An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity

Kumar et al. consider the M/M/c/N+c feedback queue with constant retrial rate [1]. They provide a solution for the steady state probabilities based on the matrix-geometric method. We show that there exists a more efficient computation method to calculate the steady state probabilities when N+c$N+c$ is large. We prove that the number of zero-eigenvalues of the characteristic matrix polynomial associated with the balance equation is ⌊(N+c+2)/2⌋$\lfloor (N+c+2)/2\rfloor$. As consequence, the remaining eigenvalues inside the unit circle can be computed in a quick manner based on the Sturm sequences. Therefore, the steady state probabilities can be determined in an efficient way.