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Fluctuation Analysis in Parallel Queues with Hysteretic Control

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Abstract

We study an enhanced hysteretic control system, with primary and secondary queues and random batch service. When the primary queue down-crosses r, the server operates on two parallel lines, servicing them asynchronously until the primary line of remaining units is processed or the number of serviced secondary units is at least S, whichever comes first. The server then waits until the primary queue length reaches N (if needed) before returning to primary service. The server capacity of primary units is limited by R with two options: r ≤ R ≤ N and R > N. Using fluctuation analysis we obtain closed-form distributions of available units during key periods of time and the steady state distribution of the primary queue. We illustrate analytical tractability by numerous analytical and computational examples.

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Acknowledgements

The authors are indebted to the anonymous referee for valuable suggestions and remarks that helped improve the paper.

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  1. Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, 32901, USA

    Jewgeni H. Dshalalow, Ahmed Merie & Ryan T. White

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  1. Jewgeni H. Dshalalow
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  2. Ahmed Merie
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  3. Ryan T. White
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Correspondence to Jewgeni H. Dshalalow.

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Dshalalow, J.H., Merie, A. & White, R.T. Fluctuation Analysis in Parallel Queues with Hysteretic Control. Methodol Comput Appl Probab 22, 295–327 (2020). https://doi.org/10.1007/s11009-019-09701-z

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