$MAP_1$, $MAP_2/G/1$ finite queues with service scheduling function dependent upon queue lengths
Bull. Korean Math. Soc. 2009 Vol. 46, No. 4, 673-689
https://doi.org/10.4134/BKMS.2009.46.4.673
Printed July 1, 2009
Doo Il Choi and Sang Min Lee
Halla University and Platform Laboratory, KT
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
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