8.1 Future directions

Future plans consists of extensions of the work presented in this dissertation, as well as exploration of new problems raised while developing our new modeling techniques and load balancing policies. In the following, we outline future research plans:

• D&C EM and D&C MM, proposed in Chapter 4, fit data sets into PH distributions in a divide and conquer fashion. The major differences between these two techniques are
  • the fitting algorithms used, i.e., D&C EM uses the EM algorithm and D&C MM uses the moment matching techniques
  • the criteria for partitioning the data set, i.e., D&C EM partitions the data in equally variable subsets and D&C MM partitions the data in subsets with equal expected value.
  We plan to work on a rigorous comparison between these two techniques and identify which are the benefits of using the available partitioning criteria and specific fitting algorithms. Based on such analysis, we intend to propose fitting techniques that are fast and accurate on capturing complex data characteristics.
• In addition to providing fitting techniques for data sets with complete and non-complete monotone CDHs, we will investigate the possibility of fitting multi-modal workloads into PH distributions. Evidence shows that such multi-modal workloads exist in communication systems.
• The ETAQA methodology, proposed in Chapter 5, presents an aggregation-based matrix-analytic technique for the solution of Markov processes with repetitive structure. We demonstrated via initial experimenting that ETAQA is numerically stable. We plan to further work in this direction and design numerical experiments that aim to the systematic evaluation of the numerical stability of matrix-analytic methods.
• Currently ETAQA provides solution for infinite Markov chains with repetitive structure. We plan to extend ETAQA for the solution of M/G/1/K-type processes, i.e., finite Markov chains with repetitive structure. With this extension, we aim to use ETAQA for the analysis of queueing systems with finite buffers, commonly encountered in computer systems.
• We will investigate the possibility of using the same aggregation technique as in ETAQA for the exact and/or approximate solution of queueing models with multiple job classes and/or multiple servers in the service center.
• We will modify ADAPTLOAD to also consider dynamic requests in the clustered Web server. We will evaluate different ways to assign requests of unknown sizes to servers of the cluster while maintaining high system performance.
• We plan to extend ADAPTLOAD to accommodate requests for different classes of service. Our objective is to evaluate if it is more beneficial to partition the servers of the cluster in dedicated subclusters for specific classes of requests, or differentiate service within a single server by allowing high priority requests to use more resources within the server than low priority requests.
• Currently the ADAPTLOAD algorithm is centralized, i.e., we collect all the information about the requests in the cluster in one single device (i.e., either dispatcher or a Web server). This device determines the ADAPTLOAD's parameters and distributes them to the servers of the cluster. We will propose a variation of ADAPTLOAD that allows distributed computation of its parameters, i.e., each server will exchange information only with its pre-determined neighbors and adapt its own size boundaries based on the workload seen by the server itself and its neighbors.