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Delay Behaviour of Asynchronous Internet Router Under Self-Similar Traffic Input–Queueing System with Markovian Input and Hyper-Erlang Services


Affiliations
1 Department of Mathematics, Kakatiya University, Warangal – 506009 (T.S.), India
     

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In this paper, we analyze the delay behaviour of asynchronous Internet router under self-similar input traffic. Router is modelled as single server queueing system. Markov modulated Poisson process (MMPP) is employed to emulate self-similar Internet traffic and the same is used as input process of queueing system. The service times (packet lengths) is assumed to be follow Hyper-Erlang (HE(p,q)) distribution with p stages in parallel and q phases in series of service. Finally, Internet router is modelled as MMPP/HE(p,q)/1/K queueing system. The performance measure, namely, mean waiting time (MWT) is computed and presented graphically.

Keywords

Internet Router, Self-Similarity, Single-Server Queue, Hyper-Erlang Distribution, Mean Waiting Time.
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  • Delay Behaviour of Asynchronous Internet Router Under Self-Similar Traffic Input–Queueing System with Markovian Input and Hyper-Erlang Services

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Authors

Ravi Kumar Gudimalla
Department of Mathematics, Kakatiya University, Warangal – 506009 (T.S.), India
Malla Reddy Perati
Department of Mathematics, Kakatiya University, Warangal – 506009 (T.S.), India

Abstract


In this paper, we analyze the delay behaviour of asynchronous Internet router under self-similar input traffic. Router is modelled as single server queueing system. Markov modulated Poisson process (MMPP) is employed to emulate self-similar Internet traffic and the same is used as input process of queueing system. The service times (packet lengths) is assumed to be follow Hyper-Erlang (HE(p,q)) distribution with p stages in parallel and q phases in series of service. Finally, Internet router is modelled as MMPP/HE(p,q)/1/K queueing system. The performance measure, namely, mean waiting time (MWT) is computed and presented graphically.

Keywords


Internet Router, Self-Similarity, Single-Server Queue, Hyper-Erlang Distribution, Mean Waiting Time.

References