Lin and Ke consider the M/M/R queue with working vacation [Chuen-Horng Lin, Jau-Chuan Ke, Multi-server system with single working vacation, Appl. Math. Modell. (2008), doi:10.1016/j.apm.2008.10.006], and derive a computable explicit form for rate matrix R of the geometric approach and the stationary probabilities of the queue. However, it contains some errors concerning the terminology, notations and the final form of rate matrix R. This note shows that the classical Quasi-birth-death (QBD) formulation of the M/M/R queue with working vacation naturally leads to the infinitesimal generator matrix of the QBD process and the probability interpretation of matrices involving in the infinitesimal generator matrix. © 2009 Elsevier Inc. All rights reserved.
Do, T. V. (2009). Comments on “multi-server system with single working vacation.” Applied Mathematical Modelling, 33(12), 4435–4437. https://doi.org/10.1016/j.apm.2009.03.017