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Related papers: The Maximum Overlap Time in the M/M/1 Queue

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We consider a general queueing system with price-sensitive customers in which the service provider seeks to balance two objectives, maximizing the average revenue rate and minimizing the average queue length. Customers arrive according to a…

Data Structures and Algorithms · Computer Science 2025-12-09 Jacob Bergquist , Adam N. Elmachtoub

This paper proposes a novel max-pressure (MP) algorithm that incorporates pedestrian traffic into the MP control architecture. Pedestrians are modeled as being included in one of two groups: those walking on sidewalks and those queued at…

Systems and Control · Electrical Eng. & Systems 2024-09-26 Hao Liu , Vikash V. Gayah , Michael Levin

Single-server queues with customer abandonment arise in call centers and many service systems, but steady-state performance measures remain analytically intractable beyond Markovian assumptions. This paper develops Robust Queueing (RQ)…

Probability · Mathematics 2026-03-03 Wei You

We consider GI/Ph/n+M parallel-server systems with a renewal arrival process, a phase-type service time distribution, n homogenous servers, and an exponential patience time distribution with positive rate. We show that in the Halfin-Whitt…

Probability · Mathematics 2014-01-14 J. G. Dai , A. B. Dieker , Xuefeng Gao

We introduce and study a queue with the Erlang service system and whose arrivals are governed by a counting process in which there is a possibility of finitely many arrivals in an infinitesimal time interval. We call it the Erlang queue…

Probability · Mathematics 2025-01-16 R. B. Pote , K. K. Kataria

A result of Ward and Glynn (2005) asserts that the sequence of scaled offered waiting time processes of the $GI/GI/1+GI$ queue converges weakly to a reflected Ornstein-Uhlenbeck process (ROU) in the positive real line, as the traffic…

Probability · Mathematics 2019-08-23 Chihoon Lee , Amy R. Ward , Heng-Qing Ye

We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals…

Probability · Mathematics 2017-11-29 Onno Boxma , Sergey Foss , Jean-Marc Lasgouttes , Rudesindo Núñez Queija

We consider transmission of packets over queue-length sensitive unreliable links, where packets are randomly corrupted through a noisy channel whose transition probabilities are modulated by the queue-length. The goal is to characterize the…

Information Theory · Computer Science 2020-09-01 Daewon Seo , Avhishek Chatterjee , Lav R. Varshney

The tandem fluid queueing model is a useful tool for performance analysis and control design for a variety of transportation systems. In this article, we study the joint impact of stochastic capacity and spillback on the long-time…

Optimization and Control · Mathematics 2019-05-07 Li Jin , Saurabh Amin

We present upper and lower bounds for the tail distribution of the stationary waiting time $D$ in the stable $GI/GI/s$ FCFS queue. These bounds depend on the value of the traffic load $\rho$ which is the ratio of mean service and mean…

Probability · Mathematics 2013-03-20 Sergey Foss , Dmitry Korshunov

Load balancing plays a critical role in efficiently dispatching jobs in parallel-server systems such as cloud networks and data centers. A fundamental challenge in the design of load balancing algorithms is to achieve an optimal trade-off…

Performance · Computer Science 2020-12-16 Mark van der Boor , Sem Borst , Johan van Leeuwaarden

We consider a polling system where a group of an infinite number of servers visits sequentially a set of queues. When visited, each queue is attended for a random time. Arrivals at each queue follow a Poisson process, and service time of…

Probability · Mathematics 2014-04-23 Maria Vlasiou , Uri Yechiali

In the present work we study Bayesian nonparametric inference for the continuous-time M/G/1 queueing system. In the focus of the study is the unobservable service time distribution. We assume that the only available data of the system are…

Statistics Theory · Mathematics 2017-09-22 Cornelia Wichelhaus , Moritz von Rohrscheidt

We study the asymptotics of the stationary sojourn time Z of a "typical customer" in a tandem of single-server queues. It is shown that, in a certain "intermediate" region of light-tailed service time distributions, Z may take a large value…

Probability · Mathematics 2011-11-29 S. G. Foss

This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The…

Probability · Mathematics 2009-09-29 H. Christian Gromoll , Łukasz Kruk

We consider an $M/M/1$ queueing system with impatient customers with multiple and single vacations. It is assumed that customers are impatient whenever the state of the server. We derive the probability generating functions of the number of…

Probability · Mathematics 2016-04-12 Assia Boumahdaf

We consider a strategic M/M/1 queueing model under a first-come-first-served regime, where customers are split into two classes and class $A$ has priority over class $B$. Customers can decide whether to join the queue or balk, and, in case…

Computer Science and Game Theory · Computer Science 2025-02-11 Maurizio D'Andrea , Marco Scarsini

This paper addresses web object size which is one of important performance measures and affects to service time in multiple access environment. Since packets arrive according to Poission distribution and web service time has arbitrary…

Networking and Internet Architecture · Computer Science 2014-08-15 Y. -J. Lee

This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those…

Probability · Mathematics 2025-03-28 Jin Guang , Yaosheng Xu , J. G. Dai

We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting…

Probability · Mathematics 2020-09-01 Lun Yu , Ohad Perry