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 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 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
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
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
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
An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arri...An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arrival and departure process is finite, irreducible, and aperiodic. The algorithm does not depend on a closed-form solution for the limiting behavior of the queue. The expected number of customers is frequently used as a measure of effectiveness to describe the behavior of the system or to optimize its design or control. To calculate such a quantity one must usually obtain a closed-form expression for the steady-state probabilities. Unfortunately, of the myriad of Markovian queueing systems, only a few have known closed-form expressions for their steady-state probabilities. The most well-known, using Kendall’s notation, are the M/M/1 and the M/M/c system. The algorithm described below estimates the expected number in the system under steady-state without a need for closed form steady-state probabilities. All that is needed is the transition matrix for the underlying Markov chain.展开更多
We analyze a Coxian stochastic queueing model with three phases. The Kolmogorov equations of this model are constructed, and limit probabilities and the stationary probabilities of customer numbers in the system are f...We analyze a Coxian stochastic queueing model with three phases. The Kolmogorov equations of this model are constructed, and limit probabilities and the stationary probabilities of customer numbers in the system are found. The performance measures of this model are obtained and in addition the optimal order of service parameters is given with a theorem by obtaining the loss probabilities of customers in the system. That is, putting the greatest service parameter at first phase and the second greatest service parameter at second phase and the smallest service parameter at third phase makes the loss probability and means waiting time minimum. We also give the loss probability in terms of mean waiting time in the system. is the transition probability from j-th phase?to??phase . In this manner while and this system turns into queueing model and while the system turns into Cox(2) queueing model. In addition, loss probabilities are graphically given in a 3D graph for corresponding system parameters and phase transient probabilities. Finally it is shown with a numeric example that this theorem holds.展开更多
It is well known, in queueing theory, that the system performance is greatly influenced by scheduling policy. No universal optimum scheduling strategy exists in systems where individual customer service demands are no...It is well known, in queueing theory, that the system performance is greatly influenced by scheduling policy. No universal optimum scheduling strategy exists in systems where individual customer service demands are not known a priori. However, if the distribution of job times is known, then the residual time (expected time remaining for a job), based on the service it has already received, can be calculated. Our particular research contribution is in exploring the use of this function to enhance system performance by increasing the probability that a job will meet its deadline. In a detailed discrete event simulation, we have tested many different distributions with a wide range of C2 and shapes, as well as for single and dual processor system. Results of four distributions are reported here. We compare with RR and FCFS, and find that in all distributions studied our algorithm performs best. In the study of the use of two slow servers versus one fast server, we have discovered that they provide comparable performance, and in a few cases the double server system does better.展开更多
The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arri...The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arrival processes modulated by queues comprise the external system,all others are belong to the internal system.It is well known that the exogenous arrival has a great influence on the asymptotic variability of performance measures in queues.For the considered queueing network in heavy traffic,we get all the LILs for the queue length,workload,busy time,idle time and departure processes,and present them by some simple functions of the primitive data.The LILs tell us some interesting insights,such as,the LILs of busy and idle times are zero and they reflect a small variability around their fluid approximations,the LIL of departure has nothing to do with the arrival process,both of the two phenomena well explain the service station’s situation of being busy all the time.The external system shows us a distinguishing effect on the performance measures:an underloaded(overloaded,critically loaded)external system affects the internal system through its arrival(departure,arrival and departure together).In addition,we also get the strong approximation of the network as an auxiliary result.展开更多
During epidemics,controlling the patients’congestion is a way to reduce disease spreading.Raising medical demands converts hospitals into one of the sources of disease outbreaks.The long patient waiting time in queue...During epidemics,controlling the patients’congestion is a way to reduce disease spreading.Raising medical demands converts hospitals into one of the sources of disease outbreaks.The long patient waiting time in queues to receive medical services leads to more casualties.The rise of patients increases their waste,which is another source of disease outbreak.In this study,a mathematical model is developed to control patients’congestion in a medical center and manage their waste,considering environmental issues.Besides a queueing system controlling the patients’congestion in the treatment center,another queue is considered for vehicles.An inventory model is employed to prevent waste accumulation.The developed model is solved and reaches an exact solution in small size,and obtains an acceptable solution in large size using the Grasshopper algorithm.A case study is considered to demonstrate the model’s applicability.Also,Sensitivity analysis and valuable managerial insights are presented.展开更多
This paper investigates a partially observable queueing system with N nodes in which each node has a dedicated arrival stream.There is an extra arrival stream to balance the load of the system by routing its customers...This paper investigates a partially observable queueing system with N nodes in which each node has a dedicated arrival stream.There is an extra arrival stream to balance the load of the system by routing its customers to the shortest queue.In addition,a reward-cost structure is considered to analyse customers'strategic behaviours.The equilibrium and socially optimal strategies are derived for the partially observable mean field limit model.Then,we show that the strategies obtained from the mean field model are good approximations to the model with finite N nodes.Finally,numerical experiments are provided to compare the equilibrium and socially optimal behaviours,including joining probabilities and social benefits for different system parameters.展开更多
Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying ...Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying the well-known stochastic decomposition property of the steady-state queue size,the probability generating function of the steady-state queue length distribution is obtained.Moreover,the explicit expressions of the expected queue length and the additional queue length distribution are derived by some algebraic manipulations.Finally,employing the renewal reward theorem,the explicit expression of the long-run expected cost per unit time is given.Furthermore,we analyze the optimal policy for economizing the expected cost and compare the optimal Min(N,D)-policy with the optimal N-policy and the optimal D-policy by using numerical examples.展开更多
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.
文摘We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the server commences service and serves exhaustively before taking another vacation. If the server finds the system empty, it waits a fixed time c. At the expiration of this time, the server commences another vacation if no customer has arrived;otherwise, it serves exhaustively before commencing another vacation. Analytical results are derived for the mean waiting time in the system. The timeout scheme is shown to be a generalized scheme of which both the single vacation and multiple vacations schemes are special cases, with c=∞and c=0, respectively. The model is extended to the N-policy vacation queueing system.
基金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.
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An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arrival and departure process is finite, irreducible, and aperiodic. The algorithm does not depend on a closed-form solution for the limiting behavior of the queue. The expected number of customers is frequently used as a measure of effectiveness to describe the behavior of the system or to optimize its design or control. To calculate such a quantity one must usually obtain a closed-form expression for the steady-state probabilities. Unfortunately, of the myriad of Markovian queueing systems, only a few have known closed-form expressions for their steady-state probabilities. The most well-known, using Kendall’s notation, are the M/M/1 and the M/M/c system. The algorithm described below estimates the expected number in the system under steady-state without a need for closed form steady-state probabilities. All that is needed is the transition matrix for the underlying Markov chain.
文摘We analyze a Coxian stochastic queueing model with three phases. The Kolmogorov equations of this model are constructed, and limit probabilities and the stationary probabilities of customer numbers in the system are found. The performance measures of this model are obtained and in addition the optimal order of service parameters is given with a theorem by obtaining the loss probabilities of customers in the system. That is, putting the greatest service parameter at first phase and the second greatest service parameter at second phase and the smallest service parameter at third phase makes the loss probability and means waiting time minimum. We also give the loss probability in terms of mean waiting time in the system. is the transition probability from j-th phase?to??phase . In this manner while and this system turns into queueing model and while the system turns into Cox(2) queueing model. In addition, loss probabilities are graphically given in a 3D graph for corresponding system parameters and phase transient probabilities. Finally it is shown with a numeric example that this theorem holds.
文摘It is well known, in queueing theory, that the system performance is greatly influenced by scheduling policy. No universal optimum scheduling strategy exists in systems where individual customer service demands are not known a priori. However, if the distribution of job times is known, then the residual time (expected time remaining for a job), based on the service it has already received, can be calculated. Our particular research contribution is in exploring the use of this function to enhance system performance by increasing the probability that a job will meet its deadline. In a detailed discrete event simulation, we have tested many different distributions with a wide range of C2 and shapes, as well as for single and dual processor system. Results of four distributions are reported here. We compare with RR and FCFS, and find that in all distributions studied our algorithm performs best. In the study of the use of two slow servers versus one fast server, we have discovered that they provide comparable performance, and in a few cases the double server system does better.
基金supported by the National Natural Science Foundation of China(No.11871116 and No.11971074).
文摘The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arrival processes modulated by queues comprise the external system,all others are belong to the internal system.It is well known that the exogenous arrival has a great influence on the asymptotic variability of performance measures in queues.For the considered queueing network in heavy traffic,we get all the LILs for the queue length,workload,busy time,idle time and departure processes,and present them by some simple functions of the primitive data.The LILs tell us some interesting insights,such as,the LILs of busy and idle times are zero and they reflect a small variability around their fluid approximations,the LIL of departure has nothing to do with the arrival process,both of the two phenomena well explain the service station’s situation of being busy all the time.The external system shows us a distinguishing effect on the performance measures:an underloaded(overloaded,critically loaded)external system affects the internal system through its arrival(departure,arrival and departure together).In addition,we also get the strong approximation of the network as an auxiliary result.
文摘During epidemics,controlling the patients’congestion is a way to reduce disease spreading.Raising medical demands converts hospitals into one of the sources of disease outbreaks.The long patient waiting time in queues to receive medical services leads to more casualties.The rise of patients increases their waste,which is another source of disease outbreak.In this study,a mathematical model is developed to control patients’congestion in a medical center and manage their waste,considering environmental issues.Besides a queueing system controlling the patients’congestion in the treatment center,another queue is considered for vehicles.An inventory model is employed to prevent waste accumulation.The developed model is solved and reaches an exact solution in small size,and obtains an acceptable solution in large size using the Grasshopper algorithm.A case study is considered to demonstrate the model’s applicability.Also,Sensitivity analysis and valuable managerial insights are presented.
基金the National Natural Science Foundation of China(No.61773014)Scientific Research Fund of Nanjing University of Posts and Telecommunications(No.NY220160)the Natural Sciences and Engineering Research Council of Canada.
文摘This paper investigates a partially observable queueing system with N nodes in which each node has a dedicated arrival stream.There is an extra arrival stream to balance the load of the system by routing its customers to the shortest queue.In addition,a reward-cost structure is considered to analyse customers'strategic behaviours.The equilibrium and socially optimal strategies are derived for the partially observable mean field limit model.Then,we show that the strategies obtained from the mean field model are good approximations to the model with finite N nodes.Finally,numerical experiments are provided to compare the equilibrium and socially optimal behaviours,including joining probabilities and social benefits for different system parameters.
基金supported by the National Natural Science Foundation of China(No.71571127)the National Natural Science Youth Foundation of China(No.72001181).
文摘Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying the well-known stochastic decomposition property of the steady-state queue size,the probability generating function of the steady-state queue length distribution is obtained.Moreover,the explicit expressions of the expected queue length and the additional queue length distribution are derived by some algebraic manipulations.Finally,employing the renewal reward theorem,the explicit expression of the long-run expected cost per unit time is given.Furthermore,we analyze the optimal policy for economizing the expected cost and compare the optimal Min(N,D)-policy with the optimal N-policy and the optimal D-policy by using numerical examples.
