Analysis and Cost Optimization of the M/G/1 Queue Under the D-Policy and LCFS Discipline

Abstract

We deal with the M/G/1 queues under the D-policy and last-come-first-served (LCFS) disciplines. We first derive the queue length and waiting time distributions in the form of probability generating functions and the Laplace–Stieltjes transforms. Then we derive the mean performance measures. Finally, we obtain the optimal values of D under a linear cost function.

Keywords:

• D-policy
• LCFS
• Optimization

Mathematics Subject Classification:

• 60K25

Acknowledgments

This work was supported by Faculty Research Fund, Sungkyunkwan University, 2005.

The authors are thankful to the anonymous referee for helpful comments; they have greatly enhanced the readability of this article.

The first and the third authors are involved in the second phase of the BK-21 (Brain Korea) program funded by the Korean government (MOEHRD).