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We derive some asymptotic results for the rate of convergence to equilibrium for the number of busy servers in an M/M/N/N queue with input rate λN and service rate 1 for N → ∞ in the ‘subcritical’ case λ ∈]0, 1[. These results improve recent contributions of Fricker, Robert and Tibi.

The classical one-compartment model with no input or pure death process is shown to be a limiting case of a ‘binomial cascade' model which has the same mean and in which particles exit the compartment in binomial clusters. The transition probabilities of the binomial cascade process are derived in closed form. The model is easily modified to allow Poisson input into the compartment. Distributional results are given for this model also. In particular, it is shown that the M/M/∞ queue is a limiting case.

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On the severity of M/M/∞ congested episodes

A note on the rate of convergence to equilibrium for Erlang's model in the subcritical case

A note on a one-compartment model with clustering

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3 results

On the severity of M/M/∞ congested episodes

A note on the rate of convergence to equilibrium for Erlang's model in the subcritical case

A note on a one-compartment model with clustering