Equilibrium and social optimality in Markovian queues with catastrophes and N-policy

We study a stochastic clearing system with N-policy from a game-theoretic perspective where the server encounters Poisson-generated catastrophes. Catastrophes result in service interruptions and clear all customers from the system. To mitigate catastrophes impacts and operational costs, the N-policy is adopted to restart service only when the number of customers accumulated in the queue exceeds a predetermined threshold N. Strategic customers must decide whether to join the queue or not upon arrival based on their benefit function under different information levels. We first analyse customer's equilibrium threshold strategy in the observable cases and the mixed joining strategy in the unobservable cases, then obtain the service provider's profit and social welfare. Some numerical experiments are carried out to illustrate our theoretic results and it is found that adopting N-policy can improve both profit and social welfare. The jointly optimal threshold and entry fee are also discussed. We observe that disclosure of the queue length or server state may be detrimental to the service provider but can improve social welfare. Interestingly, we find that catastrophes may improve the customers' willingness to join the queue and social welfare in unobservable cases due to lower waiting cost. Our findings offer crucial insights for social managers in setting the optimal threshold N to adapt to changes in catastrophes frequency.