相关论文: Heavy traffic limit for a processor sharing queue …

Low delay is an explicit requirement for applications such as cloud gaming and video conferencing. Delay-based congestion control can achieve the same throughput but significantly smaller delay than loss-based one and is thus ideal for…

We consider a load balancing model where a Poisson stream of jobs arrive at a system of many servers whose service time distribution possesses a finite second moment. A small fraction of arrivals pass through the so called power-of-choice…

In this paper, we deal with an $D/GI/1$ vacation system with impatient customers. We give a sufficient condition for the existence of a limit distribution of the waiting time and integral equations are derived in both reneging and balking…

We present a heavy traffic analysis of a single-server polling model, with the special features of retrials and glue periods. The combination of these features in a polling model typically occurs in certain optical networking models, and in…

Time spent in processing zones at an airport are an important part of the passenger's airport experience. It undercuts the time spent in the rest of the airport, and therefore the revenue that could be generated from shopping and dining. It…

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…

We address a single server queue control problem (QCP) in heavy traffic originating from Lee and Weerasinghe (2011). The state process represents the offered waiting time, the customer arrival has a state-dependent intensity, and the…

In this paper, we consider five models of heavy-tailed queues involving Mittag-Leffler distributions that generalize the classical $M/M/1$ queues. These models are suitable modifications of previously defined models in such a way that the…

In this paper we consider a real time queuing system with rewards and deadlines. We assume that packet processing time is known upon arrival, as is the case in communication networks. This assumption allows us to demonstrate that the well…

We consider a GI/GI/1 queue with the shortest remaining processing time discipline (SRPT) and light-tailed service times. Our interest is focused on the tail behavior of the sojourn-time distribution. We obtain a general expression for its…

Contrary to the conclusions of a recent body of work where approximate shortest remaining processing time first (SRPT) flow scheduling is advocated for datacenter networks, this paper aims to demonstrate that per-flow fairness remains a…

In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system…

We consider processing networks where multiple dispatchers are connected to single-server queues by a bipartite compatibility graph, modeling constraints that are common in data centers and cloud networks due to geographic reasons or data…

The busy period length distribution function knowledge is important for any queue system, and for the MGINF queue. But the mathematical expressions are in general very complicated, with a few exceptions, involving usually infinite sums and…

Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…

We study the convergence of the $M/G/1$ processor-sharing, queue length process in the heavy traffic regime, in the finite variance case. To do so, we combine results pertaining to L\'{e}vy processes, branching processes and queuing theory.…

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…

A "scheduled" arrival process is one in which the n th arrival is scheduled for time n, but instead occurs at a different time. The difference between the scheduled time and the arrival time is called the perturbation. The sequence of…

We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends…

In this paper, we analyze how well a machine can solve a general problem in queueing theory. To answer this question, we use a deep learning model to predict the stationary queue-length distribution of an $M/G/1$ queue (Poisson arrivals,…