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

• Published in: European journal of operational research Vol. 218; no. 3; pp. 708 - 715
• Main Authors: Boudali, Olga, Economou, Antonis
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: Applied sciences; Balking; Catastrophes; Catastrophic failure analysis; Customers; Exact sciences and technology; Game theory; Markov analysis; Markov processes; Mathematics; Nash equilibrium strategies; Operational research; Operational research and scientific management; Operational research. Management science; Optimization; Poisson distribution; Probability and statistics; Probability theory and stochastic processes; Queueing; Queues; Queuing theory; Queuing theory. Traffic theory; Repair time; Sciences and techniques of general use; Servers; Social optimization; Strategy; Studies; Queueing; Catastrophes; Balking; Social optimization; Nash equilibrium strategies; Markov process; Nash strategy; Input output; Costs; Volatility; Clientele; Nash equilibrium; Disaster; Single server queue; Optimization; Consumer behavior; Optimal strategy; Game equilibrium; Reward; Repair; Queue
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2011.11.043

► 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. 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.