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Related papers: On Sojourn Times in the Finite Capacity $M/M/1$ Qu…

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We introduce a non-Markovian generalization of the classical M/M/1 queue by incorporating extended nonlocal time dynamics into Kolmogorov forward equations. We obtain the model by replacing the standard time derivative with an extended…

Methodology · Statistics 2026-02-03 Mehmet Sıddık Çadırcı

Efficient data access in High-Performance Computing (HPC) systems is essential to the performance of intensive computing tasks. Traditional optimizations of the I/O stack aim to improve peak performance but are often workload specific and…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-21 Thomas Collignon , Kouds Halitim , Raphaël Bleuse , Sophie Cerf , Bogdan Robu , Éric Rutten , Lionel Seinturier , Alexandre van Kempen

Recent studies indicate that in many situations service times are affected by the experienced queueing delay of the particular customer. This effect has been detected in different areas, such as health care, call centers and…

Probability · Mathematics 2025-04-25 Bernardo D'Auria , Ivo J. B. F. Adan , René Bekker , Vidyadhar Kulkarni

We consider a discrete population of users with homogeneous service demand who need to decide when to arrive to a system in which the service rate deteriorates linearly with the number of users in the system. The users have heterogeneous…

Computer Science and Game Theory · Computer Science 2016-05-30 Liron Ravner , Moshe Haviv , Hai L. Vu

This paper purpose is to investigate exponential behavior conditions for the infinite servers queue with Poisson arrivals busy period length distribution. It is presented a general theoretical result that is the basis of this work. The…

Probability · Mathematics 2021-09-30 Manuel Alberto M. Ferreira , José António Filipe

An exact formula for the equilibrium M/U/1 waiting time density is now effectively known. What began as a numeric exploration became a symbolic banquet. Inverse Laplace transforms provided breadcrumbs in the trail; delay differential…

Probability · Mathematics 2022-10-19 Steven Finch

We consider a tandem queue with coupled processors, which is subject to global breakdowns. When the network is in the operating mode and both queues are non empty, the total service capacity is shared among the stations according to fixed…

Probability · Mathematics 2019-03-08 Ioannis Dimitriou

Shared rides are often considered to be a promising travel alternative that could efficiently pool people together while offering a door-to-door service. Notwithstanding, even though demand distribution patterns are expected to greatly…

Physics and Society · Physics 2024-09-17 Jaime Soza-Parra , Rafał Kucharski , Oded Cats

We introduce a queueing system that alternates between two modes, so-called {\it working mode} and {\it vacation mode}. During the working mode the system runs as an $M^{X}/G/1$ queue. Once the number of customers in the working mode drops…

Probability · Mathematics 2021-10-12 Igor Kleiner , Esther Frostig , David Perry

We consider the $\Delta_{(i)}/G/1$ queue, in which a a total of $n$ customers independently demand service after an exponential time. We focus on the case of heavy-tailed service times, and assume that the tail of the service time…

Probability · Mathematics 2016-05-23 Gianmarco Bet , Remco van der Hofstad , Johan S. H. van Leeuwaarden

The Join-the-Shortest-Queue routing policy is studied in an asymptotic regime where the number of processors $n$ scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as $n\to \infty$, in…

Probability · Mathematics 2025-08-12 Amarjit Budhiraja , Eric Friedlander , Ruoyu Wu

In this paper, we investigate overlap times in a two-dimensional infinite server tandem queue. Specifically, we analyze the amount of time that a pair of customers spend overlapping in any station of the two dimensional tandem network. We…

Probability · Mathematics 2024-03-13 Ruici Gao , Jamol Pender

We investigate the long-run behavior of single-server queues with Hawkes arrivals and general service distributions and related optimization problems. In detail, utilizing novel coupling techniques, we establish finite moment bounds for the…

Probability · Mathematics 2023-11-14 Xinyun Chen , Guiyu Hong

A FORTRAN program to simulate the operation of infinite servers queues is presented in this work. Poisson arrivals processes are considered but not only. For many parameters of interest in queuing systems study or application, either there…

Performance · Computer Science 2021-10-20 Manuel Alberto M. Ferreira

We give a simple derivation of the distribution of the maximum L of the length of the queue during a busy period for the M/M/1 queue with lambda<1 the ratio between arrival rate and service rate. We observe that the asymptotic behavior of…

Probability · Mathematics 2011-06-21 Patrick Eschenfeldt , Ben Gross , Nicholas Pippenger

A two-class Processor-Sharing queue with one impatient class is studied. Local exponential decay rates for its stationary distribution (N, M) are established in the heavy traffic regime where the arrival rate of impatient customers grows…

Probability · Mathematics 2021-05-07 R. Nasri , F. Simatos , A. Simonian

Exact explicit results are derived for the distribution of the partial busy period of the M/M/c multi-server queue for a general number of servers. A rudimentary spectral method leads to a representation that is amenable to efficient…

Probability · Mathematics 2023-09-06 Josef Zuk , David Kirszenblat

Approximations for the mean performance indices for the M/G/c queue rely on the approximate computation of the probability that an arriving request has to wait for service and of the minimum of residual service times if all servers are…

Networking and Internet Architecture · Computer Science 2008-03-14 Thomas Begin , Alexandre Brandwajn

The problem of exact evaluation of the mean service cycle time in tandem systems of single-server queues with both infinite and finite buffers is considered. It is assumed that the interarrival and service times of customers form sequences…

Optimization and Control · Mathematics 2012-12-24 N. K. Krivulin , V. B. Nevzorov

We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate…

Probability · Mathematics 2017-02-08 H. Christian Gromoll , Bryce Terwilliger , Bert Zwart