We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponen...We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.展开更多
In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a...In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.展开更多
In this paper exhaustive-service priority-M/G/1 queueing systems with multiple vacations, single vacation and setup times are studied under the nonpreemptive and preemptive resume priority disciplines. For each of the...In this paper exhaustive-service priority-M/G/1 queueing systems with multiple vacations, single vacation and setup times are studied under the nonpreemptive and preemptive resume priority disciplines. For each of the six models analysed, the Laplace-Stieltjes transform of the virtual waiting time Wk(t) at time t of class k is derived by the method of collective marks. A sufficient condition for , where U has the standard normal distribution, is also given.展开更多
In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodol...In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodology for applying these theorems for the benefit of service systems. The limit theorems studied here are dominant in the literature. Our contribution is primarily on the analysis leading to the application of these theorems in various problem situations for better operations. Relevant Examples are included to aid the application of the results studied in this work.展开更多
This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks, which has two types of arriving calls--handoff and originating calls, both of which follow the Markov arriving pr...This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks, which has two types of arriving calls--handoff and originating calls, both of which follow the Markov arriving process with different rates. The channel holding times of the two types of calls follow different phase-type distributions. Firstly, the joint distribution of two queue lengths is derived, and then the dropping and blocking probabilities, the mean queue length and the mean waiting time from the joint distribution are gotten. Finally, numerical examples show the impact of different call arrival rates on the performance measures.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
We develop a gradient-based simulation optimization algorithm,dabbed KWiQ-H,for joint pricing and staffing problems in single-server queues with heavy-tailed service time distributions.Our algorithm is designed based ...We develop a gradient-based simulation optimization algorithm,dabbed KWiQ-H,for joint pricing and staffing problems in single-server queues with heavy-tailed service time distributions.Our algorithm is designed based on the well-known Kiefer–Wolfowitz algorithm so that it is applicable to more general and practical settings where customer’s behavior is unknown to service providers in prior.We first establish a convergence result for KWiQ-H when the service times have a finite fifth moment.Then,we show that under a stronger condition with a finite seventh moment,KWiQ-H could achieve sample complexity with the same asymptotic order as in the case when service times are light-tailed in Chen et al.(Oper Res,2023).Complementing the theoretic results,we carry out comprehensive numerical experiments to test the efficiency and robustness of KWiQ-H in a variety of model settings.展开更多
A discrete-time GI/G/1 retrial queue with Bernoulli retrials and time-controlled vacation policies is investigated in this paper. By representing the inter-arrival, service and vacation tlmes using a Markov-based appr...A discrete-time GI/G/1 retrial queue with Bernoulli retrials and time-controlled vacation policies is investigated in this paper. By representing the inter-arrival, service and vacation tlmes using a Markov-based approach, we are able to analyze this model as a level-dependent quasi-birth-and-death （LDQBD） process which makes the model algorithmically tractable. Several performance measures such as the stationary probability distribution and the expected number of customers in the orbit have been discussed with two different policies： deterministic time-controlled system and random time-controlled system. To give a comparison with the known vacation policy in the literature, we present the exhaustive vacation policy as a contrast between these policies under the early arrival system （EAS） and the late arrival system with delayed access （LAS-DA）. Significant difference between EAS and LAS-DA is illustrated by some numerical examples.展开更多
We consider decay properties regarding decay parameter and invariant measures of Markovian bulk-arrival and bulk-service queues with state-independent control. The exact value of the decay parameter, denoted by λz, i...We consider decay properties regarding decay parameter and invariant measures of Markovian bulk-arrival and bulk-service queues with state-independent control. The exact value of the decay parameter, denoted by λz, is firstly revealed. A criterion regarding ）λz-recurrence and λz-positive is obtained. The corresponding λz-subinvariant/invariant measures and λz-subinvariant/invariant vectors are then presented.展开更多
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
This paper studies a system consisting of two parallel queues with transfers of customers.In the system,one queue is called main queue and the other one is called auxiliary queue.The main queue is monitored at exponen...This paper studies a system consisting of two parallel queues with transfers of customers.In the system,one queue is called main queue and the other one is called auxiliary queue.The main queue is monitored at exponential time instances.At a monitoring instant,if the number of customers in main queue reaches L(>K),a batch of L−K customers is transferred from the main queue to the auxiliary queue,and if the number of customers in main queue is less than or equal to K,the transfers will not happen.For this system,by using a Foster-Lyapunov type condition,we establish a sufficient stability condition.Then,we provide a sufficient condition under which,for any fixed number of customers in the auxiliary queue,the stationary probability of the number of customers in the main queue has an exact geometric tail asymptotic as the number of customers in main queue increases to infinity.Finally,we give some numerical results to illustrate the impact of some critical model parameters on the decay rate.展开更多
This paper proposes an improved multi-class dynamic network traffic flow propagation model with a consideration of physical queues. Each link is divided into two areas: Free flow area and queue area. The vehicles of t...This paper proposes an improved multi-class dynamic network traffic flow propagation model with a consideration of physical queues. Each link is divided into two areas: Free flow area and queue area. The vehicles of the same class are assumed to satisfy the first-in-first-out(FIFO) principle on the whole link, and the vehicles of the different classes also follow FIFO in the queue area but not in the free flow area. To characterize this phenomenon by numerical methods, the improved model is directly formulated in discrete time space. Numerical examples are developed to illustrate the unrealistic flows of the existing model and the performance of the improved model. This analysis can more realistically capture the traffic flow propagation, such as interactions between multi-class traffic flows, and the dynamic traffic interactions across multiple links.展开更多
This paper presents an algorthmic procedure for a busy-period subcomponent analysis of bulkqueues. A component of interest for many server queues is the period tto reduce congestion froma level k to level k-1. For an ...This paper presents an algorthmic procedure for a busy-period subcomponent analysis of bulkqueues. A component of interest for many server queues is the period tto reduce congestion froma level k to level k-1. For an M(x)/M/c system with the possibility of total or partial rejection ofbatches, it is demonstrated that the expected length of busy periods, the proportion of delayed batchand the steady state queue length probabilities can be easily obtained. The procedure is based on thenested partial sums and monotonic properties of expected lengths of the busy periods.展开更多
This paper carries out a game-theoretic analysis of a single-server queueing system with setup times under N-policy by considering both the partially observable and the partially unobservable information scenarios. Th...This paper carries out a game-theoretic analysis of a single-server queueing system with setup times under N-policy by considering both the partially observable and the partially unobservable information scenarios. The server switches off whenever the system becomes empty, and is resumed when the number of customers reaches a certain threshold value. Customers decide whether to join or to balk the system upon arrival based on their available information. The equilibrium joining strategy of customers as well as the systemzs performance measures are derived under different information levels. We find that both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors exist in our system. Numerical results show that the social welfare is unimodal in the threshold, and is decreasing in the waiting cost.展开更多
This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service co...This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service completion, begins a process of search in order to find the following customer to be served with a certain probability, or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or on vacation. Finally, the author gives two stochastic decomposition laws, and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.展开更多
For an ergodic continuous-time Markov process with a particular state in its space,the authors provide the necessary and sufficient conditions for exponential and strong ergodicity in terms of the moments of the first...For an ergodic continuous-time Markov process with a particular state in its space,the authors provide the necessary and sufficient conditions for exponential and strong ergodicity in terms of the moments of the first hitting time on the state.An application to the queue length process of M/G/1 queue with multiple vacations is given.展开更多
This paper studies customer joining behavior and system regulation strategy in nonexhaustive visible M/M/m queues with synchronous vacations of a part of the servers.Once this part of the servers are idle,they take mu...This paper studies customer joining behavior and system regulation strategy in nonexhaustive visible M/M/m queues with synchronous vacations of a part of the servers.Once this part of the servers are idle,they take multiple vacations simultaneously(vacation period).Until there are customers waiting in the queue,they are reactivated and all servers are busy or idle(busy period).The authors call this part of the servers as“partial servers”.In view of the fully visible queue and the almost visible queue,the authors obtain customers’equilibrium joining threshold strategies and their socially optimal joining threshold strategies,respectively,and observe that customer joining behavior in equilibrium generally makes the system overcrowded,which makes the equilibrium social welfare lower than the optimal social welfare.After regulation,interestingly,for optimizing social welfare,the system manager hopes not only customers arriving in vacation period pay attention to the number of partial servers,but also customers arriving in busy period should care about it rather than ignore.Moreover,arranging more servers for vacation does not necessarily lead to the decrease of social welfare on condition that the number of partial servers is close to m.As for the information advantage of the fully visible case,it is not obvious for increasing social welfare and even unfavorable to servers’profit unless the number of partial servers is big enough.Furthermore,given the different composition of social welfare,there exists the optimal number of partial servers and the optimal arrival rate of customers for maximizing social welfare.展开更多
This paper compares the performance of exhaustive and nonexhaustive M/M/l/N queues with working vacation and threshold policy. In an exhaustive queue, the server slows down its service rate only when no customers exis...This paper compares the performance of exhaustive and nonexhaustive M/M/l/N queues with working vacation and threshold policy. In an exhaustive queue, the server slows down its service rate only when no customers exist in the system, and turns to normal service until the number of customers achieves a threshold. However, in a nonexhaustive queue, the server switches service rate between a low and a high value depending on system congestion. To get equilibrium arrival rate of customers and social welfare for the two types of queues, we first derive queue length distributions and expected busy circle. Then, by making sensitivity analysis of busy circle, system cost, arrival rate and optimal social welfare, we find that customers tend to join exhaustive queues instead of nonexhaustive queues, and the optimal threshold in an exhaustive queue is probably inconsistent with the one in a nonexhaustive queue. Moreover, in general, whet her to consider system cost or not in social welfare will obviously affect the tendencies of optimal arrival rate and optimal social welfare with the threshold and system capacity for the two types of queues, especially for the nonexhaustive queues, and then affect the final decisions of social planner or system manager.展开更多
A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers dem...A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers demand the first ＂essential＂ service, whereas only some of them demand the second ＂multi-optional＂ service. The first service time and the second service all have general distribution and they are independent. We assume that the server has a service-phase dependent, exponentially distributed life time as well as a servicephase dependent, generally distributed repair time. Using a supplementary variable method, we obtain the transient and the steady-state solutions for both queueing and reliability measures of interest.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11971486)。
文摘We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.
基金Supported by the National Natural Science Foundation of China(11571372,11771452)the Innovation Program of Central South University(10900-50601010)
文摘In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.
文摘In this paper exhaustive-service priority-M/G/1 queueing systems with multiple vacations, single vacation and setup times are studied under the nonpreemptive and preemptive resume priority disciplines. For each of the six models analysed, the Laplace-Stieltjes transform of the virtual waiting time Wk(t) at time t of class k is derived by the method of collective marks. A sufficient condition for , where U has the standard normal distribution, is also given.
文摘In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodology for applying these theorems for the benefit of service systems. The limit theorems studied here are dominant in the literature. Our contribution is primarily on the analysis leading to the application of these theorems in various problem situations for better operations. Relevant Examples are included to aid the application of the results studied in this work.
基金supported by the Postgraduate Innovation Project of Jiangsu University (CX10B 003X)
文摘This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks, which has two types of arriving calls--handoff and originating calls, both of which follow the Markov arriving process with different rates. The channel holding times of the two types of calls follow different phase-type distributions. Firstly, the joint distribution of two queue lengths is derived, and then the dropping and blocking probabilities, the mean queue length and the mean waiting time from the joint distribution are gotten. Finally, numerical examples show the impact of different call arrival rates on the performance measures.
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funded by Science,Technology and Innovation Commission of Shenzhen Munici pality(No.RCYX20210609103124047)the National Natural Science Foundation of China(Nos.72171205 and 72394361)Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence(No.2023B1212010001).
文摘We develop a gradient-based simulation optimization algorithm,dabbed KWiQ-H,for joint pricing and staffing problems in single-server queues with heavy-tailed service time distributions.Our algorithm is designed based on the well-known Kiefer–Wolfowitz algorithm so that it is applicable to more general and practical settings where customer’s behavior is unknown to service providers in prior.We first establish a convergence result for KWiQ-H when the service times have a finite fifth moment.Then,we show that under a stronger condition with a finite seventh moment,KWiQ-H could achieve sample complexity with the same asymptotic order as in the case when service times are light-tailed in Chen et al.(Oper Res,2023).Complementing the theoretic results,we carry out comprehensive numerical experiments to test the efficiency and robustness of KWiQ-H in a variety of model settings.
基金supported by the National Natural Science Foundation of China(Grant Nos.10871020 and 11171019)Program for New Century Excellent Talents in University(No.NCET-11-0568)the Fundamental Research Funds for the Central Universities(Nos.2011JBZ012 and 2013JBZ019)
文摘A discrete-time GI/G/1 retrial queue with Bernoulli retrials and time-controlled vacation policies is investigated in this paper. By representing the inter-arrival, service and vacation tlmes using a Markov-based approach, we are able to analyze this model as a level-dependent quasi-birth-and-death （LDQBD） process which makes the model algorithmically tractable. Several performance measures such as the stationary probability distribution and the expected number of customers in the orbit have been discussed with two different policies： deterministic time-controlled system and random time-controlled system. To give a comparison with the known vacation policy in the literature, we present the exhaustive vacation policy as a contrast between these policies under the early arrival system （EAS） and the late arrival system with delayed access （LAS-DA）. Significant difference between EAS and LAS-DA is illustrated by some numerical examples.
文摘We consider decay properties regarding decay parameter and invariant measures of Markovian bulk-arrival and bulk-service queues with state-independent control. The exact value of the decay parameter, denoted by λz, is firstly revealed. A criterion regarding ）λz-recurrence and λz-positive is obtained. The corresponding λz-subinvariant/invariant measures and λz-subinvariant/invariant vectors are then presented.
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.
文摘This paper studies a system consisting of two parallel queues with transfers of customers.In the system,one queue is called main queue and the other one is called auxiliary queue.The main queue is monitored at exponential time instances.At a monitoring instant,if the number of customers in main queue reaches L(>K),a batch of L−K customers is transferred from the main queue to the auxiliary queue,and if the number of customers in main queue is less than or equal to K,the transfers will not happen.For this system,by using a Foster-Lyapunov type condition,we establish a sufficient stability condition.Then,we provide a sufficient condition under which,for any fixed number of customers in the auxiliary queue,the stationary probability of the number of customers in the main queue has an exact geometric tail asymptotic as the number of customers in main queue increases to infinity.Finally,we give some numerical results to illustrate the impact of some critical model parameters on the decay rate.
基金jointly supported by the National Natural Science Foundation of China (Grant Nos. 71571150 and 71361006)the Humanities and Social Science Foundation of The Ministry of Education (Grant No. 14YJA630026)the Fundamental Research Funds for the Central Universities (Grant No. 26815WCX03)
文摘This paper proposes an improved multi-class dynamic network traffic flow propagation model with a consideration of physical queues. Each link is divided into two areas: Free flow area and queue area. The vehicles of the same class are assumed to satisfy the first-in-first-out(FIFO) principle on the whole link, and the vehicles of the different classes also follow FIFO in the queue area but not in the free flow area. To characterize this phenomenon by numerical methods, the improved model is directly formulated in discrete time space. Numerical examples are developed to illustrate the unrealistic flows of the existing model and the performance of the improved model. This analysis can more realistically capture the traffic flow propagation, such as interactions between multi-class traffic flows, and the dynamic traffic interactions across multiple links.
文摘This paper presents an algorthmic procedure for a busy-period subcomponent analysis of bulkqueues. A component of interest for many server queues is the period tto reduce congestion froma level k to level k-1. For an M(x)/M/c system with the possibility of total or partial rejection ofbatches, it is demonstrated that the expected length of busy periods, the proportion of delayed batchand the steady state queue length probabilities can be easily obtained. The procedure is based on thenested partial sums and monotonic properties of expected lengths of the busy periods.
基金the National Natural Science Foundation of China under Grant Nos.71871008 and 71571014.
文摘This paper carries out a game-theoretic analysis of a single-server queueing system with setup times under N-policy by considering both the partially observable and the partially unobservable information scenarios. The server switches off whenever the system becomes empty, and is resumed when the number of customers reaches a certain threshold value. Customers decide whether to join or to balk the system upon arrival based on their available information. The equilibrium joining strategy of customers as well as the systemzs performance measures are derived under different information levels. We find that both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors exist in our system. Numerical results show that the social welfare is unimodal in the threshold, and is decreasing in the waiting cost.
基金supported by the National Natural Science Foundation of China under Grant No.11171019the Fundamental Research Funds for the Central Universities under Grant No.2011JBZ012the Program for New Century Excellent Talents in University under Grant No.NCET-11-0568
文摘This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service completion, begins a process of search in order to find the following customer to be served with a certain probability, or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or on vacation. Finally, the author gives two stochastic decomposition laws, and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.
基金the National Natural Science Foundation of China(No.10671212)the Research Fund for the Doctoral Program of Higher Education(No.20050533036).
文摘For an ergodic continuous-time Markov process with a particular state in its space,the authors provide the necessary and sufficient conditions for exponential and strong ergodicity in terms of the moments of the first hitting time on the state.An application to the queue length process of M/G/1 queue with multiple vacations is given.
基金supported by the National Natural Science Foundation of China under Grant No.71971188the Humanities and Social Science Fund of Ministry of Education of China under Grant No.22YJCZH086the Hebei Natural Science Foundation under Grant Nos.G2023203008 and G2022203003。
文摘This paper studies customer joining behavior and system regulation strategy in nonexhaustive visible M/M/m queues with synchronous vacations of a part of the servers.Once this part of the servers are idle,they take multiple vacations simultaneously(vacation period).Until there are customers waiting in the queue,they are reactivated and all servers are busy or idle(busy period).The authors call this part of the servers as“partial servers”.In view of the fully visible queue and the almost visible queue,the authors obtain customers’equilibrium joining threshold strategies and their socially optimal joining threshold strategies,respectively,and observe that customer joining behavior in equilibrium generally makes the system overcrowded,which makes the equilibrium social welfare lower than the optimal social welfare.After regulation,interestingly,for optimizing social welfare,the system manager hopes not only customers arriving in vacation period pay attention to the number of partial servers,but also customers arriving in busy period should care about it rather than ignore.Moreover,arranging more servers for vacation does not necessarily lead to the decrease of social welfare on condition that the number of partial servers is close to m.As for the information advantage of the fully visible case,it is not obvious for increasing social welfare and even unfavorable to servers’profit unless the number of partial servers is big enough.Furthermore,given the different composition of social welfare,there exists the optimal number of partial servers and the optimal arrival rate of customers for maximizing social welfare.
基金the support from the National Natural Science Foundation of China under Grant 71671159, the Humanity and Social cience Foundation of Ministry of Education of China under Grant 16YJC630106, the Natural Science Foundation of Hebei Province under Grants G2016203236 and G2018203302,and the project Funded by Hebei Education epartment under Grants BJ2016063 and BJ2017029, and Hebei Talents Program under Grant A2017002108.
文摘This paper compares the performance of exhaustive and nonexhaustive M/M/l/N queues with working vacation and threshold policy. In an exhaustive queue, the server slows down its service rate only when no customers exist in the system, and turns to normal service until the number of customers achieves a threshold. However, in a nonexhaustive queue, the server switches service rate between a low and a high value depending on system congestion. To get equilibrium arrival rate of customers and social welfare for the two types of queues, we first derive queue length distributions and expected busy circle. Then, by making sensitivity analysis of busy circle, system cost, arrival rate and optimal social welfare, we find that customers tend to join exhaustive queues instead of nonexhaustive queues, and the optimal threshold in an exhaustive queue is probably inconsistent with the one in a nonexhaustive queue. Moreover, in general, whet her to consider system cost or not in social welfare will obviously affect the tendencies of optimal arrival rate and optimal social welfare with the threshold and system capacity for the two types of queues, especially for the nonexhaustive queues, and then affect the final decisions of social planner or system manager.
基金Supported by the National Natural Science Foundation of China (No. 10871020)
文摘A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers demand the first ＂essential＂ service, whereas only some of them demand the second ＂multi-optional＂ service. The first service time and the second service all have general distribution and they are independent. We assume that the server has a service-phase dependent, exponentially distributed life time as well as a servicephase dependent, generally distributed repair time. Using a supplementary variable method, we obtain the transient and the steady-state solutions for both queueing and reliability measures of interest.
