$MAP_1$, $MAP_2/G/1$ finite queues with service scheduling function dependent upon queue lengths

Doo Il Choi; Sang Min Lee

doi:10.4134/BKMS.2009.46.4.673

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2009; 46(4): 673-689

Printed July 1, 2009

https://doi.org/10.4134/BKMS.2009.46.4.673

$MAP_1$, $MAP_2/G/1$ finite queues with service scheduling function dependent upon queue lengths

Doo Il Choi and Sang Min Lee

Halla University and Platform Laboratory, KT

Abstract

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Abstract

We analyze $MAP_1$, $MAP_2/G/1$ finite queues with service scheduling function dependent upon queue lengths. The customers are classified into two types. The arrivals of customers are assumed to be the Markovian Arrival Processes (MAPs). The service order of customers in each buffer is determined by a service scheduling function dependent upon queue lengths. Methods of embedded Markov chain and supplementary variable give us information for queue length of two buffers. Finally, the performance measures such as loss probability and mean waiting time are derived. Some numerical examples also are given with applications in telecommunication networks.

Keywords: $MAP_1, MAP_2/G/1$, service scheduling function, loss, mean delay

MSC numbers: 60K25, 68M20, 98B22