IJPAM: Volume 40, No. 2 (2007)

EXPLICIT DELAY DISTRIBUTION IN FIRST-COME
FIRST-SERVED M/M/m/K AND M/M/m/K/n
QUEUES AND A MIXED LOSS-DELAY SYSTEM

Hideaki Takagi
Graduate School of Systems and Information Engineering
University of Tsukuba
1-1-1 Tennoudai, Tsukuba-Shi, Ibaraki, 305-8573 JAPAN
e-mail: takagi@sk.tsukuba.ac.jp


Abstract.The distribution function for the delay (waiting time plus service time) of an arbitrary accepted customer is derived explicitly for M/M/$ m $/$ K $ and M/M/$ m $/$ K $/$ n $ queues with first-come, first-served discipline. The distribution function is needed for calculating percentiles as quality of service. The moments of distribution are also given explicitly. We also study a mixed loss-delay system similarly.

Received: July 6, 2007

AMS Subject Classification: 60K25

Key Words and Phrases: queue, M/M/$ m $/$ K $, M/M/$ m $/$ K $/$ n $, loss-delay system

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 2