Abstract
Transient solutions for M/M/c queues are important for many purposes, in particular for staffing facilities such as call centers. In this article, we show how to use spectral analysis to find such solutions. The difficulty is that unless the number in line is bounded, one has to deal with matrices of infinite size, and hence with a countable infinite number of eigenvalues. This problem can be overcome by noting that the spectrum is dense with few exceptions. We also show how many discrete eigenvalues remain. Our theory may also work to obtain spectra for other infinite-dimensional matrices. Numerical properties of our approach are explored.
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