arXiv subjects

Eliran Sherzer

Publications and source records attributed to Eliran Sherzer.

9 recordsLinked to original sources

arXiv2026

A Learning-Based Superposition Operator for Non-Renewal Arrival Processes in Queueing Networks

The superposition of arrival processes is a fundamental yet analytically intractable operation in queueing networks when inputs are general non-renewal streams. Classical methods either reduce merged flows to renewal surrogates, rely on computationally prohibitive Markovian representations, or focus solely on mean-value performance measures. We propose a scalable data-driven superposition operator that maps low-order moments and autocorrelation descriptors of multiple arrival streams to those of their merged process. The operator is a deep learning model trained on synthetically generated Markovian Arrival Processes (MAPs), for which exact superposition is available, and learns a compact representation that accurately reconstructs the first five moments and short-range dependence structure of the aggregate stream. Extensive computational experiments demonstrate uniformly low prediction errors across heterogeneous variability and correlation regimes, substantially outperforming classical renewal-based approximations. When integrated with learning-based modules for departure-process and steady-state analysis, the proposed operator enables decomposition-based evaluation of feed-forward queueing networks with merging flows. The framework provides a scalable alternative to traditional analytical approaches while preserving higher-order variability and dependence information required for accurate distributional performance analysis.

cs.LG↗

arXiv2026

Supervised Learning for the (s,S) Inventory Model with General Interarrival Demands and General Lead Times

The continuous-review (s,S) inventory model is a cornerstone of stochastic inventory theory, yet its analysis becomes analytically intractable when dealing with non-Markovian systems. In such systems, evaluating long-run performance measures typically relies on costly simulation. This paper proposes a supervised learning framework via a neural network model for approximating stationary performance measures of (s,S) inventory systems with general distributions for the interarrival time between demands and lead times under lost sales. Simulations are first used to generate training labels, after which the neural network is trained. After training, the neural network provides almost instantaneous predictions of various metrics of the system, such as the stationary distribution of inventory levels, the expected cycle time, and the probability of lost sales. We find that using a small number of low-order moments of the distributions as input is sufficient to train the neural networks and to accurately capture the steady-state distribution. Extensive numerical experiments demonstrate high accuracy over a wide range of system parameters. As such, it effectively replaces repeated and costly simulation runs. Our framework is easily extendable to other inventory models, offering an efficient and fast alternative for analyzing complex stochastic systems.

cs.LG↗

arXiv2025

An Unconstrained Optimization Approach to Moment Fitting with Phase Type Distributions

Phase type (PH) distributions are widely used in modeling and simulation due to their generality and analytical properties. In such settings, it is often necessary to construct a PH distribution that aligns with real-world data by matching a set of prescribed moments. Existing approaches provide either exact closed-form solutions or iterative procedures that may yield exact or approximate results. However, these methods are limited to matching a small number of moments using PH distributions with a small number of phases, or are restricted to narrow subclasses within the PH family. We address the problem of approximately fitting a larger set of given moments using potentially large PH distributions. We introduce an optimization methodology that relies on a re-parametrization of the Markovian representation, formulated in a space that enables unconstrained optimization of the moment-matching objective. This reformulation allows us to scale to significantly larger PH distributions and capture higher moments. Results on a large and diverse set of moment targets show that the proposed method is, in the vast majority of cases, capable of fitting as many as 20 moments to PH distributions with as many as 100 phases, with small relative errors on the order of under 0.5% from each target. We further demonstrate an application of the optimization framework where we search for a PH distribution that conforms not only to a given set of moments but also to a given shape. Finally, we illustrate the practical utility of this approach through a queueing application, presenting a case study that examines the influence of the i^{th} moment of the inter-arrival and service time distributions on the steady-state probabilities of the GI/GI/1 queue length.

math.OC↗

arXiv2025

Analyzing homogenous and heterogeneous multi-server queues via neural networks

In this paper, we use a machine learning approach to predict the stationary distributions of the number of customers in a single-staiton multi server system. We consider two systems, the first is $c$ homogeneous servers, namely the $GI/GI/c$ queue. The second is a two-heterogeneous server system, namely the $GI/GI_i/2$ queue. We train a neural network for these queueing models, using the first four inter-arrival and service time moments. We demonstrate empirically that using the fifth moment and beyond does not increase accuracy. Compared to existing methods, we show that in terms of the stationary distribution and the mean value of the number of customers in a $GI/GI/c$ queue, we are state-of-the-art. Further, we are the only ones to predict the stationary distribution of the number of customers in the system in a $GI/GI_i/2$ queue. We conduct a thorough performance evaluation to assert that our model is accurate. In most cases, we demonstrate that our error is less than 5\%. Finally, we show that making inferences is very fast, where 5000 inferences can be made in parallel within a fraction of a second.

cs.PF↗

arXiv2024

Computing the steady-state probabilities of a tandem queueing system, a Machine Learning approach

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 that the arrival process for the first station is governed by a general renewal process, which implies that arrivals at subsequent stations will likely deviate from a renewal pattern. This study leverages neural networks (NNs) to approximate the steady-state distribution of the marginal number of customers at each station in the tandem queueing system, based on the external inter-arrival and service time distributions. Our approach involves decomposing each station and estimating the departure process by characterizing its first five moments and auto-correlation values, without limiting the analysis to linear or first-lag auto-correlation. We demonstrate that this method outperforms existing models, establishing it as state-of-the-art. Furthermore, we present a detailed analysis of the impact of the i^th moments of inter-arrival and service times on steady-state probabilities, showing that the first five moments are nearly sufficient to determine these probabilities. Similarly, we analyze the influence of inter-arrival auto-correlation, revealing that the first two lags of the first- and second-degree polynomial auto-correlation values almost completely determine the steady-state probabilities of a G/GI/1 queue.

math.PR↗

arXiv2024

Approximating G(t)/GI/1 queues with deep learning

In this paper, we apply a supervised machine-learning approach to solve a fundamental problem in queueing theory: estimating the transient distribution of the number in the system for a G(t)/GI/1. We develop a neural network mechanism that provides a fast and accurate predictor of these distributions for moderate horizon lengths and practical settings. It is based on using a Recurrent Neural Network (RNN) architecture based on the first several moments of the time-dependant inter-arrival and the stationary service time distributions; we call it the Moment-Based Recurrent Neural Network (RNN) method (MBRNN ). Our empirical study suggests MBRNN requires only the first four inter-arrival and service time moments. We use simulation to generate a substantial training dataset and present a thorough performance evaluation to examine the accuracy of our method using two different test sets. We show that even under the configuration with the worst performance errors, the mean number of customers over the entire timeline has an error of less than 3%. While simulation modeling can achieve high accuracy, the advantage of the MBRNN over simulation is runtime, while the MBRNN analyzes hundreds of systems within a fraction of a second. This paper focuses on a G(t)/GI/1; however, the MBRNN approach demonstrated here can be extended to other queueing systems, as the training data labeling is based on simulations (which can be applied to more complex systems) and the training is based on deep learning, which can capture very complex time sequence tasks. In summary, the MBRNN can potentially revolutionize our ability to perform transient analyses of queueing systems.

cs.LG↗

arXiv2022

Can machines solve general queueing systems?

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, general service times, one server). To the best of our knowledge, this is the first time a machine learning model is applied to a general queueing theory problem. We chose $M/G/1$ queue for this paper because it lies "on the cusp" of the analytical frontier: on the one hand exact solution for this model is available, which is both computationally and mathematically complex. On the other hand, the problem (specifically the service time distribution) is general. This allows us to compare the accuracy and efficiency of the deep learning approach to the analytical solutions. The two key challenges in applying machine learning to this problem are (1) generating a diverse set of training examples that provide a good representation of a "generic" positive-valued distribution, and (2) representations of the continuous distribution of service times as an input. We show how we overcome these challenges. Our results show that our model is indeed able to predict the stationary behavior of the $M/G/1$ queue extremely accurately: the average value of our metric over the entire test set is $0.0009$. Moreover, our machine learning model is very efficient, computing very accurate stationary distributions in a fraction of a second (an approach based on simulation modeling would take much longer to converge). We also present a case-study that mimics a real-life setting and shows that our approach is more robust and provides more accurate solutions compared to the existing methods. This shows the promise of extending our approach beyond the analytically solvable systems (e.g., $G/G/1$ or $G/G/c$).

cs.LG↗

arXiv2017

Customers' abandonment strategy in an M/G/1 queue

We consider an M/G/1 queue in which the customers, while waiting in line, may renege from it. We study the Nash equilibrium profile among customers, and show that it is defined by two sequences of thresholds. For each customer, the decision is based on the observed past (which determines from what sequence the threshold is taken), and the observed queue length (which determines the appropriate element in the chosen sequence). We construct the a of equations that has the Nash equilibrium as its solution, and discuss the relationships between the properties of the service time distribution and the properties of the Nash equilibrium, such as uniqueness and finiteness.

math.PR↗

arXiv2017

When to arrive at a queue with earliness, tardiness and waiting costs

We consider a queueing facility where customers decide when to arrive. All customers have the same desired arrival time (w.l.o.g.\ time zero). There is one server, and the service times are independent and exponentially distributed. The total number of customers that demand service is random, and follows the Poisson distribution. Each customer wishes to minimize the sum of three costs: earliness, tardiness and waiting. We assume that all three costs are linear with time and are defined as follows. Earliness is the time between arrival and time zero, if there is any. Tardiness is simply the time of entering service, if it is after time zero. Waiting time is the time from arrival until entering service. We focus on customers' rational behaviour, assuming that each customer wants to minimize his total cost, and in particular, we seek a symmetric Nash equilibrium strategy. We show that such a strategy is mixed, unless trivialities occur. We construct a set of equations that its solution provides the symmetric Nash equilibrium. The solution is a continuous distribution on the real line. We also compare the socially optimal solution (that is, the one that minimizes total cost across all customers) to the overall cost resulting from the Nash equilibrium.

math.OC↗