Analysis of two components parallel repairable degenerate system with vacation

<abstract><p>This article studies a parallel repairable degradation system with two similar components and a repairman who can take a single vacation. Suppose that the system consists of two components that cannot be repaired "as good as new" after failures; when the repairman has a single vacation, the fault component of system may not be repaired immediately, namely, if a component fails and the repairman is on vacation, the repair of the component will be delayed, if a component fails and the repairman is on duty, the fault component can be repaired immediately. Under these assumptions, a replacement policy $ N $ based on the failed times of component 1 is studied. The explicit expression of the system average cost rate $ C(N) $ and the optimal replacement policy $ N^{\ast} $ by minimizing the $ C(N) $ are obtained, which means the two components of the system will be replaced at the same time if the failures of component 1 reach $ N^{\ast} $. To show the advantage of a parallel system, a replacement policy $ N $ of the cold standby system consisting of the two similar components is also considered. The numerical results of both systems are given by the numerical analysis. The optimal replacement policy $ N^* $ for both systems are obtained. Finally, the comparison of numerical results shows the advantages of the parallel system.</p></abstract>

Comparisons of customer behavior in Markovian queues with vacation policies and geometric abandonments

This paper mainly studies customers’ equilibrium balking behavior in Markovian queues with single vacation and geometric abandonments. Whenever the system becomes empty, the server begins a vacation. If it is still empty when the vacation ends, the server stays idle and waits for new arrivals. During a vacation, abandonment opportunities occur according to a Poisson process, and at an abandonment epoch, customers decide sequentially whether they renege and leave the system or not. We consider four information levels: the fully/almost observable cases and the almost/fully unobservable cases, and get the customers’ equilibrium balking strategies, respectively. Then we also get their optimal balking strategies for the almost observable and the almost/fully unobservable cases, and make comparisons of customer strategies and social welfare for the almost observable and the almost/fully unobservable queues with single vacation and multiple vacations. Because of abandonment, we find that the customers’ equilibrium threshold in a vacation may exceed the one in a busy period in the fully observable queues. However, it has little effect on their equilibrium threshold in the almost observable queues, although frequent abandonment opportunity arrival inhibits their optimal threshold. Interestingly, for the almost unobservable queues, customers who arrive in a busy period are not affected by reneging that happened in the previous vacation when they make decisions of joining or balking, whereas the social planner expects that the customers can take it into consideration for social optimization. In the fully unobservable queues, because of no information, possible reneging surely influences customers’ equilibrium and optimal balking behavior. For the almost observable and the almost/fully unobservable queues, the optimal social welfare is greater in the queues with single vacation than that in the queues with multiple vacations.

Strategic behavior in the constant retrial queue with a single vacation

We study customers’ joining strategies in an M/M/1 constant retrial queue with a single vacation. There is no waiting space in front of the server and a vacation is triggered when the system is empty. If an arriving customer finds the server idle, he occupies the server immediately. Otherwise, if the server is found unavailable, the customer enters a retrial pool called orbit with infinite capacity and becomes a repeated customer. According to the different information provided for customers, we consider two situations, where we investigate system characteristics and customers’ joining or balk decisions based on a linear reward-cost structure. Furthermore, we establish the social welfare of the system and make comparisons between the two information levels. It is found that there exist thresholds of system parameters such that the social planner would prefer revealing more information when the system parameter is greater than or less than the corresponding threshold.