A discrete-time queueing model with periodically scheduled arrival and departure slots
Performance Evaluation
On the application of Rouché's theorem in queueing theory
Operations Research Letters
Synchronized reneging in queueing systems with vacations
Queueing Systems: Theory and Applications
Model predictive control for the acquisition queue and related queueing networks
Proceedings of the 5th International Conference on Queueing Theory and Network Applications
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We propose a new queueing model named the acquisition queue. It differs from conventional queueing models in that the server not only serves customers, but also performs acquisition of new customers. The server has to divide its energy between both activities. The number of newly acquired customers is uncertain, and the effect of the server's acquisition efforts can only be seen after some fixed time period 驴 (delay). The acquisition queue constitutes a (驴+1)-dimensional Markov chain. The limiting queue length distribution is derived in terms of its probability generating function, and an exact expression for the mean queue length is given. For large values of 驴 the numerical procedures needed for calculating the mean queue length become computationally cumbersome. We therefore complement the exact expression with a fluid approximation. One of the key features of the acquisition queue is that the server performs more acquisition when the queue is small. Together with the delay, this causes the queue length process to show a strongly cyclic behavior. We propose and investigate several ways of planning the acquisition efforts. In particular, we propose an acquisition scheme that is designed specifically to reduce the cyclic behavior of the queue length process.