networks using different ways that can be more efficient.展开更多
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.
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.
文摘This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability generating functions of the steady state probabilities of several states of the system including the steady state queue size distribution. Further, we discuss some particular cases of the proposed queueing model. We present numerical examples in order to demonstrate the effects of server vacation and reneging on the various states of the system. The study revealed that an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, the probability of server vacation, the probability of system is under repair and the probabilities that the server provides service in three fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates.
基金the National Natural Science Foundation of China(No.10371053)
文摘We prove a heavy traffic limit theorem to justify diffusion approximations for multiclass queueing networks under preemptive priority service discipline and provide effective stochastic dynamical models for the systems. Such queueing networks appear typically in high-speed integrated services packet networks about telecommunication system. In the network, there is a number of packet traffic types. Each type needs a number of job classes （stages） of processing and each type of jobs is assigned the same priority rank at every station where it possibly receives service. Moreover, there is no inter-routing among different traffic types throughout the entire network.
基金Supported by the National High Technology Research and Development Program of China under Grant No.2011AA110101the National Natural Science Foundation of China under Grant No.61201314China Scholarship Council
文摘In recent years, the transportation system has been faced by increasing challenge in congestion and inefficiency, and research in traffic network has become a significant area of interest. In this paper, we introduce a dynamic-information-based （DIB） queueing strategy into network traffic model under the efficient routing strategy. DIB makes a packet with higher priority to be delivered if there are less packets travelling along its path from the current node to the destination. It is found that, compared with the traditional first-in-first-out （FIFO） queueing strategy, DIB can effectively bMance the traffic load of the system via delaying packets to be delivered to congested nodes. Although the network capacity has no obvious changes, some other indexes which reflect transportation efficiency are efficiently improved in the congestion state. Besides, extensive simulation results and discussions are provided to explain the phenomena. The results may provide novel insights for research on traffic systems.
基金Supported by the National High Technology Research and Development Program of China(2004AA639690)the Ph. D.Programs Foundation of Ministry of Education of China(20040486049)the Wuhan Chenguang Project (20055003059-27)
文摘The impaction of aggregated network traffic on queueing system is studied in this paper. It shows that the network traffic stayed in buffer has different impaction on queueing performance when it is aggregated at different scales. And its influence is related not only to traffic parameters but also to system parameter, such as buffer size. The increased buffer size can absorb the effect of short-range dependence （SRD） in network traffic and only the effect of long-range dependence （LRD） is expressed. The queueing length is asymptotic Weibull distribution with increasing buffer size, which is irrespective with the effect of short-range dependence character. Monte-Carlo based simulation confirmed the validity of these results.
基金the National Natural Science Foundation of China(699740 37) the National HighPerformance Computing Foundation of China (0 0 2 12 )
文摘In this paper,the concept of the infinitesimal realization factor is extended to the parameter dependent performance functions in closed queueing networks.Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced,and the relations between infinitesimal realization factors and these two quantities are discussed.This provides a united framework for both IPA and non IPA approaches.Finally,another physical meaning of the service rate is given.
基金supported by the National Social Science Fund of China (19BGL100)。
文摘This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.Upon each arrival, an admission/routing decision is made, and the accepted job is routed to one of the two servers with each being associated with a queue.After each service completion, the servers have an option of serving a job from its own queue, serving a jockeying job from another queue, or staying idle.The system performance is inclusive of the revenues from accepted jobs, the costs of holding jobs in queues, the service costs and the job jockeying costs.To maximize the total expected discounted return, we formulate a Markov decision process(MDP) model for this system.The value iteration method is employed to characterize the optimal policy as a hedging point policy.Numerical studies verify the structure of the hedging point policy which is convenient for implementing control actions in practice.
文摘In this paper, the open queueing network model is proposed for solving the problem of public transportation in cities. The vertices of the networks(i.e., the bus stops) are determined by means of the fuzzy clustering method. The arcs (i.e., the paths of the public transportation) can be set up by using the shortest path model in the time sense or the 0 1 integer programming method.Applying the statistics method, we can calculate the parameters(such as the passenger flow's distribution, passenger flow's transition probability, mean waiting time for the bus etc. ) of the public transportation network. In this paper, we suggest to divide the network into two or three stages to implement the public transportation system in the form of ``frog jumping' fast transfer and ``permeation' fast dispersion.Combining the computer simulation and the evaluation of the achievement and effect of public transportation system, we modify the model so as to solve the public transportation problem better.
基金Supported by the National Natural Science Foundation of China(Grant No.11801485)
文摘In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on the left real line and these results describe the point spectra of the operator. Then, we show that the essential growth bound of the C_0-semigroup generated by the operator is 0 and therefore it is not quasi compact, the essential spectral bound of the C_0-semigroup is equal to 1. Moreover, our results imply it is impossible that the time-dependent solution of the model exponentially converges to its steady-state solution.
基金partially supported by the Fundamental Research Funds for the Central Universities (BUPT2011RC0703)
文摘The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of the service distribution,but not on the interarrival distribution.We shall also give explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases（Case 1：the rate function r（n）=exp（sn1/1＋α）,α〉0,s〉0;Case 2：polynomial rate function r（n）=nα,α〉0;Case 3：logarithmic rate function r（n）=logαn,α〉0）.
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.
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Weighted priority queueing is a modification of priority queueing that eliminates the possibility of blocking lower priority traffic. The weights assigned to priority classes determine the fractions of the bandwith that are guaranteed for individual traffic classes, similarly as in weighted fair queueing. The paper describes a timed Petri net model of weighted priority queueing and uses discrete-event simulation of this model to obtain performance characteristics of simple queueing systems. The model is also used to analyze the effects of finite queue capacity on the performance of queueing systems.
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.
文摘Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.
文摘The Distributed Queuing (DQ) algorithm is predicted as one of the solutions to the issues currently found in IoT networks over the use of Aloha based algorithms. Since recently, the algorithm has been of interest to many IoT researchers as a replacement of those Aloha variants for channel access. However, previous works analyzed and evaluated the DQ algorithm without any consideration of the stability of its queues, assuming it is stable for any given number of nodes in the network. In this paper, we define the DQ stability condition in a single-channel M2M environment considering a traffic model of periodic and urgent frames from each node in the network. Besides, a steady-state evaluation of the algorithm’s performance metrics is also presented. In general, the DQ algorithm, when it is stable, was observed not to efficiently use the contention slots for the collision resolution. In a single-channel environment, the DQ algorithm is found to outperform the Aloha based algorithms only in an idle-to-saturation scenario.
文摘In this paper, we present an approach for model transformation from Queueing Network Models (QNMs) into Queueing Petri Nets (QPNs). The performance of QPNs can be analyzed using a powerful simulation engine, SimQPN, designed to exploit the knowledge and behavior of QPNs to improve the efficiency of simulation. When QNMs are transformed into QPNs, their performance can be analyzed efficiently using SimQPN. To validate our approach, we apply it to analyze the performance of several queueing network models including a model of a database system. The evaluation results show that the performance analysis of the transformed QNMs has high accuracy and low overhead. In this context, model transformation enables the performance analysis of queueing networks using different ways that can be more efficient.
