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.
Asymptotic behaviour of the loss probability of the M/G/1/K and G/M/1/K queues / Baiocchi, Andrea. - In: QUEUEING SYSTEMS. - ISSN 0257-0130. - 10:3(1992), pp. 235-248. [10.1007/BF01159208]
Asymptotic behaviour of the loss probability of the M/G/1/K and G/M/1/K queues
BAIOCCHI, Andrea
1992
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.