| Random service systems are widely used in daily life,computer networks,indus-trial systems and other fields.In industrial production systems,due to the limited re-sources of the working machinery,the operating units that need to be serviced are ran-dom in their arrival and service time,which causes queuing.For example,in a large car maintenance 4s shop,the mechanical arm for maintenance work is the server in the system.The car that needs to be maintained by each car owner is the customer in the system,so the maintenance line forms a queuing system.From the perspective of economics,the customer develops the corresponding team entry strategy for maximiz-ing self-interest,and the service provider formulates the appropriate pricing strategy to make the global optimal,and the two form a non-cooperative game.In order to save energy and increase the reliability of the system in the industrial production system,the service provider will prepare spare parts for the parts that provide the service.When the working parts fail,the spare parts will replace the faulty parts in time.The system continues to operate and the failed parts that are replaced are repaired,which forms a repairable system.This paper focuses on the customer equilibrium and social bene-fits of the multiple vacation queuing system under the control of N-strategy and the reliability analysis of the warm standby repairable system.The first part of this paper studies the customer equilibrium strategy and social benefits of the multi-vacation queuing system under N-strategy control.We consider a M/M/1 queuing system in which the server is simultaneously controlled by the N-policy and multiple vacation strategies.That is,when the server is on vacation,the system only needs to meet one of the control strategies,then the server is reactivated and then start working.Whenever the system becomes empty,the server will start a vacation.If there are N customers waiting in the queue,or the queue length is positive at the end of the holiday,the system is reactivated.Otherwise,if the system is empty when the first vacation is completed,the server will continue for another holiday.We derive the equilibrium strategy for the customer based on the different information of the system status.That is,the arriving customer may or may not know the status of the server and/or the number of customers in the system.We assume that the arriving customer decides whether to enter the system based on the reward cost structure.We also compared the social benefits of different information situations and analyzed the sensitivity of the parameters N and ? to social benefits.The second part of this paper studies the reliability analysis of the warm standby repairable system.We believe that the server in the production system may fail.In order to improve the overall efficiency of the system,we prepare the standby server to replace the failed server to continue the service,and repair the failed server.However,the standby server may also fail during the reserve process.In order to study the relia-bility analysis of the system,we regard the server as a component and consider a warm standby repairable system consisting of two different components,one switch and one repairman are composed.The component have two failure modes,a machine defect and a severe human error.It is assumed that the working life of both components are subject to an exponential distribution,and the repair time of the component is subject to a general distribution.The repaired parts are as good as the new ones.In addition,we assume that the transfer switch in the system is reliable and that the component 1 has priority in use.By using the Markov update method,we obtained some impor-tant reliability metrics,such as the mean time to first failure of the system(MTTFF),the steady-state reliability of the system,and the system within the time period(0,t)The average number of failures.We also analyzed the effects of system parameters on these reliability metrics by numerical examples under special condition. |
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