IJPAM: Volume 2, No. 1 (2002)

CUSTOMER MOTION IN QUEUEING MODELS:
THE USE OF TANGENT VECTOR FIELDS

Dieter Baum$^1$, János Sztrik$^2$
$^1$University of Trier
Dept. IV, D-54286 Trier, GERMANY
e-mail: baum@uni-trier.de
$^2$Institute of Mathematics and Informatics
University of Debrecen
Debrecen, P.O.Box 12, H-4010, HUNGARY
e-mail: jsztrik@math.klte.hu


Abstract.Recently, no-waiting stations with spatial arrival process and arbitrary service time distribution have been analyzed [#!Baum2!#], [#!BaKa1!#]. Such stations represent adequate models of, for example, mobile communication networks based on code division multiple access (CDMA) techniques. Also, the inclusion of customer movements in space in such models has been performed. In [#!BaKa2!#], [#!BaKa3!#], movements were represented as group operations, which mapped a region ${\frk R}$ of interest into itself. In this paper we present a method to construct these group operations by means of velocity tangent vector fields. Field curves are to be interpreted as curves along which customers move. We show, how the varying behaviour of customers in space (e.g. calls in progress in a mobile communication network model) in a system fed by a spatial arrival process can be adequately described. Former results allow to compute the transient as well as equilibrium distribution of numbers of customers in any Borel subset of ${\frk R}$.

Received: January 8, 2002

AMS Subject Classification: 60K25, 60K30, 90B18

Key Words and Phrases: mobile communication, CDMA, tangent vector fields, spatial arrival processes, $SBMAP/G/\infty$ and $SMAPA/G/{\bf c}/{\bf c}$ models

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 1