Externalities in the M/G/1 queue: LCFS-PR versus FCFS

Royi Jacobovic*, Nikki Levering, Onno Boxma

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Consider a stable M/G/1 system in which, at time t= 0 , there are exactly n customers with residual service times equal to v1, v2, … , vn . In addition, assume that there is an extra customer c who arrives at time t= 0 and has a service requirement of x. The externalities which are created by c are equal to the total waiting time that others will save if her service requirement is reduced to zero. In this work, we study the joint distribution (parameterized by n, v1, v2, … , vn, x) of the externalities created by c when the underlying service distribution is either last-come, first-served with preemption or first-come, first-served. We start by proving a decomposition of the externalities under the above-mentioned service disciplines. Then, this decomposition is used to derive several other results regarding the externalities: moments, asymptotic approximations as x→ ∞ , asymptotics of the tail distribution, and a functional central limit theorem.

Original languageEnglish
Pages (from-to)239-267
Number of pages29
JournalQueueing Systems
Issue number3-4
StatePublished - Aug 2023
Externally publishedYes


FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek024.002.003


    • Externalities
    • FCFS
    • Gaussian approximation
    • Heavy-tailed distribution
    • LCFS-PR
    • M/G/1 queue


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