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.