A formal proof for the insensitivity of simple bounds for finite multi-server non-exponential tandem queues based on monotonicity results

AbstractIn Van Dijk and Lamond (1985) and Van Dijk and Van der Wal (1986) simple and intuitively obvious bounds were provided for finite tandem queues with blocking in the exponential case. This technical note formally proves that these bounds are insensitive, that is remain valid in the non-exponential case, for multi-server disciplines. The proof is based on showing structured monotonicity results by means of Markov reward theory. This technique extends standard approaches for proving monotonicity results. It seems promising for further application