Requirements for an optimal service ordering policy

Lemma 3: An optimal policy is non-processor-sharing

Proof: Consider a portion of the sample path over which the server processes two jobs to completion
Three possibilities:

  1. serve job 1 then serve job 2
  2. serve job 2 then serve job 1
  3. serve both until one completes, then serve the other.
The expected revenue for (3) = q E(1) + (1-q) E(2)

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