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"

Unreliable Retrial Queues in a Random Environment

This dissertation investigates stability conditions and approximate steady-state performance measures for unreliable, single-server retrial queues operating in a randomly evolving environment. In such systems, arriving customers that find the server busy or failed join a retrial queue from which they attempt to regain access to the server at random intervals. Such models are useful for the performance evaluation of communications and computer networks which are characterized by time-varying arrival, service and failure rates. To model this time-varying behavior, we study systems whose parameters are modulated by a finite Markov process. Two distinct cases are analyzed. The first considers systems with Markov-modulated arrival, service, retrial, failure and repair rates assuming all interevent and service times are exponentially distributed. The joint process of the orbit size, environment state, and server status is shown to be a tri-layered, level-dependent quasi-birth-and-death (LDQBD) process, and we provide a necessary and sufficient condition for the positive recurrence of LDQBDs using classical techniques. Moreover, we apply efficient numerical algorithms, designed to exploit the matrix-geometric structure of the model, to compute the approximate steady-state orbit size distribution and mean congestion and delay measures. The second case assumes that customers bring generally distributed service requirements while all other processes are identical to the first case. We show that the joint process of orbit size, environment state and server status is a level-dependent, M/G/1-type stochastic process. By employing regenerative theory, and exploiting the M/G/1-type structure, we derive a necessary and sufficient condition for stability of the system. Finally, for the exponential model, we illustrate how the main results may be used to simultaneously select mean time customers spend in orbit, subject to bound and stability constraints

Essays on Service Information, Retrials and Global Supply Chain Sourcing

In many service settings, customers have to join the queue without being fully aware of the parameters of the service provider (for e.g., customers at check-out counters may not know the true service rate prior to joining). In such blind queues\u27\u27, customers typically make their decisions based on the limited information about the service provider\u27s operational parameters from past experiences, reviews, etc. In the first essay, we analyze a firm serving customers who make decisions under arbitrary beliefs about the service parameters. We show, while revealing the service information to customers improves revenues under certain customer beliefs, it may however destroy consumer welfare or social welfare. When consumers can self-organize the timing of service visits, they may avoid long queues and choose to retry later. In the second essay, we study an observable queue in which consumers make rational join, balk and (costly) retry decisions. Retrial attempts could be costly due to factors such as transportation costs, retrial hassle and visit fees. We characterize the equilibrium under such retrial behavior, and study its welfare effects. With the additional option to retry, consumer welfare could worsen compared to the welfare in a system without retrials. Surprisingly, self-interested consumers retry too little (in equilibrium compared to the socially optimal policy) when the retrial cost is low, and retry too much when the retrial cost is high. We also explore the impact of myopic consumers who may not have the flexibility to retry. In the third essay, we propose a comprehensive model framework for global sourcing location decision process. For decades, off-shoring of manufacturing to China and other low-cost countries was a no-brainer decision for many U.S. companies. In recent years, however, this trend is being challenged by some companies to re-shore manufacturing back to the U.S., or to near-shore manufacturing to Mexico. Our model framework incorporates perspectives over the entire life cycle of a product, i.e., product design, manufacturing and delivering, and after-sale service support, and we use it to test the validity of various competing theories on global sourcing. We also provide numerical examples to support our findings from the model

Sojourn time in a single server queue with threshold service rate control

We study the sojourn time in a queueing system with a single exponential server, serving a Poisson stream of customers in order of arrival. Service is provided at low or high rate, which can be adapted at exponential inspection times. When the number of customers in the system is above a given threshold, the service rate is upgraded to the high rate, and otherwise, it is downgraded to the low rate. The state dependent changes in the service rate make the analysis of the sojourn time a challenging problem, since the sojourn time now also depends on future arrivals. We determine the Laplace transform of the stationary sojourn time and describe a procedure to compute all moments as well. First we analyze the special case of continuous inspection, where the service rate immediately changes once the threshold is crossed. Then we extend the analysis to random inspection times. This extension requires the development of a new methodological tool, that is "matrix generating functions". The power of this tool is that it can also be used to analyze generalizations to phase-type services and inspection times.Comment: 16 pages, 13 figure

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

A Note on an M/M/s Queueing System with two Reconnect and two Redial Orbits

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new attempt to reach the primary queue, and when a customer finishes his conversation with a server, he may comeback to the system, to one of the reconnect orbits where he will wait for another service. In this paper, a fluid model is used to derive a first order approximation for the number of customers in the redial and reconnect orbits in the heavy traffic. The fluid limit of such a model is a unique solution to a system of three differential equations