M/G/1 Queueing system and its applications

Abstract

The M/G/1 and the M/G/1/K queueing systems are widely used to mathematically model a large number of real-life computer and networking applications. In this thesis, we compare the performances of the M/G/1 and the M/G/1/K queueing system, and show that the higher moments as well as the first two moments of the service time distribution may have a significant impact on the steady state probability distribution of the number of customers in the M/G/1 and the M/G/1/K queueing systems. That is, the expected number of customers in the system is perfectly determined by the first two moment of the service distributuion in the case of the M/G/1 queueig system. On the other hand, in the case of a finite capacity system such as the M/G/1/K queueing system the expected number of customers in the system depends not only on the first two momens of the service time distribution but also on the higher moments. Through numerical analysis we investigate the behavior of the expected number of customers in the M/G/1/K queueing system as the service time distribution is changed.