We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the exter...We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.展开更多
In cognitive radio networks(CRNs),multiple secondary users may send out requests simultaneously and one secondary user may send out multiple requests at one time,i.e.,request arrivals usually show an aggregate manner....In cognitive radio networks(CRNs),multiple secondary users may send out requests simultaneously and one secondary user may send out multiple requests at one time,i.e.,request arrivals usually show an aggregate manner.Moreover,a secondary user packet waiting in the buffer may leave the system due to impatience before it is transmitted,and this impatient behavior inevitably has an impact on the system performance.Aiming to investigate the influence of the aggregate behavior of requests and the likelihood of impatience on a dynamic spectrum allocation scheme in CRNs,in this paper a batch arrival queueing model with possible reneging and potential transmission interruption is established.By constructing a Markov chain and presenting a transition rate matrix,the steady-state distribution of the queueing model along with a dynamic spectrum allocation scheme is derived to analyze the stochastic behavior of the system.Accordingly,some important performance measures such as the loss rate,the balk rate and the average delay of secondary user packets are given.Moreover,system experiments are carried out to show the change trends of the performance measures with respect to batch arrival rates of secondary user packets for different impatience parameters,different batch sizes of secondary user packets,and different arrival rates of primary user packets.Finally,a pricing policy for secondary users is presented and the dynamic spectrum allocation scheme is socially optimized.展开更多
An appointment scheduling problem is studied with the consideration of customer impatience.On the assumption that both the time of leaving queue and the time of service are exponentially distributed,in order to minimi...An appointment scheduling problem is studied with the consideration of customer impatience.On the assumption that both the time of leaving queue and the time of service are exponentially distributed,in order to minimize the joint cost,the optimal appointment schedule of the fixed number of customers is studied.The joint cost function is composed of customers expected delay time and service availability time.The expected delay time of each customer in the queue is recursively computed in terms of customer interarrival time.Furthermore,the effect of impatience on the optimal schedule as well as the total operating cost is studied.The results show that as the impatience rate increases,the optimal interarrival time becomes shorter and the interarrival time of the last few customers gradually approaches that of the customers in the middle.In addition,impatient behaviors can increase the joint cost.展开更多
The cellular automaton(CA)model is an essential tool for studying pedestrian evacuation dynamics;moreover,improving simulations of actual evacuation environments and increasing the reliability of evacuation data are i...The cellular automaton(CA)model is an essential tool for studying pedestrian evacuation dynamics;moreover,improving simulations of actual evacuation environments and increasing the reliability of evacuation data are important problems for researchers.The complex psychological dynamics of pedestrians during evacuation and the evacuation velocities are essential components of such models.This study proposes and verifies a synchronously updated multi-velocity evacuation impatient CA model with a corresponding time correction formula.Our model that considers pedestrians’psychological impatience can simulate complex scenarios in which different pedestrians simultaneously evacuate at different speeds.In addition,our model accurately simulates and reproduces the phenomena found in actual experiments:as the self-growth parameter of impatience increases,the evacuation efficiency first increases and then decreases,and as the contagion parameter of impatience increases,the evacuation efficiency decreases.The time correction method and formula are critical for obtaining reliable results from simulations in which pedestrians evacuate at various speeds,and they are expected to be indispensable parts of multi-velocity CA models for predicting complex evacuation scenes.展开更多
Individuals seeking services through drive-thru queuing and waiting,anticipate speedy service.However,long queues often prompt customers’impatience,leading to reneging and the early departure from a queue due to perc...Individuals seeking services through drive-thru queuing and waiting,anticipate speedy service.However,long queues often prompt customers’impatience,leading to reneging and the early departure from a queue due to perceived excessive waiting.Reneging behavior is often disregarded in queuing analysis,undermining the accuracy and management of queues,resulting in a misrepresentation of real-world scenarios.This study delves into an extensive analysis of a 123-h M/M/1 drive-thru service queue,examining reneging probability and its correlation with customers’sensitivity to arrival times.Findings reveal that the time between reneging events follows an Exponential distribution,challenging the assumption of a Poisson distribution for reneging rates.The traditional calculation of queue intensity neglects reneging and service abandonment,necessitating modifications to core queuing theory equations for practicality.Integrating reneging behavior enhances the theory’s applicability to real-life queuing dilemmas,improving accuracy and interpretability for effective queue management analysis and strategies,thus directly benefiting business management of queuing systems.展开更多
Developing a comprehensive service strategy to optimize customer satisfaction presents an ongoing challenge for effective facility provider.The essence of comprehensive systems is selecting the suitable service design...Developing a comprehensive service strategy to optimize customer satisfaction presents an ongoing challenge for effective facility provider.The essence of comprehensive systems is selecting the suitable service design,establishing an effective service delivery process,and building continuous improvement.This research analyzes a finite capacity service system incorporating several realistic customer-server dynamics:customer impatience,server’s partial breakdown,and threshold recovery policy.When the number of customers is more,the server is under pressure to increase the service rate to mitigate the service system’s load.Motivating from this fact,the concept of service pressure condition is also incorporated.For characterization,we evaluate state probabilities derived using the matrix-analytic method and henceforth several performance measures.To address the cost optimization problem involving the developed Chapman-Kolmogorov forward differential-difference equations and determine optimal operational parameters,we employ the recently devised cuckoo search(CS)optimization approach.A comparative analysis is performed with the semi-classical optimizer:quasi-Newton(QN)method,and metaheuristics technique:particle swarm optimization(PSO),to validate the efficacy of results.Lastly,several numerical illustrations are depicted in different tables and graphs to understand essential characteristics quickly.展开更多
In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operati...In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operative phase j,j=1,K¯,customers are served one by one.Once the system is empty,the servers have to wait a random period of time before leaving,causing the system to move to vacation phase 0 at which new arrivals can be served at lower rate.Using the method of the probability generating functions,we establish the steady-state analysis of the system.Special cases of the queueing model are presented.Then,explicit expressions of the useful system characteristics are derived.In addition,a cost model is constructed to define the optimal values of service rates,simultaneously,to minimize the total expected cost per unit time via a quadratic fit search method.Numerical examples are provided to display the impact of different system characteristics.展开更多
基金Supported by the National Natural Science Foundation of China(No.11671404)the Fundamental Research Funds for the Central Universities of Central South University 2016zzts014
文摘We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.
基金supported in part by National Natural Science Foundation of China under Grant Nos.61872311,61973261 and 62006069supported in part by MEXT,Japan.Also。
文摘In cognitive radio networks(CRNs),multiple secondary users may send out requests simultaneously and one secondary user may send out multiple requests at one time,i.e.,request arrivals usually show an aggregate manner.Moreover,a secondary user packet waiting in the buffer may leave the system due to impatience before it is transmitted,and this impatient behavior inevitably has an impact on the system performance.Aiming to investigate the influence of the aggregate behavior of requests and the likelihood of impatience on a dynamic spectrum allocation scheme in CRNs,in this paper a batch arrival queueing model with possible reneging and potential transmission interruption is established.By constructing a Markov chain and presenting a transition rate matrix,the steady-state distribution of the queueing model along with a dynamic spectrum allocation scheme is derived to analyze the stochastic behavior of the system.Accordingly,some important performance measures such as the loss rate,the balk rate and the average delay of secondary user packets are given.Moreover,system experiments are carried out to show the change trends of the performance measures with respect to batch arrival rates of secondary user packets for different impatience parameters,different batch sizes of secondary user packets,and different arrival rates of primary user packets.Finally,a pricing policy for secondary users is presented and the dynamic spectrum allocation scheme is socially optimized.
基金The National Natural Science Foundation of China(No.71671036)the Scientific Innovation Research of Graduate Students in Jiangsu Province(No.KYLX_0211)
文摘An appointment scheduling problem is studied with the consideration of customer impatience.On the assumption that both the time of leaving queue and the time of service are exponentially distributed,in order to minimize the joint cost,the optimal appointment schedule of the fixed number of customers is studied.The joint cost function is composed of customers expected delay time and service availability time.The expected delay time of each customer in the queue is recursively computed in terms of customer interarrival time.Furthermore,the effect of impatience on the optimal schedule as well as the total operating cost is studied.The results show that as the impatience rate increases,the optimal interarrival time becomes shorter and the interarrival time of the last few customers gradually approaches that of the customers in the middle.In addition,impatient behaviors can increase the joint cost.
基金supported by a grant from the City University of Hong Kong,Strategic Research Grant no.7005895.
文摘The cellular automaton(CA)model is an essential tool for studying pedestrian evacuation dynamics;moreover,improving simulations of actual evacuation environments and increasing the reliability of evacuation data are important problems for researchers.The complex psychological dynamics of pedestrians during evacuation and the evacuation velocities are essential components of such models.This study proposes and verifies a synchronously updated multi-velocity evacuation impatient CA model with a corresponding time correction formula.Our model that considers pedestrians’psychological impatience can simulate complex scenarios in which different pedestrians simultaneously evacuate at different speeds.In addition,our model accurately simulates and reproduces the phenomena found in actual experiments:as the self-growth parameter of impatience increases,the evacuation efficiency first increases and then decreases,and as the contagion parameter of impatience increases,the evacuation efficiency decreases.The time correction method and formula are critical for obtaining reliable results from simulations in which pedestrians evacuate at various speeds,and they are expected to be indispensable parts of multi-velocity CA models for predicting complex evacuation scenes.
文摘Individuals seeking services through drive-thru queuing and waiting,anticipate speedy service.However,long queues often prompt customers’impatience,leading to reneging and the early departure from a queue due to perceived excessive waiting.Reneging behavior is often disregarded in queuing analysis,undermining the accuracy and management of queues,resulting in a misrepresentation of real-world scenarios.This study delves into an extensive analysis of a 123-h M/M/1 drive-thru service queue,examining reneging probability and its correlation with customers’sensitivity to arrival times.Findings reveal that the time between reneging events follows an Exponential distribution,challenging the assumption of a Poisson distribution for reneging rates.The traditional calculation of queue intensity neglects reneging and service abandonment,necessitating modifications to core queuing theory equations for practicality.Integrating reneging behavior enhances the theory’s applicability to real-life queuing dilemmas,improving accuracy and interpretability for effective queue management analysis and strategies,thus directly benefiting business management of queuing systems.
基金The third author(MD)extends his sincere thanks to the funding agency CSIR-UGC,India,for the financial support(SRF/NET 1081/(CSIR-UGC NET DEC.2018)).
文摘Developing a comprehensive service strategy to optimize customer satisfaction presents an ongoing challenge for effective facility provider.The essence of comprehensive systems is selecting the suitable service design,establishing an effective service delivery process,and building continuous improvement.This research analyzes a finite capacity service system incorporating several realistic customer-server dynamics:customer impatience,server’s partial breakdown,and threshold recovery policy.When the number of customers is more,the server is under pressure to increase the service rate to mitigate the service system’s load.Motivating from this fact,the concept of service pressure condition is also incorporated.For characterization,we evaluate state probabilities derived using the matrix-analytic method and henceforth several performance measures.To address the cost optimization problem involving the developed Chapman-Kolmogorov forward differential-difference equations and determine optimal operational parameters,we employ the recently devised cuckoo search(CS)optimization approach.A comparative analysis is performed with the semi-classical optimizer:quasi-Newton(QN)method,and metaheuristics technique:particle swarm optimization(PSO),to validate the efficacy of results.Lastly,several numerical illustrations are depicted in different tables and graphs to understand essential characteristics quickly.
文摘In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operative phase j,j=1,K¯,customers are served one by one.Once the system is empty,the servers have to wait a random period of time before leaving,causing the system to move to vacation phase 0 at which new arrivals can be served at lower rate.Using the method of the probability generating functions,we establish the steady-state analysis of the system.Special cases of the queueing model are presented.Then,explicit expressions of the useful system characteristics are derived.In addition,a cost model is constructed to define the optimal values of service rates,simultaneously,to minimize the total expected cost per unit time via a quadratic fit search method.Numerical examples are provided to display the impact of different system characteristics.
