id: 06002504
dt: j
an: 06002504
au: Dong, Hailing; Hou, Zhenting; Jiang, Guochao
ti: The application of semi-Markov processes in $GI/M/1$ and $M/G/1$ queuing
    systems.
so: Chin. J. Eng. Math. 28, No. 3, 315-322 (2011).
py: 2011
pu: Editorial Board of Chinese Journal of Engineering Mathematics, Faculty of
    Science, Xi’an Jiaotong University, Xi’an
la: ZH
cc: 
ut: homogeneous denumerable semi-Markov processes; $GI/M/1$ queuing system;
    $M/G/1$ queuing system; backward equations; forward equations
ci: 
li: 
ab: Summary: In this paper, the backward equations and forward equations of
    homogeneous denumerable semi-Markov processes are used to study the
    instantaneous distribution of queue lengths of $GI/M/1$ and $M/G/1$
    queuing systems, respectively. For the $GI/M/1$ queuing system, the
    backward equations of the Laplace transform of the transition
    probability of its queue length are obtained. For the $M/GI/1$ queuing
    system, the forward equations of the Laplace transform of the
    transition probability of its queue length are obtained. These backward
    equations and forward equations, whose coefficient matrices are
    quasi-triangular matrices, can be easily solved by using the iterative
    method.
rv: