Upper bound for the decay rate of the joint queue-length distribution in a two-node Markovian queueing system
This paper studies the geometric decay property of the joint queue-length distribution {p(n(1), n(2))} of a two-node Markovian queueing system in the steady state. For arbitrarily given positive integers c(1), c(2), d(1) and d(2), an upper bound (eta) over bar (c(1), c(2)) of the decay rate is derived in the sense exp{lim sup n(n-->infinity)(-1) log p(c(1)n + d(1), c(2)n + d(2))}  (c(1), c(2)) takes one of eight types, and the types explain some curious properties reported in Fujimoto and Takahashi (J. Oper. Res. Soc. Jpn. 39:525-540 1996).
joint queue-length distribution geometric decay property markovian queueing network