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 introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to st...In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to stochastic orderings.Performance measures of such a system are available explicitly,while their forms are cumbersome(these formulas include integrals of Laplace transform,solutions of functional equations,etc.).Therefore,they are not exploitable from the application point of view.To overcome these difficulties,we present stochastic comparison methods in order to get qualitative estimates of these measures.In particular,we prove the monotonicity of the transition operator of the embedded Markov chain.In addition,we establish conditions for which transition operators as well as stationary probabilities,associated with two embedded Markov chains,having the same structure but with different parameters,are comparable relative to the given stochastic orderings.Further,numerical examples are carried out to illustrate the theoretical results.展开更多
In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the di...In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.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.
文摘In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to stochastic orderings.Performance measures of such a system are available explicitly,while their forms are cumbersome(these formulas include integrals of Laplace transform,solutions of functional equations,etc.).Therefore,they are not exploitable from the application point of view.To overcome these difficulties,we present stochastic comparison methods in order to get qualitative estimates of these measures.In particular,we prove the monotonicity of the transition operator of the embedded Markov chain.In addition,we establish conditions for which transition operators as well as stationary probabilities,associated with two embedded Markov chains,having the same structure but with different parameters,are comparable relative to the given stochastic orderings.Further,numerical examples are carried out to illustrate the theoretical results.
文摘In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.
