A functional law of the iterated logarithm for multi-class queues with batch arrivals

Yongjiang Guo (), Xiyang Hou () and Yunan Liu ()
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Yongjiang Guo: Beijing University of Posts and Telecommunications
Xiyang Hou: Huazhong University of Science and Technology
Yunan Liu: North Carolina State University

Annals of Operations Research, 2021, vol. 300, issue 1, No 3, 77 pages

Abstract: Abstract A functional law of the iterated logarithm (LIL) and its corresponding LIL are established for a multiclass single-server queue with first come first served (FCFS) service discipline. The functional LIL and its LIL quantify the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. The functional LIL and LIL are established in three cases: underloaded, critically loaded and overloaded, for performance measures including the total workload, idle time, queue length, workload, busy time, departure and sojourn time processes. The proofs of the functional LIL and LIL are based on a strong approximation approach, which approximates discrete performance processes with reflected Brownian motions. Numerical examples are considered to provide insights on these limit results.

Keywords: Functional law of the iterated logarithm; Law of the iterated logarithm; Multi-class queue; First come first served service discipline; Strong approximation; 60K25; 60F17; 60B10; 90B22 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10479-020-03864-6

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