On one problem of load balancing in two-phase tandem queues

Consideration is given to the dispatching system with a single dispatcher without a queue for storing incoming jobs. There is a finite number of infinite capacity queues running in parallel, each having a single server for serving jobs one-by-one in FIFO (first in, first out) manner. It is assumed that the dispatcher has perfect information about the system upon making a routing decision about the arrived job. Once the decision is made, it is irrevocable but is executed by the job with a random delay. The system is modeled by a two-phase tandem queue, with an infinite-server queue at the first phase and a fixed number of single-server queues at the second phase. The method to construct simple dispatching policies by mixing is proposed, which can result in robust rules, having better performance than conventional static and dynamic policies. Simulations show significant reductions in mean response times (as well as its percentiles) in large-scale systems.