ABSTRACT

We study an M/M/1 retrial queueing system with constant retrial rate and Poisson generated catastrophes. When a catastrophe arrives to the system that the server is working, it deletes all customers in system and breaks the server down. The failed server is repaired immediately and the repair time is exponentially distributed. We investigate a joining/balking dilemma of customers with a natural reward-cost structure under two information levels, i.e. the unobservable case where customers can only observe server’s state, and the observable case where customers know both the queue length in orbit and the status of the server. Individual equilibrium joining probabilities and socially optimal strategies are obtained in these two cases. Finally, numerical experiments are carried out to illustrate our theoretic findings and the impact of information levels on social welfare. Interestingly, by comparing the corresponding results in the standard system without catastrophes, we find that customers in our system incur a lower waiting cost, which results in the fact that customers will receive more benefit and they are more inclined to join the system with catastrophes.

摘要

我们研究了具有恒定重试率和Poisson产生灾难的M / M / 1重试排队系统。当灾难到达服务器正在运行的系统时，它将删除系统中的所有客户并破坏服务器。发生故障的服务器将立即得到修复，并且修复时间以指数方式分配。我们研究了在两个信息级别下具有自然奖励成本结构的客户的加入/拒绝困境，即客户仅能观察服务器状态的不可观察情况，以及客户既了解在轨队列长度又了解卫星状态的可观察情况。服务器。在这两种情况下，可以获得个体均衡的加入概率和社会最优策略。最后，进行了数值实验，以说明我们的理论发现以及信息水平对社会福利的影响。有趣的是，通过比较标准系统中没有灾难的相应结果，我们发现系统中的客户的等待成本更低，这导致客户将获得更多收益，并且他们更倾向于加入灾难系统。