Transient solutions for multi-server queues with finite buffers

Authors:
Winfried K. Grassmann;Javad Tavakoli
Affiliations:
Department of Computer Science, University of Saskatchewan, Saskatoon, Canada S7N 5C9;Department of Mathematics, Statistics & Physics, University of British Columbia Okanagan, Kelowna, Canada V1V 1V7
Venue:
Queueing Systems: Theory and Applications
Year:
2009

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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.