A survey of the machine interference problem

This paper surveys the research published on the machine interference problem since the 1985 review by Stecke & Aronson. After introducing the basic model, we discuss the literature along several dimensions. We then note how research has evolved since the 1985 review, including a trend towards the modelling of stochastic (rather than deterministic) systems and the corresponding use of more advanced queuing methods for analysis. We conclude with some suggestions for areas holding particular promise for future studies.Natural Sciences and Engineering Research Council (NSERC) Discovery Grant 238294-200

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"

Study of feedback retrial queueing system with working vacation, setup time, and perfect repair

This manuscript analyses a retrial queueing system with working vacation, interruption, feedback, and setup time with the perfect repair. In the proposed model, the server takes vacation whenever the system gets empty but it still serves the customers at a relatively lower speed. The concept of power saving is included in the model. To save the power the server is turned off immediately on being empty at vacation completion instant. The customer who arrives when the system is turned off activates the server and he has to wait for his turn till the server is turned on. The unreliable server may sometimes fail to activate during setup. It is then sent for repair and repaired server immediately starts serving the waiting customers. Using probability generating function, explicit expressions for system size and different states of server for the model are obtained and results are analyzed graphically using MATLAB software

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

A Retrieval Queueing Model With Feedback

A multi-server retrial queuing model with feedback is considered in this paper.Input flow of calls is modeled using a Markovian Arrival Process (M AP) and the service time is assumed to follow an exponential distribution. An arriving call enters into service should there be a free server. Otherwise, in accordance to Bernoulli trials, the call will enter into an infinite orbit (referred to as a retrial orbit) to retry along with other calls to get into service or will leave the system forever. After obtaining a service each call, independent of the others, will either enter into a finite orbit (referred to as a feedback orbit) for another service or leave the system forever. The decision to enter into the feedback orbit or not is done according to another Bernoulli trial. Calls from these two buffers will compete with the main source of calls based on signals received from two independent Poisson processes.The rates of these processes depend on the phase of the M AP. The steady-state analysis of the model is carried out and illustrative numerical examples including economical aspects are presented

Analysis of repairable M[X]/(G1,G2)/1 - feedback retrial G-queue with balking and starting failures under at most J vacations

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of services and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them get into the orbit. The negative customer, is arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters the orbit or leaves the system. If the orbit is empty at the service completion of each type of service, the server takes at most J vacations until at least one customer is received in the orbit when the server returns from a vacation. While the busy server may breakdown at any instant and the service channel may fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Numerical illustrations are discussed to see the effect of the system parameters

Analysis of repairable M[X]/(G1,G2)/1 - feedback retrial G-queue with balking and starting failures under at most J vacations

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of service and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. The negative customer, arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters into the orbit or leaves the system. If the orbit is empty at the service completion of each type of service, the server takes at most J vacations until at least one customer is received in the orbit when the server returns from a vacation. The busy server may breakdown at any instant and the service channel will fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Numerical illustrations are discussed to see the effect of system parameters

Queues in Reliability

Queueing models can be useful in solving many complex reliability problems. Component failures are usually interpreted as the arrival of customers and the repair or replacement of failed components is typically associated with the service facility. A distinctive characteristic of queues in reliability is that requests for service are usually generated by a finite customer population because, in general, there are a limited number of units, e.g. machines which can fail, and when they are all in the system, being repaired or waiting for repair, no more can arrive. Thus the arrivals do not form a renewal process as they may depend on the number of units in the system. This is an essential difference from typical queueing systems, where the population of potential arrivals can be considered to be effectively limitless. This article overviews the main queueing models used in reliability which are illustrated using the classical machine repairmen model. Some statistical methods to estimate the main quantities of interest in a queue are also discussed

Queues in a random environment

Exponential single server queues with state dependent arrival and service rates are considered which evolve under influences of external environments. The transitions of the queues are influenced by the environment's state and the movements of the environment depend on the status of the queues (bi-directional interaction). The structure of the environment is constructed in a way to encompass various models from the recent Operation Research literature, where a queue is coupled e.g. with an inventory or with reliability issues. With a Markovian joint queueing-environment process we prove separability for a large class of such interactive systems, i.e. the steady state distribution is of product form and explicitly given: The queue and the environment processes decouple asymptotically and in steady state. For non-separable systems we develop ergodicity criteria via Lyapunov functions. By examples we show principles for bounding throughputs of non-separable systems by throughputs of two separable systems as upper and lower bound