Analysis of a discrete-time queueing system with a single server and heterogeneous Markovian arrivals

Analysis of a discrete-time queueing system with a single server and heterogeneous Markovian arrivals

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Article ID: iaor20041331
Country: Netherlands
Volume: 42
Issue: 3
Start Page Number: 221
End Page Number: 237
Publication Date: Nov 2002
Journal: Queueing Systems
Authors: ,
Keywords: markov processes
Abstract:

We consider a discrete-time queueing system with a single deterministic server, heterogeneous Markovian arrivals and finite capacity. Most existing techniques model the queueing system using a direct bivariate Markov chain which requires a state space that grows rapidly as the number of customer types increases. In this paper, we define renewal cycles in terms of the input process and model the system occupancy level on each renewal cycle using a one-dimensional Markov chain. We derive the exact joint steady-state probability distribution of both states of input and system occupancy with a considerably reduced state space, which leads to the efficient calculation of overall/individual performance measures such as loss probability and average delay.

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