Related papers: Can machines solve general queueing systems?
We consider a general queueing system with price-sensitive customers in which the service provider seeks to balance two objectives, maximizing the average revenue rate and minimizing the average queue length. Customers arrive according to a…
It is well known that building analytical performance models in practice is difficult because it requires a considerable degree of proficiency in the underlying mathematics. In this paper, we propose a machine-learning approach to derive…
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…
Tandem queueing networks are widely used to model systems where services are provided in sequential stages. In this study, we assume that each station in the tandem system operates under a general renewal process. Additionally, we assume…
Ensuring the conformance of a service system's end-to-end delay to service level agreement (SLA) constraints is a challenging task that requires statistical measures beyond the average delay. In this paper, we study the real-time prediction…
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 propose a generalization of the classical M/M/1 queue process. The resulting model is derived by applying fractional derivative operators to a system of difference-differential equations. This generalization includes both non-Markovian…
Diffusion approximations are widely used in the analysis of service systems, providing tractable insights into complex models. While heavy-traffic limit theorems justify these approximations asymptotically, they do not quantify the error…
We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…
The application of the max-algebra to describe queueing systems by both linear scalar and vector equations is discussed. It is shown that these equations may be handled using ordinary algebraic manipulations. Examples of solving the…
Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where…
A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a…
We introduce the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues with general interarrival time and service time distributions. Our algorithm is built on the classical dominated coupling…
We study the MAP/M/s+G queuing model with MAP (Markovian Arrival Process) arrivals, exponentially distributed service times, infinite waiting room, and generally distributed patience times. Using sample-path arguments, we propose to obtain…
Machine learning can help us in solving problems in the context big data analysis and classification, as well as in playing complex games such as Go. But can it also be used to find novel protocols and algorithms for applications such as…
Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…
Recent advances in Machine Learning (ML) have shown a great potential to build data-driven solutions for a plethora of network-related problems. In this context, building fast and accurate network models is essential to achieve functional…
A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a…
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…
In this work, nonparametric statistical inference is provided for the continuous-time M/G/1 queueing model from a Bayesian point of view. The inference is based on observations of the inter-arrival and service times. Beside other…