Two Sample-Path Inequalities For G/G/K Queues

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Abstract
Two sample-path results are obtained for the G/G/k-FIFS, queueing system. The first states an explicit upper bound on the difference between the work-loads of any two servers. This upper bounding variable is a Markov chain, remaining finite even for ρ ≥ 1, The second result establishes that k consecutive delays in the G/G/k-FIFS system may not be all larger than the corresponding delays in the associated G/G/A-cyclical assignment of servers (CAS).

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