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
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.
文摘传统联邦学习训练模型时假定所有参与方可信,但实际场景存在恶意参与方或恶意攻击模型,现有的联邦学习算法面对投毒攻击时,存在模型性能严重下降的问题。针对模型投毒问题,本文提出一种基于联邦平均(federated averaging,Fedavg)与异常检测的联邦检测算法——FedavgCof,该算法考虑到所有参与方之间的差异对比,在中心服务器和本地模型之间添加异常检测层,通过基于聚类的本地异常检测因子(cluster-based local outlier factor,COF)异常检测算法剔除影响模型性能的异常参数,提升模型鲁棒性。实验结果表明,虽然新型投毒方式攻击性更强,但是FedavgCof能够有效防御投毒攻击,降低模型性能损失,提高模型抗投毒攻击能力,相较于Median和模型清洗算法平均提升精度达到10%以上,大幅提升了模型的安全性。
