Performance and Reliability of Non-Markovian Heterogeneous Distributed Computing Systems

Jorge E. Pezoa, Member, IEEE, and Majeed M. Hayat, Senior Member, IEEE
IEEE T ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 23, NO. 7, JULY 2012

Abstract—
Average service time, quality-of-service (QoS), and service reliability associated with heterogeneous parallel and distributed computing systems (DCSs) are analytically characterized in a realistic setting for which tangible, stochastic communication delays are present with nonexponential distributions. The departure from the traditionally assumed exponential distributions for event times, such as task-execution times, communication arrival times and load-transfer delays, gives rise to a non-Markovian dynamical problem for which a novel age dependent, renewal-based distributed queuing model is developed. Numerical examples offered by the model shed light on the operational and system settings for which the Markovian setting, resulting from employing an exponential distribution assumption on the event times, yields inaccurate predictions. A key benefit of the model is that it offers a rigorous framework for devising optimal dynamic task reallocation (DTR) policies systematically in heterogeneous DCSs by optimally selecting the fraction of the excess loads that need to be exchanged among the servers, thereby controlling the degree of cooperative
processing in a DCSs. Key results on performance prediction and optimization of DCSs are validated using Monte-Carlo (MC) simulation as well as experiments on a distributed computing testbed. The scalability, in the number of servers, of the age-dependent model is studied and a linearly scalable analytical approximation is derived.

Index Terms—Renewal theory, non-Markovian processes, distributed queuing theory, reliability, distributed computing, load balancing.

1 INTRODUCTION

This paper is organized as follows: 
1) Section 2 state formally the problem tackled in this paper. 
2) Section 3 build the novel age-dependent renewal theory for the random service time of applications in a DCS, describe the scalability issues and derive analytical approximations for the service time of an application. 
3) Section 4 compare our age-dependent approach with our previous Markovian renewal-based solution with emphasis on DTR policies for minimal average service time, maximal QoS and maximal reliability. 
4) Section 5 gives our conclusions

2 PROBLEM DESCRIPTION

3 AGE-DEPENDENT QUEUING THEORY

4 RESULTS

4.1 Predicting Performance and Reliability in Non-Markovian Heterogeneous DCSs

5 CONCLUSIONS