Infinite server queues in a random fast oscillatory environment

2020/04/10 by Harsha Honnappa, Yiran Liu, Honnappa, Harsha +5
Business, Management and Accounting · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2004.05034

openalex publication_date 2020/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a G_t/G_t/∞ infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluctuating stochastic process, which arguably takes into account some small time scale variations often observed in practice. We show a homogenization property for this system, which yields an approximation by a M_t/G_t/∞ queue with modified parameters. Our limiting results include the description of the number of active servers, the total accumulated input and the solution of the storage equation. Hence in the fast oscillatory context under consideration, we show how the queuing system in a random environment can be approximated by a more classical Markovian system.

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