Esa Hyytiä, D.Sc. (Tech.)

• Model:
  • Identical FCFS servers and i.i.d. distributed service times
  • Size-aware setting: service time of the new job and the backlogs are known
  • Objective is the minimize the mean response time
  
• Optimal actions:
  • Optimal actions can be derived numerically in the MDP framework.
  • Figure on the right illustrates the optimal dispatching actions for a two server system.
  • The green color means a job is routed to the shorter queue in the given state.
  • The red color means that a job will find itself in the longer queue!
• Observations:
  • Very short jobs are always assigned to the shorter queue (makes sense!)
  • The shorter queue is preferred also when the system is sufficiently empty (for all jobs)
  • The naïve greedy policy (LWL) would choose the shorter queue for every job, but that is not optimal!
  • Actions are very similar to those of the lookahead policy.

Move the mouse pointer over the figure to see how the optimal policy looks with different system parameters!