On exact computational analysis of distributions of numbers in systems for M/G/1/N + 1 and GI/M/1/N + 1 queues using roots

In this paper, we obtain the distribution of number in system and other measures of efficiency for the M/G/1/N + 1 queuing system in terms of the roots of the associated characteristic equation (CE). Results for the GI/M/1/N + 1 queuing system have also been obtained from those of M/G/1/N + 1. Numerical results in the form of tables and graphs have been presented for a variety of service-(interarrival-) time distributions, e.g. Erlang (E_k), generalized Erlang (GE_k) and hyperexponential (HE_k).