On the distribution of the number of customers in the symmetric M/G/1 queue
Queueing Systems: Theory and Applications
On Kelly networks with shuffling
Queueing Systems: Theory and Applications
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We settle a conjecture of Kella et al. (J. Appl. Probab. 42:223---234, 2005): the distribution of the number of jobs in the system of a symmetric M/G/1 queue at a fixed time is independent of the service discipline if the system starts empty. Our derivations are based on a time-reversal argument for regenerative processes and a connection with a clearing model.