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

Royi Jacobovic (), Nikki Levering () and Onno Boxma ()
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Royi Jacobovic: University of Amsterdam
Nikki Levering: University of Amsterdam
Onno Boxma: Eindhoven University of Technology

Queueing Systems: Theory and Applications, 2023, vol. 104, issue 3, No 6, 239-267

Abstract: Abstract Consider a stable M/G/1 system in which, at time $$t=0$$ t = 0 , there are exactly n customers with residual service times equal to $$v_1,v_2,\ldots ,v_n$$ v 1 , v 2 , … , v n . In addition, assume that there is an extra customer c who arrives at time $$t=0$$ 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 $$n,v_1,v_2,\ldots ,v_n,x$$ n , v 1 , v 2 , … , v n , 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 $$x\rightarrow \infty $$ x → ∞ , asymptotics of the tail distribution, and a functional central limit theorem.

Keywords: Externalities; M/G/1 queue; LCFS-PR; FCFS; Heavy-tailed distribution; Gaussian approximation; 60K25; 60K30; 60K37 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-023-09878-8

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