Customers' joining behavior in an unobservable GI/Geo/m queue

<p style='text-indent:20px;'>This paper studies the equilibrium balking strategies of impatient customers in a discrete-time multi-server renewal input queue with identical servers. Arriving customers are unaware of the number of customers in the queue before making a decision whether to join or balk the queue. We model the decision-making process as a non-cooperative symmetric game and derive the Nash equilibrium mixed strategy and optimal social strategies. The stationary system-length distributions at different observation epochs under the equilibrium structure are obtained using the roots method. Finally, some numerical examples are presented to show the effect of the information level together with system parameters on the equilibrium and social behavior of impatient customers.</p>

Synchronized abandonment in discrete-time renewal input queues with vacations

<p style='text-indent:20px;'>We consider a discrete-time infinite buffer renewal input queue with multiple vacations and synchronized abandonment. Waiting customers get impatient during the server's vacation and decide whether to take service or abandon simultaneously at the vacation completion instants. Using the supplementary variable technique and difference operator method, we obtain an explicit expression to find the steady-state system-length distributions at pre-arrival, random, and outside observer's observation epochs. We provide the stochastic decomposition structure for the number of customers and discuss the various performance measures. With the help of numerical experiments, we show that the method formulated in this work is analytically elegant and computationally tractable. The results are appropriate for light-tailed inter-arrival distributions and can also be leveraged to find heavy-tailed inter-arrival distributions.</p>