Transient solutions for multi-server queues with finite buffers

Transient solutions for multi-server queues with finite buffers

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Article ID: iaor200971395
Country: Netherlands
Volume: 62
Issue: 1
Start Page Number: 35
End Page Number: 49
Publication Date: Jun 2009
Journal: Queueing Systems
Authors: ,
Keywords: M/M/c queues
Abstract:

Transient solutions for M/M/c queues are important for staffing call centers, police stations, hospitals and similar institutions. In this paper we show how to find transient solutions for M/M/c queues with finite buffers by using eigenvalues and eigenvectors. To find the eigenvalues, we create a system of difference equations where the coefficients depend on a parameter x. These difference equations allow us to search for all eigenvalues by changing x. To facilitate the search, we use Sturm sequences for locating the eigenvalues. We also show that the resulting method is numerically stable.

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