# Variance of Departure Process in Two-Node Tandem Queue with Unreliable Servers and Blocking

### Yang Woo Shin, Dug Hee Moon

#### Abstract

This paper provides an effective method for evaluating the second moments such as variance and covariance for the number of departures in two-node tandem queue with unreliable servers. The behavior of the system is described by a level dependent quasi-birth-and-death process and the output process is modeled by a Markovian arrival process. Algorithms for the transient behavior, the variance and covariance structure for the output process and the time to the nth departure are developed. We show that the results can be applied to derive approximate formulae for the due-date performance and the distribution of the number of outputs in a time interval.

#### References

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#### Paper Citation

#### in Harvard Style

Shin Y. and Moon D. (2017). **Variance of Departure Process in Two-Node Tandem Queue with Unreliable Servers and Blocking** . In *Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-218-9, pages 258-264. DOI: 10.5220/0006119302580264

#### in Bibtex Style

@conference{icores17,

author={Yang Woo Shin and Dug Hee Moon},

title={Variance of Departure Process in Two-Node Tandem Queue with Unreliable Servers and Blocking},

booktitle={Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2017},

pages={258-264},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006119302580264},

isbn={978-989-758-218-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Variance of Departure Process in Two-Node Tandem Queue with Unreliable Servers and Blocking

SN - 978-989-758-218-9

AU - Shin Y.

AU - Moon D.

PY - 2017

SP - 258

EP - 264

DO - 10.5220/0006119302580264