Fluctuation Analysis in Parallel Queues with Hysteretic Control

Jewgeni H. Dshalalow (), Ahmed Merie () and Ryan T. White ()
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Jewgeni H. Dshalalow: Florida Institute of Technology
Ahmed Merie: Florida Institute of Technology
Ryan T. White: Florida Institute of Technology

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 1, 295-327

Abstract: 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.

Keywords: Single-server queue; Hysteresis; Bivariate fluctuations; Marked point processes; Semi-regenerative process; 60K10; 60K25; 60G51; 60G55; 60K05; 60G57 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09701-z

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