Equilibrium Analysis Of Repairable Fluid Queueing Systems

With the fast growth of the Internet users population,customers’ arrival and service of several queueing system are typically precessed at a much faster time-scale in comparison with changes in the server status.Such systems are modelled as the fluid queues,which have been used as the approximation of the queues with discrete units.In the fluid queue,customers are represented as continuous fluid that flows into and out of the buffer at a rate related to the state of the server(vacations,breakdowns and repairs etc.).At the same time,considering fluid queue from a strategic or economic viewpoint is also a hot topic in the field of queuing theory.It is also plausible to study the unreliable server due to the loss of service facilities in real life.Based on these,the objective of the paper is to study the equilibrium strategy of customers in the fluid queue with breakdowns and repairs.Firstly,the customers’ equilibrium behaviour and socially optimal threshold strategy for the fluid model with two types of parallel customers and an unreliable server is inves-tigated.The two types of customers are modelled as two independent fluids that enter the buffer at different arrival rates.The server is unreliable,and will stop working completely once it is faulty.Customers compete for the buffer share in order to maximize their utilities,the exponential utility function is used to compute the expected utilities of the tagged cus-tomer.It is assumed that all customers are risk neutral and have the right to decide whether to enter or not.Based on these characteristics,the equilibrium strategies are derived for the fully and partially observable cases.Secondly,the equilibrium threshold strategy for a fluid queue with congestion control and an unreliable server is introduced.A congestion control fluid queue in this paper refers to that when the buffer level exceeds the congestion control threshold,the input rate of the fluid will be reduced to alleviate the system congestion.Taking into account the server failures,once the breakdown occurs,the server stops working completely until it is repaired.Assuming that each customer makes decisions so as to optimize its own utility.Accordingly,the Nash equilibrium strategy and socially optimal threshold strategy are presented.Finally,the equilibrium balking strategies in the fluid queue with catastrophes is dis-cussed.The system is subject to catastrophes according to a Poisson process.Once a catas-trophe occurs,the system becomes invalid and all customers are forced to leave.Customers use a linear reward-cost structure to evaluate the utilities they obtained after receiving the service.In the fully observable case,customers are informed about the state of the system before making their decisions,then the Nash equilibrium balking strategies and the expected social benefit function per unit time are derived.