Strategic behavior in a vacation queue with delayed observations

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.

An Unreliable Batch Arrival Retrial Queueing System With Bernoulli Vacation Schedule and Linear Repeated Attempts

This article deals with the steady-state behavior of an MX/G/1 retrial queue with the Bernoulli vacation schedule and unreliable server, under linear retrial policy. Breakdowns can occur randomly at any instant while the server is providing service to the customers. Further, the concept of Bernoulli admission mechanism is introduced. This model generalizes both the classical MX/G/1 retrial queue with unreliable server as well as the MX/G/1 retrial queue with the Bernoulli vacation model. The authors carry out an extensive analysis of this model. Namely, the embedded Markov chain, the stationary distribution of the number of units in the orbit, and the state of the server are studied. Some important performance measures and reliability indices of this model are obtained. Finally, numerical illustrations are provided and sensitivity analyses on some of the system parameters are conducted.