Abstract:
Nowadays, datacenters consist of many servers, usually identical, and serve multiple classes of requests (jobs) coming from the users. Jobs differ by their frequency of arrival, their demand for resources, and their service time. These could originate problems, especially in heavily loaded datacenters, where they must face the problem of defining a queuing policy for those incoming jobs. First-Come First-Served (FCFS) discipline is widely used but may produce an under-utilization problem of the resources, or in other words, some servers could potentially be wasted. Namely, a job that requires many processors can block the service of younger jobs that could be served because they require fewer resources. In the literature, the classical model for studying this problem is known as the Multiservers Job Queueing Model (MJQM). However, at the state of the art, very little is known about this model, especially because of the waste of resources that depends on the granularity of the job demands. This granularity of the incoming jobs also plays a part in some possible bottlenecks that hinder the overall system performance. In this thesis, we propose a simulation model for the MJQM and study both the idle and busy periods of the servers. Moreover, we propose, for the first time, a solution of the model for two classes of customers based on the matrix geometrics method. Our findings hold significant relevance for the analysis of performance and energy consumption within large datacenters dealing with heterogeneous incoming traffic. These results offer valuable insights into how the behavior of queueing lines influences server utilization and overall system performance. By enhancing our comprehension of these dynamics, datacenters can optimize resource allocation and identify areas requiring improvement, ultimately leading to more efficient management of such complex systems.
