Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes

We consider a Markovian queue subject to Poisson generated catastrophes. Whenever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. We assume that the arriving customers decide whether to join the system or balk, based on a natural reward-cost structure. We study the balking behavior of the customers and derive the corresponding Nash equilibrium and social optimal strategies.

► A queueing system subject to catastrophes that remove all customers.
► Game-theoretic framework: Customers decide whether to join or balk.
► Novelty of the reward-cost structure: inclusion of a compensation for the customers that are forced to leave.
► Main results: Nash equilibrium and social optimal balking strategies in the observable and the unobservable cases.
► The value of the information: In most cases, informed selfish customers behave better than uninformed altruistic customers.