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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 consider a load balancing system comprised of a fixed number of single server queues, operating under the well-known Join-the-Shortest Queue policy, and where jobs/customers are impatient and abandon if they do not receive service after…

Probability · Mathematics 2023-04-05 Prakirt Raj Jhunjhunwala , Martin Zubeldia , Siva Theja Maguluri

Task replication has recently been advocated as a practical solution to reduce latencies in parallel systems. In addition to several convincing empirical studies, some others provide analytical results, yet under some strong assumptions…

Performance · Computer Science 2016-02-26 Felix Poloczek , Florin Ciucu

Max-algebra models of tandem single-server queueing systems with both finite and infinite buffers are developed. The dynamics of each system is described by a linear vector state equation similar to those in the conventional linear systems…

Numerical Analysis · Mathematics 2012-11-27 N. K. Krivulin

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

We consider a switch operating under the MaxWeight scheduling algorithm, under any traffic pattern such that all the ports are loaded. This system is interesting to study since the queue lengths exhibit a multi-dimensional state-space…

Probability · Mathematics 2015-06-11 Siva Theja Maguluri , R. Srikant

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

Let $P$ be the transition matrix of a finite, irreducible and reversible Markov chain. We say the continuous time Markov chain $X$ has transition matrix $P$ and speed $\lambda$ if it jumps at rate $\lambda$ according to the matrix $P$. Fix…

Probability · Mathematics 2015-06-26 Louigi Addario-Berry , Roberto I. Oliveira , Yuval Peres , Perla Sousi

We study the optimal provision of information for two natural performance measures of queuing systems: throughput and makespan. A set of parallel links is equipped with deterministic capacities and stochastic travel times where the latter…

Computer Science and Game Theory · Computer Science 2023-10-12 Svenja M. Griesbach , Max Klimm , Philipp Warode , Theresa Ziemke

In a batch of synchronized queues, customers can only be serviced all at once or not at all, implying that service remains idle if at least one queue is empty. We propose that a batch of $n$ synchronized queues in a discrete-time setting is…

Probability · Mathematics 2020-06-26 Richard Schoeffauer , Gerhard Wunder

We study the load balancing system operating under Join the Shortest Queue (JSQ) in the many-server heavy-traffic regime. If $N$ is the number of servers, we let the difference between the total service rate and the total arrival rate be…

Probability · Mathematics 2022-08-25 Daniela Hurtado-Lange , Siva Theja Maguluri

We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating…

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

Zero queueing delay is highly desirable in large-scale computing systems. Existing work has shown that it can be asymptotically achieved by using the celebrated Power-of-$d$-choices (pod) policy with a probe overhead $d =…

Performance · Computer Science 2020-11-03 Wentao Weng , Weina Wang

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this…

Probability · Mathematics 2017-03-07 Mariska Heemskerk , Julia Kuhn , Michel Mandjes

In general, obtaining the exact steady-state distribution of queue lengths is not feasible. Therefore, we establish bounds for the tail probabilities of queue lengths. Specifically, we examine queueing systems under Heavy-Traffic (HT)…

Probability · Mathematics 2023-06-21 Prakirt Raj Jhunjhunwala , Daniela Hurtado-Lange , Siva Theja Maguluri

We consider multi-component matching systems in heavy traffic consisting of $K\geq 2$ distinct perishable components which arrive randomly over time at high speed at the assemble-to-order station, and they wait in their respective queues…

Probability · Mathematics 2024-05-21 Bowen Xie

In this paper we analyze the average queue backlog in a combined input-output queued switch using a maximal size matching scheduling algorithm. We compare this average backlog to the average backlog achieved by an optimal switch. We model…

Networking and Internet Architecture · Computer Science 2007-05-23 Randy Cogill , Sanjay Lall

This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks in the quarter plane are characterized by the fact that the one-step transition probabilities…

Networking and Internet Architecture · Computer Science 2019-07-11 Ioannis Dimitriou

Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling…

Statistical Mechanics · Physics 2009-11-10 Meesoon Ha , Jussi Timonen , Marcel den Nijs