Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 301-310
doi:10.1155/S1048953398000252

Moment estimation of customer loss rates from transactional data

D. J. Daley1 and L. D. Servi2

1Australian National University, School of Mathematical Sciences, ACT, Canberra 0200 , Australia
2GTE Laboratories Incorporated, 40 Sylvan Road, Waltham 02254, MA, USA

Received 1 October 1997

Copyright © 1998 D. J. Daley and L. D. Servi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Moment estimators are proposed for the arrival and customer loss rates of a many-server queueing system with a Poisson arrival process with customer loss via balking or reneging. These estimators are based on the lengths {Sj1} of the initial inter-departure intervals of the busy periods j=1,…,M observed in a dataset consisting of service starting and finishing times and encompassing both busy and idle periods of the process, and whether those busy periods are of length 1 or >1. The estimators are compared with maximum likelihood and parametric model-based estimators found previously.