THE MACLAURIN SERIES FOR THE GI G 1 QUEUE

We derive the MacLaurin series for the moments of the system time and the delay with respect to the parameters in the service time or intera rrival time distributions in the GI/G/1 queue. The coefficients in the se series are expressed in terms of the derivatives of the interarriva l time density function evaluated at zero and the moments of the servi ce time distribution, which can be easily calculated through a simple recursive procedure. The light traffic derivatives can be obtained fro m these series. For the M/G/1 queue, we are able to recover the formul as for the moments of the system time and the delay, including the Pol laczek-Khinchin mean-value formula.