Asymptotic behaviour of the loss probability of the M/G/1/K and G/M/1/K queues

This paper investigates the asymptotic behaviour of the loss probability of the M / G/1/K and G/M/1/K queues as the buffer size increases. It is shown that the loss probability approaches its limiting value, which depends on the offered load, with an exponential decay in essentially all cases. The value of the decay rate can be easily computed from the main queue parameters. Moreover, the close relation existing between the loss behaviour of the two examined queueing systems is highlighted and a duality concept is introduced. Finally some numerical examples are given to illustrate on the usefulness of the asymptotic approximation. © 1992 J.C. Baltzer A.G. Scientific Publishing Company.