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
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, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distr...In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj }, j≥ 1 is studied. By a simple method （techniques of probability decomposition, renewal process theory） that is different from the techniques used by Hunter（1983）, the transient property of the queue with initial state i（i ≥ 0） is discussed. The recursion expression for u -transform of transient queue-length distribution at any time point n^＋ is obtained, and the recursion expression of the limiting queue length distribution is also obtained.展开更多
In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of ...In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system.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
In order to meet people’s demand for various types of network services,researchers have conducted extensive research on authentication schemes for multi-server architecture.Although various schemes have been proposed...In order to meet people’s demand for various types of network services,researchers have conducted extensive research on authentication schemes for multi-server architecture.Although various schemes have been proposed,most of them still have safety defects and fail to meet safety requirements.Recently,Haq et al presented an efficient Hash-based authenticated key agreement scheme for multi-server scheme and claimed that their scheme can withstand all well-known attacks.However,we find that their scheme is vulnerable to replay attack,tracking attack and malicious server impersonation user attack.Then we propose an improved scheme.We also analyze the security of the improved scheme and compare with Haq et al’s scheme in security and computational efficiency.Furthermore,we use the AVISPA(Automated Validation of Internet Security Protocols and Applications)tool to verify the security of the improved scheme.展开更多
We construct the membership functions of the fuzzy objective values of a controllable queueing model,in which cost elements,arrival rate and service rate are all fuzzy numbers. Based on Zadeh's extension principle...We construct the membership functions of the fuzzy objective values of a controllable queueing model,in which cost elements,arrival rate and service rate are all fuzzy numbers. Based on Zadeh's extension principle,a set of parametric nonlinear programs is developed to find the upper and lower bounds of the minimal average total cost per unit time at the possibility level. The membership functions of the minimal average total cost are further constructed using different values of the possibility level. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the object value is expressed and governed by the membership functions,the optimization problem in a fuzzy environment for the controllable queueing models is represented more accurately and analytical results are more useful for system designers and practitioners.展开更多
Multi-server authenticated key agreement schemes have attracted great attention to both academia and industry in recent years.However,traditional authenticated key agreement schemes in the single-server environment ar...Multi-server authenticated key agreement schemes have attracted great attention to both academia and industry in recent years.However,traditional authenticated key agreement schemes in the single-server environment are not suitable for the multi-server environment because the user has to register on each server when he/she wishes to log in various servers for different service.Moreover,it is unreasonable to consider all servers are trusted since the server in a multi-server environment may be a semi-trusted party.In order to overcome these difficulties,we designed a secure three-factor multi-server authenticated key agreement protocol based on elliptic curve cryptography,which needs the user to register only once at the registration center in order to access all semi-trusted servers.The proposed scheme can not only against various known attacks but also provides high computational efficiency.Besides,we have proved our scheme fulfills mutual authentication by using the authentication test method.展开更多
During the past decade,rapid advances in wireless communication technologies have made it possible for users to access desired services using hand-held devices.Service providers have hosted multiple servers to ensure ...During the past decade,rapid advances in wireless communication technologies have made it possible for users to access desired services using hand-held devices.Service providers have hosted multiple servers to ensure seamless online services to end-users.To ensure the security of this online communication,researchers have proposed several multi-server authentication schemes incorporating various cryptographic primitives.Due to the low power and computational capacities of mobile devices,the hash-based multi-server authenticated key agreement schemes with offline Registration Server(RS)are the most efficient choice.Recently,Kumar-Om presented such a scheme and proved its security against all renowned attacks.However,we find that their scheme bears an incorrect login phase,and is unsafe to the trace attack,the Session-Specific Temporary Information Attack(SSTIA),and the Key Compromise Impersonation Attack(KCIA).In fact,all of the existing multi-server authentication schemes(hash-based with offline RS)do not withstand KCLA.To deal with this situation,we propose an improved hash-based multi-server authentication scheme(with offline RS).We analyze the security of the proposed scheme under the random oracle model and use the t4Automated Validation of Internet Security Protocols and Applications''(AVISPA)tool.The comparative analysis of communication overhead and computational complexity metrics shows the efficiency of the proposed scheme.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
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
We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson stream...We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.展开更多
In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems the...In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems themselves—Queueing Systems. This article is dedicated to computer software modelling of processes taking place in the systems in question, Markov processes in particular. In this article, by means of Matlab environment, software realization of one of the typical models of queueing service theory-multichannel QS with unreliable recoverable servers and limited number of requirements in the system, is fulfilled. The results of this research are important because it gives the possibility to use received results to determine optimality degree of some real queueing systems that possess Markov property.展开更多
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
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
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 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
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This work was supported by the Scientific Research Fund of Southwestern University of Finance and Economics and the Science Foundation of Sichuan Normal University.
文摘In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj }, j≥ 1 is studied. By a simple method （techniques of probability decomposition, renewal process theory） that is different from the techniques used by Hunter（1983）, the transient property of the queue with initial state i（i ≥ 0） is discussed. The recursion expression for u -transform of transient queue-length distribution at any time point n^＋ is obtained, and the recursion expression of the limiting queue length distribution is also obtained.
文摘In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system.
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.
基金Supported by the Applied Basic and Advanced Technology Research Programs of Tianjin(15JCYBJC15900)。
文摘In order to meet people’s demand for various types of network services,researchers have conducted extensive research on authentication schemes for multi-server architecture.Although various schemes have been proposed,most of them still have safety defects and fail to meet safety requirements.Recently,Haq et al presented an efficient Hash-based authenticated key agreement scheme for multi-server scheme and claimed that their scheme can withstand all well-known attacks.However,we find that their scheme is vulnerable to replay attack,tracking attack and malicious server impersonation user attack.Then we propose an improved scheme.We also analyze the security of the improved scheme and compare with Haq et al’s scheme in security and computational efficiency.Furthermore,we use the AVISPA(Automated Validation of Internet Security Protocols and Applications)tool to verify the security of the improved scheme.
文摘We construct the membership functions of the fuzzy objective values of a controllable queueing model,in which cost elements,arrival rate and service rate are all fuzzy numbers. Based on Zadeh's extension principle,a set of parametric nonlinear programs is developed to find the upper and lower bounds of the minimal average total cost per unit time at the possibility level. The membership functions of the minimal average total cost are further constructed using different values of the possibility level. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the object value is expressed and governed by the membership functions,the optimization problem in a fuzzy environment for the controllable queueing models is represented more accurately and analytical results are more useful for system designers and practitioners.
基金This work is supported by the Sichuan education department research project(No.16226483)Sichuan Science and Technology Program(No.2018GZDZX0008)+1 种基金Chengdu Science and Technology Program(No.2018-YF08-00007-GX)the National Natural Science Foundation of China(No.61872087).
文摘Multi-server authenticated key agreement schemes have attracted great attention to both academia and industry in recent years.However,traditional authenticated key agreement schemes in the single-server environment are not suitable for the multi-server environment because the user has to register on each server when he/she wishes to log in various servers for different service.Moreover,it is unreasonable to consider all servers are trusted since the server in a multi-server environment may be a semi-trusted party.In order to overcome these difficulties,we designed a secure three-factor multi-server authenticated key agreement protocol based on elliptic curve cryptography,which needs the user to register only once at the registration center in order to access all semi-trusted servers.The proposed scheme can not only against various known attacks but also provides high computational efficiency.Besides,we have proved our scheme fulfills mutual authentication by using the authentication test method.
文摘During the past decade,rapid advances in wireless communication technologies have made it possible for users to access desired services using hand-held devices.Service providers have hosted multiple servers to ensure seamless online services to end-users.To ensure the security of this online communication,researchers have proposed several multi-server authentication schemes incorporating various cryptographic primitives.Due to the low power and computational capacities of mobile devices,the hash-based multi-server authenticated key agreement schemes with offline Registration Server(RS)are the most efficient choice.Recently,Kumar-Om presented such a scheme and proved its security against all renowned attacks.However,we find that their scheme bears an incorrect login phase,and is unsafe to the trace attack,the Session-Specific Temporary Information Attack(SSTIA),and the Key Compromise Impersonation Attack(KCIA).In fact,all of the existing multi-server authentication schemes(hash-based with offline RS)do not withstand KCLA.To deal with this situation,we propose an improved hash-based multi-server authentication scheme(with offline RS).We analyze the security of the proposed scheme under the random oracle model and use the t4Automated Validation of Internet Security Protocols and Applications''(AVISPA)tool.The comparative analysis of communication overhead and computational complexity metrics shows the efficiency of the proposed scheme.
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.
文摘We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.
文摘In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems themselves—Queueing Systems. This article is dedicated to computer software modelling of processes taking place in the systems in question, Markov processes in particular. In this article, by means of Matlab environment, software realization of one of the typical models of queueing service theory-multichannel QS with unreliable recoverable servers and limited number of requirements in the system, is fulfilled. The results of this research are important because it gives the possibility to use received results to determine optimality degree of some real queueing systems that possess Markov property.
基金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.
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.
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.
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.
