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, the authors 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. 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 (Ek), generalized Erland (GEk) and hyperexponential (HEk).