Strategic behavior in a vacation queue with delayed observations

¹ School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, P.R. China.
² Business School, Sun Yat-sen University, Guangzhou 510275, Guangdong, P.R. China.

^* Corresponding author: math_lzm@csu.edu.cn

Received: 7 August 2020
Accepted: 21 July 2021

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.