Abstract

Non-Markov-type queueing systems are often used as mathematical models in studying some practical engineering problems, such as communication networks. In this paper, we consider the problems of sensitivity analysis and estimates of the steady-state performance for an M/G/1 queueing system. By studying its embedded Markov chain, we give the sensitivity formulas expressed by the potentials of the embedded Markov chain. Based on the performance potential theory and these formulas, we propose an algorithm to compute system potentials and performance derivatives for M/G/1 queueing systems. This algorithm can be directly used in controlling and optimization problems since it is based on analyzing a single sample path of the system. A numerical example is provided to illustrate the application of the algorithm.

Keywords: M/G/1 queuing system; Performance potential; Sensitivity analysis; Sensitivity estimate; Simulation

Article Outline

1. Introduction

2. Sensitivity analysis of Markov chains

3. M/G/1 queueing systems

4. M/M/1 and M/C₂/1

4.1. The M/M/1 queue

4.2. The M/C₂/1 queue

5. Analysis of the simulation algorithm

6. An algorithm and an example

7. Conclusions

Acknowledgements

References

Vitae

Supported by the National Natural Science Foundation of China under Grant No. 60574065, Hi-Tech Research and Development Program of China under Grant No. 2005AA103320 and the Natural Science Foundation of Anhui Province under Grant No. 050420301.