2016/02/01 by Mariska Heemskerk, Heemskerk, Mariska, Johan S. H. van Leeuwaarden +4
Business, Management and Accounting · Decision Sciences · Mathematics · #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60K25
paper · pdf · doi:10.48550/arxiv.1602.00499
arxiv created 2016/02/01 · openalex publication_date 2016/02/01 · arxiv updated 2016/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate Λ from a given distribution every Δ time units, yielding an i.i.d. sequence of arrival rates Λ1,Λ2, …. Applying a martingale central limit theorem, we obtain a functional central limit theorem for the scaled queue length process. We proceed to large deviations and derive the logarithmic asymptotics of the queue length's tail probabilities. As it turns out, in a rapidly changing environment (i.e., Δ is small relative to Λ) the overdispersion of the arrival process hardly affects system behavior, whereas in a slowly changing random environment it is fundamentally different; this general finding applies to both the central limit and the large deviations regime. We extend our results to the setting where each arrival creates a job in multiple infinite-server queues.