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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This research was supported by the Natural Sciences and Engineering Research Council of Canada. We also thank the referees for their useful comments.
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Grassmann, W.K., Tavakoli, J. Transient solutions for multi-server queues with finite buffers. Queueing Syst 62, 35–49 (2009). https://doi.org/10.1007/s11134-009-9113-1
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DOI: https://doi.org/10.1007/s11134-009-9113-1