Abstract
We study an emerging computer network model of delayed observations in which the system is unobservable for the customers at their arrival instants, but after a while, they are informed about their current positions and they may renege. We develop a queueing-game-theoretic vacation model to explore customers’ equilibrium strategy, stationary system behavior and social welfare based on a reward-cost structure. Our main results are as follows. First, we determine a closed form of the customers’ equilibrium strategy, the expected net benefit of a customer and social welfare in the service system. Second, extensive numerical experiments that demonstrate the effect of vacation rate θ and system announcement rate δ on the equilibrium strategy and social welfare. We find that the impact of announcement rate δ is greater than vacation rate θ in some cases. Finally, we show that the equilibrium strategy can give customers more information and reduce the cost of waiting. Moreover, our results can also provide more precise information to the system administrators.
Highlights
The information asymmetry between customers and administrators is a very important element in most service systems
To study the equilibrium and social welfare on customer behavior in such systems, we aim to extend the aforementioned studies by considering a vacation queueing system with a delayed observations structure
We investigate the booming computer networks with vacation and delayed observations in a service system and explore its economic impact
Summary
The information asymmetry between customers and administrators is a very important element in most service systems. The study of delayed observations is essential and has attracted the attention in some burgeoning computer networks in recent years, which is the arriving customers decide whether to join or balk without knowing the state of the system, but after a while, the administrator of the system announces to customers of their current positions and they may renege. If the system is in the vacation state, the server does not handle any applications, but to check if the system is infected with virus and upgrade the system, and the system enters the working state if the system is nonempty Another example in practice of the proposed model occurs when the information-providing mechanism has to respect some periodicity of the mode of operation of the systems. To study the equilibrium and social welfare on customer behavior in such systems, we aim to extend the aforementioned studies by considering a vacation queueing system with a delayed observations structure.
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