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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

We consider a discrete-time system comprising a first-come-first-served queue, a non-preemptive server, and a scheduler that governs the assignment of tasks in the queue to the server. The server has an availability state that indicates, at…

Applications · Statistics 2021-01-15 Michael Lin , Richard J. La , Nuno C. Martins

We consider a one-dimensional stochastic reaction-diffusion generalizing the totally asymmetric simple exclusion process, and aiming at describing single lane roads with vehicles that can change speed. To each particle is associated a jump…

Statistical Mechanics · Physics 2011-09-09 Cyril Furtlehner , Jean-Marc Lasgouttes

A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routing choices) form a tree (in…

Probability · Mathematics 2014-03-28 Alexander Stolyar

We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and…

Probability · Mathematics 2018-01-19 Abhishek , Marko Boon , Onno Boxma , Rudesindo Núñez-Queija

We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools, mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing…

Probability · Mathematics 2015-03-17 Alexander L. Stolyar , Elena Yudovina

We consider a single-server system with service stations in each point of the circle. Customers arrive after exponential times at uniformly-distributed locations. The server moves at finite speed and adopts a greedy routing mechanism. It…

Probability · Mathematics 2018-09-10 Leonardo T. Rolla , Vladas Sidoravicius

We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the "averaged" Halfin-Whitt regime, which means…

Probability · Mathematics 2019-07-15 Ari Arapostathis , Anirban Das , Guodong Pang , Yi Zheng

In this paper, we consider systems that can be modelled by $M \mid M \mid n$ queues with heterogeneous servers and non informed customers. Considering any two servers: we show that the probability that the fastest server is busy is smaller…

Probability · Mathematics 2007-06-06 Fabricio Bandeira Cabral

In this paper we consider a single-server, cyclic polling system with switch-over times and Poisson arrivals. The service disciplines that are discussed, are exhaustive and gated service. The novel contribution of the present paper is that…

Probability · Mathematics 2014-08-04 Marko Boon

We analyze the latency or sojourn time L(m,n) for the last customer in a batch of n customers to exit from the m-th queue in a tandem of m queues in the setting where the queues are in equilibrium before the batch of customers arrives at…

Probability · Mathematics 2014-04-21 Jinho Baik , Raj Rao Nadakuditi

We consider a horizontal traffic queue (HTQ) on a periodic road segment, where vehicles arrive according to a spatio-temporal Poisson process, and depart after traveling a distance that is sampled independently and identically from a…

Dynamical Systems · Mathematics 2016-05-25 Mohammad Motie , Ketan Savla

We consider an M/M/N/K/FCFS system (N>0, K>=N), where the servers operate at (possibly) heterogeneous service rates. In this situation, the steady state behavior depends on the routing policy that is used to select which idle server serves…

Performance · Computer Science 2016-03-23 Sherwin Doroudi , Ragavendran Gopalakrishnan

We study a single-server Markovian queueing model with $N$ customer classes in which priority is given to the shortest queue. Under a critical load condition, we establish the diffusion limit of the workload and queue length processes in…

Probability · Mathematics 2018-10-26 Rami Atar , Asaf Cohen

We prove a many-server heavy-traffic fluid limit for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the…

Probability · Mathematics 2013-01-24 Ohad Perry , Ward Whitt

We study the heavy-traffic limit of the generalized switch operating under MaxWeight, without assuming that the CRP condition is satisfied and allowing for correlated arrivals. The main contribution of this paper is the steady-state mean of…

Probability · Mathematics 2021-03-03 D. Hurtado-Lange , S. T. Maguluri

Multi-server queueing systems are widely used models for job scheduling in machine learning, wireless networks, crowdsourcing, and healthcare systems. This paper considers a multi-server system with multiple servers and multiple types of…

Machine Learning · Computer Science 2023-06-05 Zixian Yang , R. Srikant , Lei Ying

In discrete time, customers arrive at random. Each waits until one of three servers is available; each thereafter departs at random. We seek the distribution of maximum line length of idle customers. Algebraic expressions obtained for the…

History and Overview · Mathematics 2022-08-30 Steven Finch

We prove that the scaled maximum steady-state waiting time and the scaled maximum steady-state queue length among $N$ $GI/GI/1$-queues in the $N$-server fork-join queue, converge to a normally distributed random variable as $N\to\infty$.…

Probability · Mathematics 2023-09-18 Dennis Schol , Maria Vlasiou , Bert Zwart

In this paper we study a two-queue polling model with zero switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$, $i=1,2$) in each queue. The arrival processes at the two queues are…

Probability · Mathematics 2019-02-20 Marko Boon , Erik Winands