Pooling is not the answer

This note studies practical and theoretical scenarios to improve a completely pooled or unpooled scenario for two server groups (e.g. call center groups) with short and long jobs (e.g. calls). First, simple overflow (reported earlier) scenarios and priority rules are compared. Next, threshold rules are investigated for further practical improvement. Finally, a threshold rule is sought for a strict improvement over pooling for both short and long jobs. The practical value is illustrated numerically and appears to be consistent also for larger server numbers. The results show:

(i) An overall average improvement by prioritizing short jobs.
(ii) A slight but strict improvement over pooling by prioritizing long jobs.

The first result is of practical interest; the second one is more theoretical. A practical scheme is provided for an ordering of scenarios, up to realistically large numbers of servers as in call centers.
Keywords: Pooling; Queueing; Overflow; Priority rule; Threshold rule