The acquisition queue

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 δ (delay). The acquisition queue constitutes a (δ + 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 δ 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 d...

• Type: Journal
• Year: 2007
• Where: QUESTA
• Authors: Dee Denteneer, J. S. H. van Leeuwaarden, Ivo J. B. F. Adan
• Keywords: Acquisition Queue, Mean Queue Length, QUESTA 2007, Queue Length