Related papers: Scaling limits for some Mittag-Leffler queues
Recently, Atar and Miyazawa [2] introduced a multi-level GI/G/1 queue with a finite number of levels, where both the arrival and service rates depend on the level corresponding to the current queue length. For this model, they proved that…
In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a…
Service systems like data centers and ride-hailing are popularly modeled as queueing systems in the literature. Such systems are primarily studied in the steady state due to their analytical tractability. However, almost all applications in…
This study proposes a generalised macroscopic traffic simulation using a Mt/D/1/K queue to model congestion, using the Enniskillen to Belfast route as a case study. Empirical traffic data from Google's Directions API is used to calibrate…
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,…
We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M^X/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer…
We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the $\Delta_{(i)}/G/1$ queue, the customers decide…
A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…
In queueing systems, effective scheduling algorithms are essential for optimizing performance. Optimal scheduling for the M/G/k queue has been explored in the heavy traffic limit, but much remains unknown in the intermediate load regime. In…
In this paper, we display methods for the computation of convergence and perturbation bounds for $M_t/M_t/1$ system with balking, catastrophes, server failures and repairs. Based on the logarithmic norm of linear operators, the bounds on…
The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…
We consider the $\Delta_{(i)}/G/1$ queue, in which a a total of $n$ customers independently demand service after an exponential time. We focus on the case of heavy-tailed service times, and assume that the tail of the service time…
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.…
We introduce a framework and develop a theory of transitory queueing models. These are models that are not only non-stationary and time-varying but also have other features such as the queueing system operates over finite time, or only a…
In this paper, we analyze the steady state maximum overlap time in the M/M/1 queue. We derive the maximum overlap time tail distribution, its moments and the moment generating function. We also analyze the steady state minimum overlap time…
Large language models (LLMs) propel the prosperity of interactive AI applications showcased by ChatGPT that demand timely response of inference services. However, LLM inference is computation intensive and memory intensive, and improper…
We consider optimizing average queueing delay and average power consumption in a nonpreemptive multi-class M/G/1 queue with dynamic power control that affects instantaneous service rates. Four problems are studied: (1) satisfying per-class…
This paper studies the asymptotic behavior of the steady-state waiting time, W_infty, of the M/G/1 queue with subexponenential processing times for different combinations of traffic intensities and overflow levels. In particular, we provide…
We say that a random variable is $light$-$tailed$ if moments of order $2+\epsilon$ are finite for some $\epsilon>0$; otherwise, we say that it is $heavy$-$tailed$. We study queueing networks that operate under the Max-Weight scheduling…
In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service…