Functional law of the iterated logarithm for multi-server queues with batch arrivals and customer feedback

Yongjiang Guo (), Yunan Liu () and Renhu Pei
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Yongjiang Guo: Beijing University of Posts and Telecommunications
Yunan Liu: North Carolina State University
Renhu Pei: Beijing University of Posts and Telecommunications

Annals of Operations Research, 2018, vol. 264, issue 1, No 6, 157-191

Abstract: Abstract A functional law of the iterated logarithm (FLIL) and its corresponding law of the iterated logarithm (LIL) are established for a multi-server queue with batch arrivals and customer feedback. The FLIL and LIL, which quantify the magnitude of asymptotic fluctuations of the stochastic processes around their mean values, are developed in three cases: underloaded, critically loaded and overloaded, for five performance measures: queue length, workload, busy time, idle time and departure process. Both FLIL and LIL are proved using an approach based on strong approximations.

Keywords: Functional law of the iterated logarithm; Multi-server queue; Batch arrival; Customer feedback; Nonexponential service times; Strong approximation (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10479-017-2529-9

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