The majority of jobs submitted to modern computing clusters and data centres are capable of running on a flexible number of computing cores or servers. We refer to such jobs as flexible multi-server jobs. Although allocating more servers to a job results in a higher speed-up in the job's execution, it reduces the number of servers available to future jobs. Furthermore, the speed-up obtained by a job is typically a concave, increasing function of the number of servers allocated to it. So a natural question in this setting is: how to optimally allocate servers to jobs such that average time a job spends in the system is minimised? This is the key question that we shall address in this talk by modelling the system as a loss system where jobs not finding any servers available upon entry are blocked. We shall discuss server allocation schemes which result in the minimum average sojourn time of accepted jobs while ensuring that the blocking probability of jobs vanishes as the system becomes large (i.e., all jobs are accepted in the limiting system). We shall consider settings with both linear and sub-linear speed-up functions. We shall also consider settings where the jobs have limited and full system access.
The talk will be based on joint works with Samira Ghanbarian (uWaterloo), Ravi R. Mazumdar (uWaterloo), and Fabrice Guillemin (Orange Labs, France).
Dr. Arpan Mukhopadhyay is currently an Assistant Professor in the Department of Computer Science at the University of Warwick, U.K. His research interests include applied probability, performance analysis of computer and communication networks, and distributed network algorithms. He has received Best Paper Awards at IFIP Performance 2015 and the International Teletraffic Congress (ITC) 2015. He was also awarded the Rising Scholar Award at the International Teletraffic Congress 2018 for his contributions to mean-field analysis of large heterogeneous networks.