Abstract

This paper develops time-based rejuvenation policies to improve the performability measures of a cluster system. Three rejuvenation policies, namely standard rejuvenation, delayed rejuvenation and mixed rejuvenation, are designed to improve the cluster’s performability under varying workload. Analytic models are built to evaluate these three policies. Since deterministic transitions are used in this paper and analytical models based on homogeneous continuous-time Markov chains (CTMC) do not allow non-exponential distributions, we utilize deterministic and stochastic Petri nets (DSPN), in which the underlying stochastic process is a Markov regenerative process (MRGP), to capture both exponential and deterministic distributions. System performability measures under these three rejuvenation policies are derived based on the DSPN models. We show that the mixed rejuvenation policy achieves the maximum performability among the three policies, which results in 12% improvement on the system throughput in the example shown in this paper. The delayed rejuvenation is better than the standard rejuvenation with respect to the optimal job blocking probability and system throughput. For longer rejuvenation-triggering intervals, the standard rejuvenation yields a better result than delayed rejuvenation, while for shorter rejuvenation-triggering intervals the delayed rejuvenation policy outperforms standard rejuvenation policy.

Keywords: Clustered system; Performability; Software rejuvenation; Stochastic Petri net

Article Outline

1. Introduction

2. Rejuvenation policies for clustered systems

3. Rejuvenation model

3.1. Basic rejuvenation model

3.2. Introduction to Petri nets

3.3. Model description

Transition rates

3.4. Performability analysis

3.5. Stationary analysis of the DSPN

4. Numerical results

4.1. System availability

4.2. Blocking probability

4.3. Throughput

4.4. Influence of peak period duration

4.5. Influence of node MTTF

4.6. Influence of performance degradation

5. Conclusions

References

Vitae