EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Loss systems in a random environment

We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove an if-and-only-if-condition for a product form steady state distribution of the joint queueing-environment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, e.g. from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, e.g. of queueing-inventory processes. We investigate further classical loss systems, where due to finite waiting room loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise. We further investigate the embedded Markov chains at departure epochs and show that the behaviour of the embedded Markov chain is often considerably different from that of the continuous time Markov process. This is different from the behaviour of the standard M/G/1, where the steady state of the embedded Markov chain and the continuous time process coincide. For exponential queueing systems we show that there is a product form equilibrium of the embedded Markov chain under rather general conditions. For systems with non-exponential service times more restrictive constraints are needed, which we prove by a counter example where the environment represents an inventory attached to an M/D/1 queue. Such integrated queueing-inventory systems are dealt with in the literature previously, and are revisited here in detail

Analyzing the make-to-stock queue in the supply chain and eBusiness settings

Thesis (Ph.D.)--Massachusetts Institute of Technology, Sloan School of Management, 2001.Includes bibliographical references (p. 149-154).This thesis presents two applications of the prototypical make-to-stock queue model that are mainly motivated by supply chain management and e-commerce issues. In the first part, we consider the decentralized version of the make-to-stock model. Two different agents that we call the supplier and the retailer control production and finish goods inventory level independently. The retailer carries finished goods inventory to service an exogenous demand and specifies a policy for replenishing his/her inventory from the upstream supplier. The supplier, on the other hand, chooses the capacity of his manufacturing facility. Demand is backlogged and both agents share the backorder cost. In addition, a linear inventory holding cost is charged to the retailer, and a linear cost for building production capacity is incurred by the supplier. The inventory level, demand rate and cost parameters are common knowledge to both agents. Under the continuous state approximation that the M/M/1 queue has an exponential rather than geometric steady-state distribution, we characterize the optimal centralized and Nash solutions, and show that a contract with linear transfer payments based on backorder, inventory and capacity levels coordinates the system in the absence of participation constraints.(cont.) We also derive explicit formulas to assess the inefficiency of the Nash equilibrium, compare the agents' decision variables and the customer service level of the centralized versus Nash solutions, and identify conditions under which a coordinating contract is desirable for both agents. In the second part, we return to the centralized version of the make-to-stock model and analyze the situation where the price that the end customers are willing to pay for the good changes dynamically and stochastically over time. We also as- sume that demand is fully backlogged and that holding and backordering costs are linearly incurred by the manufacturer. In this setting, we formulate the stochastic control problem faced by the manager. That is, at each moment of time and based on the current inventory position, the manager decides (i) whether or not to accept an incoming order and (ii) whether or not to idle the machine. We use the expected long-term average criteria to compute profits. Under heavy traffic conditions, we approximate the problem by a dynamic diffusion control problem and derive optimality (Bellman) conditions. Given the mathematical complexity of the Bellman equations, numerical and approximated solutions are presented as well as a set of computational experiments showing the quality of the proposed policies.by René Caldentey.Ph.D

Provably near-optimal algorithms for multi-stage stochastic optimization models in operations management

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 157-165).Many if not most of the core problems studied in operations management fall into the category of multi-stage stochastic optimization models, whereby one considers multiple, often correlated decisions to optimize a particular objective function under uncertainty on the system evolution over the future horizon. Unfortunately, computing the optimal policies is usually computationally intractable due to curse of dimensionality. This thesis is focused on providing provably near-optimal and tractable policies for some of these challenging models arising in the context of inventory control, capacity planning and revenue management; specifically, on the design of approximation algorithms that admit worst-case performance guarantees. In the first chapter, we develop new algorithmic approaches to compute provably near-optimal policies for multi-period stochastic lot-sizing inventory models with positive lead times, general demand distributions and dynamic forecast updates. The proposed policies have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. We also describe a 6-approximation algorithm for the counterpart model under uniform capacity constraints. In the second chapter, we study a class of revenue management problems in systems with reusable resources and advanced reservations. A simple control policy called the class selection policy (CSP) is proposed based on solving a knapsack-type linear program (LP). We show that the CSP and its variants perform provably near-optimal in the Halfin- Whitt regime. The analysis is based on modeling the problem as loss network systems with advanced reservations. In particular, asymptotic upper bounds on the blocking probabilities are derived. In the third chapter, we examine the problem of capacity planning in joint ventures to meet stochastic demand in a newsvendor-type setting. When resources are heterogeneous, there exists a unique revenue-sharing contract such that the corresponding Nash Bargaining Solution, the Strong Nash Equilibrium, and the system optimal solution coincide. The optimal scheme rewards every participant proportionally to her marginal cost. When resources are homogeneous, there does not exist a revenue-sharing scheme which induces the system optimum. Nonetheless, we propose provably good revenue-sharing contracts which suggests that the reward should be inversely proportional to the marginal cost of each participant.by Cong Shi.Ph.D

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Applications of robust optimization to queueing and inventory systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 105-111).This thesis investigates the application of robust optimization in the performance analysis of queueing and inventory systems. In the first part of the thesis, we propose a new approach for performance analysis of queueing systems based on robust optimization. We first derive explicit upper bounds on performance for tandem single class, multiclass single server, and single class multi-server queueing systems by solving appropriate robust optimization problems. We then show that these bounds derived by solving deterministic optimization problems translate to upper bounds on the expected steady-state performance for a variety of widely used performance measures such as waiting times and queue lengths. Additionally, these explicit bounds agree qualitatively with known results. In the second part of the thesis, we propose methods to compute (s,S) policies in supply chain networks using robust and stochastic optimization and compare their performance. Our algorithms handle general uncertainty sets, arbitrary network topologies, and flexible cost functions including the presence of fixed costs. The algorithms exhibit empirically practical running times. We contrast the performance of robust and stochastic (s,S) policies in a numerical study, and we find that the robust policy is comparable to the average performance of the stochastic policy, but has a considerably lower standard deviation across a variety of networks and realized demand distributions. Additionally, we identify regimes when the robust policy exhibits particular strengths even in average performance and tail behavior as compared with the stochastic policy.by Alexander Anatolyevich Rikun.Ph.D

Stochastic Approximation Methods for Systems Over an Infinite Horizon

The paper develops efficient and general stochastic approximation (SA) methods for improving the operation of parametrized systems of either the continuous- or discrete-event dynamical systems types and which are of interest over a long time period. For example, one might wish to optimize or improve the stationary (or average cost per unit time) performance by adjusting the systems parameters. The number of applications and the associated literature are increasing at a rapid rate. This is partly due to the increasing activity in computing pathwise derivatives and adapting them to the average-cost problem. Although the original motivation and the examples come from an interest in the infinite-horizon problem, the techniques and results are of general applicability in SA. We present an updating and review of powerful ordinary differential equation-type methods, in a fairly general context, and based on weak convergence ideas. The results and proof techniques are applicable to a wide variety of applications. Exploiting the full potential of these ideas can greatly simplify and extend much current work. Their breadth as well as the relative ease of using the basic ideas are illustrated in detail via typical examples drawn from discrete-event dynamical systems, piecewise deterministic dynamical systems, and a stochastic differential equations model. In these particular illustrations, we use either infinitesimal perturbation analysis-type estimators, mean square derivative-type estimators, or finite-difference type estimators. Markov and non-Markov models are discussed. The algorithms for distributed/asynchronous updating as well as the fully synchronous schemes are developed