The effect of service time variability on maximum queue lengths in M^X/G/1 queues

2004/03/19 by Ger Koole, Koole, Ger, Misja Nuyens +3
Business, Management and Accounting · Computer Science · Decision Sciences · Mathematics · #60K25 #90B22 #Advanced Queuing Theory Analysis #FOS: Mathematics #Network Traffic and Congestion Control #Probability (math.PR) #Simulation Techniques and Applications #math.PR #msc:60K25 #msc:90B22

paper · pdf · doi:10.48550/arxiv.math/0403318

12 pages

openalex publication_date 2004/03/19 · arxiv created 2005/01/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M^X/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite buffer (M/G/1/n) systems. We show the somewhat surprising result that for three variations of the preemptive LCFS discipline, the maximum queue length during a busy period is smaller when service times are more variable (in the convex sense).

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