Analysis of an N/G/1 finite queue with the supplementary variable method

In this paper, we suggest a new approach to the analysis of an N/G/1 finite queue with the supplementary variable method. Compared to the conventional approach, our approach yields a simpler formula for the queue length distribution, which in turn gives a more efficient computational algorithm. Also, the new approach enables us to derive the joint density of the queue length and the elapsed service time.

Supplementary variable method applied to the MAP/G/1 queueing system

In this paper we consider the MAP/G/1 queueing system with infinite capacity. In analysis, we use the supplementary variable method to derive the double transform of the queue length and the remaining service time of the customer in service (if any) in the steady state. As will be shown in this paper, our method is very simple and elegant. As a one-dimensional marginal transform of the double transform, we obtain the generating function of the queue length in the system for the MAP/G/1 queue, which is consistent with the known result.

Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations

This note introduces reliability issues to the analysis of queueing systems. We consider an M/G/1 queue with Bernoulli vacations and server breakdowns. The server uptimes are assumed to be exponential, and the server repair times are arbitrarily distributed. Using a supplementary variable method we obtain a transient solution for both queueing and reliability measures of interest. These results provide insight into the effect of server breakdowns and repairs on system performance.

Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations

This note introduces reliability issues to the analysis of queueing systems. We consider an M/G/1 queue with Bernoulli vacations and server breakdowns. The server uptimes are assumed to be exponential, and the server repair times are arbitrarily distributed. Using a supplementary variable method we obtain a transient solution for both queueing and reliability measures of interest. These results provide insight into the effect of server breakdowns and repairs on system performance.