Optimal performance of parallel-server systems with job size prediction errors

[EN] Modern communication networks integrate distributed computing architectures, in which customers are processed in parallel. We show how to minimize the waiting time of customer’s jobs by leveraging a simple threshold-based job dispatching policy. The optimal policy leverages the SITA routing, which assigns jobs to servers according to the size of the job. Moreover, the optimal policy permits to optimize system performance even when the job size is not known a priori and is estimated by means of error-prone predictors.The work of Josu Doncel has been supported by the Department of Education of the Basque Government through the Consolidated Research Group MATHMODE (IT1294-19), by the Marie Sklodowska-Curie grant agreement No 777778 and by the Spanish Ministry of Science and Innovation with reference PID2019-108111RB-I00 (FEDER/AEI). The work of Vincenzo Mancuso has been supported by the Ramon y Cajal grant RYC-2014-16285 from the Spanish Ministry of Economy and Competitiveness, and by the Region of Madrid through the TAPIR-CM program (S2018/TCS-4496)

Size-based routing to balance performance of the queues

\u3cp\u3eWe study a queueing system with a Poisson arrival process, in which a dispatcher sends the jobs to K homogeneous queues. The dispatcher knows the size of each job, and can implement a size-aware policy. Instead of trying to optimize system performance, we propose a Size Interval Task Assignment (SITA) policy that aims to equalize the performance (mean waiting times, or mean queue lengths) of all queues by allocating the jobs to the queues according to size. Such SITA routing requires no communication between the servers and the dispatcher, and is hence easily implemented. We study existence and uniqueness of the allocation thresholds. For FCFS and PS queues in heavy traffic, those thresholds coincide with those of a dispatching rule, SITA-E, in which loads are balanced. Preliminary numerical studies suggest that a SITA dispatching policy that equalizes performance is close to optimal when the difference between the size of the largest and the smallest job is small.\u3c/p\u3

Size-based routing to balance performance of the queues

We study a queueing system with a Poisson arrival process, in which a dispatcher sends the jobs to K homogeneous queues. The dispatcher knows the size of each job, and can implement a size-aware policy. Instead of trying to optimize system performance, we propose a Size Interval Task Assignment (SITA) policy that aims to equalize the performance (mean waiting times, or mean queue lengths) of all queues by allocating the jobs to the queues according to size. Such SITA routing requires no communication between the servers and the dispatcher, and is hence easily implemented. We study existence and uniqueness of the allocation thresholds. For FCFS and PS queues in heavy traffic, those thresholds coincide with those of a dispatching rule, SITA-E, in which loads are balanced. Preliminary numerical studies suggest that a SITA dispatching policy that equalizes performance is close to optimal when the difference between the size of the largest and the smallest job is small