This paper investigates a warm standby repairable retrial system with two types of components and a single reparman,where type 1 components have priority over type 2 in use.Failure and repair times for each type of co...This paper investigates a warm standby repairable retrial system with two types of components and a single reparman,where type 1 components have priority over type 2 in use.Failure and repair times for each type of component are assumed to be exponential distributions.The retrial feature is considered and the retrial time of each failed component is exponentially distributed.By using Markov process theory and matrix analytic method,the system steady-state probabil-ities are derived,and the system steady-state availability and some steady-state performance indices are obtained.Using the Bayesian approach,the system parameters can be estimated.The cost-benefit ratio function of the system is constructed based on the failed components and repairman's states.Numerical experiments are given to evaluate the effect of each parameter on the system steady-state availability and optimize the system cost-benefit ratio with repair rate as a decision variable.展开更多
An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a P...An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served （FCFS） discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.展开更多
The M/M/r/r＋d retrial queuing system with unreliable server is considered. The customers arrive according to a Poisson process and the service time distribution is negative exponential. The life time of the server an...The M/M/r/r＋d retrial queuing system with unreliable server is considered. The customers arrive according to a Poisson process and the service time distribution is negative exponential. The life time of the server and repair times are also negative exponential. If the system is full at the time of arrival of a customer, the customer enters into an orbit. From the orbit the customer tries his luck. The time between two successive retrial follows negative exponential distribution. The model is analyzed using Matrix Geometric Method. The joint distribution of system size and orbit size in steady state is studied. Some system performance measures are obtained. We also provide numerical examples by taking particular values to the parameters.展开更多
There are abundant research results related to cognitive radio systems (CR systems), but using queueing models to portray CR systems is a new research trend. In this paper, a single-server retrial cognitive radio syst...There are abundant research results related to cognitive radio systems (CR systems), but using queueing models to portray CR systems is a new research trend. In this paper, a single-server retrial cognitive radio system with a linear retrial rate has been considered. The system has two types of users: primary users and secondary users. Secondary users have no effect on primary users because primary users have preemptive precedence. As a result, our purpose is to examine some performance indicators such as the expected queue length for primary users, the probability of the system being idle or occupied by a secondary user, and the probability of the system being busy. This paper begins by deriving the expressions for the generating functions based on the balance equations, so that we can calculate our goal conveniently.展开更多
基金This work was supported by the National Natural Science Foundation of China[Grant Number 72071175,72001070].
文摘This paper investigates a warm standby repairable retrial system with two types of components and a single reparman,where type 1 components have priority over type 2 in use.Failure and repair times for each type of component are assumed to be exponential distributions.The retrial feature is considered and the retrial time of each failed component is exponentially distributed.By using Markov process theory and matrix analytic method,the system steady-state probabil-ities are derived,and the system steady-state availability and some steady-state performance indices are obtained.Using the Bayesian approach,the system parameters can be estimated.The cost-benefit ratio function of the system is constructed based on the failed components and repairman's states.Numerical experiments are given to evaluate the effect of each parameter on the system steady-state availability and optimize the system cost-benefit ratio with repair rate as a decision variable.
基金Research sponsored by BJTU Research Foundation (2005SM064),the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Education Ministry and the National Natural Science Foundation of China (10526004,60504016).
文摘An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served （FCFS） discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.
文摘The M/M/r/r＋d retrial queuing system with unreliable server is considered. The customers arrive according to a Poisson process and the service time distribution is negative exponential. The life time of the server and repair times are also negative exponential. If the system is full at the time of arrival of a customer, the customer enters into an orbit. From the orbit the customer tries his luck. The time between two successive retrial follows negative exponential distribution. The model is analyzed using Matrix Geometric Method. The joint distribution of system size and orbit size in steady state is studied. Some system performance measures are obtained. We also provide numerical examples by taking particular values to the parameters.
文摘There are abundant research results related to cognitive radio systems (CR systems), but using queueing models to portray CR systems is a new research trend. In this paper, a single-server retrial cognitive radio system with a linear retrial rate has been considered. The system has two types of users: primary users and secondary users. Secondary users have no effect on primary users because primary users have preemptive precedence. As a result, our purpose is to examine some performance indicators such as the expected queue length for primary users, the probability of the system being idle or occupied by a secondary user, and the probability of the system being busy. This paper begins by deriving the expressions for the generating functions based on the balance equations, so that we can calculate our goal conveniently.
