EAI Endorsed Transactions on Internet of Things 15(2): e5

Research Article

Approximate Transient Analysis of Queuing Networks by Decomposition based on Time-Inhomogeneous Markov Arrival Processes

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  • @ARTICLE{10.4108/icst.valuetools.2014.258192,
        author={Andras Horvath and Alessio Angius},
        title={Approximate Transient Analysis of Queuing Networks by Decomposition based on Time-Inhomogeneous Markov Arrival Processes},
        journal={EAI Endorsed Transactions on Internet of Things},
        volume={15},
        number={2},
        publisher={EAI},
        journal_a={IOT},
        year={2015},
        month={2},
        keywords={queuing networks, markovian arrival processes, transient analysis, approximate analysis},
        doi={10.4108/icst.valuetools.2014.258192}
    }
    
  • Andras Horvath
    Alessio Angius
    Year: 2015
    Approximate Transient Analysis of Queuing Networks by Decomposition based on Time-Inhomogeneous Markov Arrival Processes
    IOT
    EAI
    DOI: 10.4108/icst.valuetools.2014.258192
Andras Horvath1,*, Alessio Angius1
  • 1: Dept. of Computer Science, University of Turin, Italy
*Contact email: horvath@di.unito.it

Abstract

We address the transient analysis of networks of queues with exponential service times. Such networks can easily have such a huge state space that their exact transient analysis is unfeasible. In this paper we propose an approximate transient analysis technique based on decomposing the queues of the network using a compact and approximate representation of the departure process of each queue. Namely, we apply time-inhomogeneous Markov arrival processes (IMAP) to describe the stream of clients leaving the queues. By doing so, the overall approximate model of the network is a time-inhomogeneous continuous time Markov chain (ICTMC) with significantly less number of states than there are in the original Markov chain. The proposed construction of the output IMAP of a queue is based on its transient state probabilities. We illustrate the approach first on a single M/M/1 queue and analyze the goodness of fitting of the departure process by numerical examples. Then we extend the approach to networks of queues and evaluate the precision of the resulting technique on several simple numerical examples by comparing the exact and the approximate transient probabilities of the queues.