Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 814740, 14 pages
doi:10.1155/2008/814740
Research Article
An Erlang Loss Queue with Time-Phased Batch Arrivals as a Model for Traffic Control in Communication Networks
1Institute of Information and Communication, Chonbuk National University, Chonju 561-765, South Korea
2Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk 220030, Belarus
Received 16 June 2008; Revised 16 October 2008; Accepted 9 December 2008
Academic Editor: Oded Gottlieb
Copyright © 2008 Moon Ho Lee and Sergey A. Dudin. 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
A multiserver queueing model that does not have a buffer but has batch arrival of customers is considered. In contrast to the standard batch arrival, in which the entire batch arrives at the system during a single epoch, we assume that the customers of a batch (flow) arrive individually in exponentially distributed times. The service time is exponentially distributed. Flows arrive according to a stationary Poisson arrival process. The flow size distribution is geometric. The number of flows that can be simultaneously admitted to the system is under control. The loss of any customer from an admitted flow, with a fixed probability, implies termination of the flow arrival. Analysis of the sojourn time and loss probability of an arbitrary
flow is performed.