Strategic shield against external shocks in a Markovian queue with vulnerable server

Abstract

<p style='text-indent:20px;'>A threshold-type queue-length control strategy is proposed in the paper to investigate the influence of external shocks to a queueing system where customers are strategic and the server is vulnerable. An empty system is required to initiate service only when the number of waiting customers reaches a given threshold. External shocks occur according to a Poisson process, and once occur, the server breaks down and the customer being served is forced to leave the system. Arriving customers have to decide whether to join the system or not based on a reward-cost structure under different levels of information. The focus is on examining the equilibrium performance of the system under the interaction between the server's states and customers' joining decisions for different information levels. The equilibrium threshold in the observable queue and mixed joining probability in the unobservable queue are obtained. The optimal value of threshold <inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula> is discussed by taking strategic customer behavior and vulnerability of the server into consideration. These findings have important managerial implications on the evaluation of the shield threshold for the system with external attacks and unreliability factor, and also on optimal operation management of the system.</p>