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Related papers: On the $M_t/M_t/K_t+M_t$ queue in heavy traffic

200 papers

We consider the queuing networks, which are made from servers, exchanging their positions. The customers, using the network, try to reach their destinations, which is complicated by the movements of the servers, taking their customers with…

Probability · Mathematics 2013-11-18 François Baccelli , Alexandre Rybko , Senya Shlosman

This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The…

Probability · Mathematics 2013-03-28 Richard G. Clegg

In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…

In many important real-world queueing settings, arrival and service rates fluctuate over time. We consider the MAMS system, where the arrival and service rates each vary according to an arbitrary finite-state Markov chain, allowing…

Performance · Computer Science 2024-10-02 Isaac Grosof , Yige Hong , Mor Harchol-Balter

We study a multiclass M/M/1 queueing control problem with finite buffers under heavy-traffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions…

Probability · Mathematics 2019-03-19 Asaf Cohen

We consider a Markovian single server queue in which customers are preemptively scheduled by exogenously assigned priority levels. The novelty in our model is that the priority levels are randomly assigned from a continuous probability…

Probability · Mathematics 2017-01-09 Neal Master , Zhengyuan Zhou , Nicholas Bambos

We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…

Probability · Mathematics 2011-05-04 David Gamarnik , Alexander Stolyar

We consider $M/G/\infty$ queues with gated service and obtain results on the distribution of the stage length and the number of customers served in a stage when the system is stationary. The stage length density is expressed as an infinite…

Probability · Mathematics 2026-03-23 Dimitra Pinotsi , Michael A. Zazanis

Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they…

Dynamical Systems · Mathematics 2021-08-11 Philip Doldo , Jamol Pender , Richard Rand

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks…

Probability · Mathematics 2018-12-05 F. Baccelli , A. Rybko , S. Shlosman , A. Vladimirov

Motivated by timeouts in Internet services, we consider networks of infinite server queues in which routing decisions are based on deadlines. Specifically, at each node in the network, the total service time equals the minimum of several…

Performance · Computer Science 2016-09-20 Neal Master , Nicholas Bambos

Explicit and exact results are obtained for the joint queue-length distribution for the two-level non-preemptive Markovian priority queue. Marginal distributions are derived for the general multi-level problem. The results are based on a…

Probability · Mathematics 2023-12-08 Josef Zuk , David Kirszenblat

In this paper, we consider an $N$-queue overloaded polling network attended by a single cyclically roving server. Upon the completion of his service, a customer is either routed to another queue or leaves the system. All the switches are…

Probability · Mathematics 2017-01-17 Zaiming Liu , Yuejiao Wang , Yuqing Chu , Yingqiu Li

There are two contributions to the literature in this note. Firstly, we point out that under some weak conditions the result in Swensen (1986) on the remaining loads in a GI/M/$c$ queue with impatient customers, derived under the assumption…

Probability · Mathematics 2022-04-22 Anders Rygh Swensen

This paper serves as a companion to "Asymptotic Product-form Steady-state for Multiclass Queueing Networks with SBP Service Policies in Multi-scale Heavy Traffic." In this short paper, we illustrate the main results of the main paper…

Probability · Mathematics 2024-11-05 Jim Dai , Dongyan Huo

We consider the processor sharing $M/M/1$-PS queue which also models balking. A customer that arrives and sees $n$ others in the system "balks" (i.e., decides not to enter) with probability $1-b_n$. If $b_n$ is inversely proportional to…

Probability · Mathematics 2011-04-26 Qiang Zhen , Johan S. H. van Leeuwaarden , Charles Knessl

Consider the problem of a multiple access channel in a time dependent environment with a large number of users. In such a system, mostly due to practical constraints (e.g., decoding complexity), not all users can be scheduled together, and…

Information Theory · Computer Science 2018-11-07 Ori Shmuel , Asaf Cohen , Omer Gurewitz

We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks with state dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state…

Probability · Mathematics 2012-12-18 Chihoon Lee , Anatolii puhalskii

We consider exponential single server queues with state-dependent arrival and service rates which evolve under influences of external environments. The transitions of the queues are influenced by the environment's state and the movements of…

Probability · Mathematics 2023-07-19 Sonja Otten , Ruslan Krenzler , Hans Daduna , Karsten Kruse

In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction $p$ of an available resource is deployed in a centralized manner…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-03-23 Kuang Xu