Abstract

In studying or designing parallel and distributed systems one should have available a robust analytical model that includes the major parameters that determine the system performance. Jackson networks have been very successful in modeling computer systems. However, the ability of Jackson networks to predict performance with system changes remains an open question, since they do not apply to systems where there are population size constraints. Also, the product-form solution of Jackson networks assumes steady-state and exponential service centers or certain specialized queueing discipline. In this paper, we present a transient model for Jackson networks that is applicable to any population size and any finite workload (no new arrivals). Using several non-exponential distributions we show to what extent the exponential distribution can be used to approximate other distributions and transient systems with finite workloads. When the number of tasks to be executed is large enough, the model approaches the product-form solution (steady-state solution). We also, study the case where the non-exponential servers have queueing (Jackson networks cannot be applied). Finally, we show how to use the model to analyze the performance of parallel and distributed systems.

Keywords: Analytical modeling; Performance prediction; Queueing models; Jackson networks and transient analysis

Article Outline

1. Introduction

2. Background

3. Theoretical background

3.1. Definitions

3.2. Matrix representation of distribution functions

4. The transient model

4.1. Case 1 (N = K)

4.2. Case 2 (N > K)

5. Modeling parallel and distributed systems

5.1. Application model

5.2. System model

5.3. Task activity

5.4. Modeling a central cluster

5.4.1. Erlangian distributions

5.4.2. Hyperexponential distributions

5.5. Modeling a distributed storage cluster

6. Results

6.1. Shared servers with non-exponential service times

6.1.1. Performance behavior

6.1.2. Steady state

6.1.3. Performance prediction

6.1.4. Speedup

6.2. Dedicated servers with non-exponential service times

6.2.1. Performance behavior

6.2.2. Performance prediction

6.2.3. Speedup

7. Conclusion

References

Vitae