Effect of polynomial intensity functions on cumulant derivation procedures

Recent investigations into the accuracy of cumulant derivation procedures for the transient analysis of state-dependent Markovian queueing networks have shown this approach to be sensitive to the polynomial representation of the intensity functions. In particular, cumulant-based procedures involve defining a partial differential equation that relates the polynomial intensity functions of the network to a truncated cumulant generating function, from which an approximating set of ordinary differential equations is generated. We study the effect of both the order and specification of these polynomial functions on the approximation of the low-order cumulants (moments) of the state-distribution of the network in this paper.