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"

Analysis of classical retrial queue with differentiated vacation and state dependent arrival rate.

In present paper we have introduced the concept of differentiated vacations in a retrial queueing model with state dependent arrival rates of customers. The arrival rate of customers is different in various states of the server. The vacation types are differentiated by means of their durations as well as the previous state of the server. In type I vacation, server goes just after providing service to at least one customer whereas in type II, it comes after remaining free for some time. In steady state, we have obtained the system size probabilities and other system performance measures. Finally, sensitivity and cost analysis of the proposed model is also performed. The probability generating function technique, parabolic method and MATLAB is used for the purpose

(R1984) Analysis of M^[X1], M^[X2]/G1, G_2^(a,b)/1 Queue with Priority Services, Server Breakdown, Repair, Modified Bernoulli Vacation, Immediate Feedback

In this investigation, the steady state analysis of two individualistic batch arrival queues with immediate feedback, modified Bernoulli vacation and server breakdown are introduced. Two different categories of customers like priority and ordinary are to be considered. This model propose nonpreemptive priority discipline. Ordinary and priority customers arrive as per Poisson processes. The server consistently afford single service for priority customers and the general bulk service for the ordinary customers and the service follows general distribution. The ordinary customers to be served only if the batch size should be greater than or equal to a , else the server should not start service until a customers have accumulated. Meanwhile priority queue is empty; the server becomes idle or go for vacation. If server gets breakdown while the priority customers are being served, they may wait in the head of the queue and get fresh service after repair completion, but in case of ordinary customers they may leave the system. After completion of each priority service, customer may rejoin the system as a feedback customer for receiving regular service because of inappropriate quality of service. Supplementary variable technique and probability generating function are generally used to solve the Laplace transforms of time-dependent probabilities of system states. Finally, some performance measures are evaluated and express the numerical results

Analysis of M[X1],M[X2]/G1,G2/1 retrial queueing system with priority services, working breakdown, collision, Bernoulli vacation, immediate feedback, starting failure and repair

This paper considers an M[X1] , M[X2] /G1,G2/1 general retrial queueing system with priority services. Two types of customers from different classes arrive at the system in different independent compound Poisson processes. The server follows the non-pre-emptive priority rule subject to working breakdown, Bernoulli vacation, starting failure, immediate feedback, collision and repair. After completing each service, the server may go for a vacation or remain idle in the system. The priority customers who find the server busy are queued in the system. If a low-priority customer finds the server busy, he is routed to orbit that attempts to get the service. The system may become defective at any point of time while in operation. However, when the system becomes defective, instead of stopping service completely, the service is continued to the interrupted customer only at a slower rate. Using the supplementary variable technique, the joint distribution of the server state and the number of customers in the queue are derived. Finally, some performance measures are obtained

Bulk queueing system with starting failure and single vacation

To analyze an M^([X])/G(a,b)/1 queue with starting failure, repair and single vacation. This type of queueing model has a wide range of applications in production/manufacturing systems. Important performance measures and stability conditions are obtained. Further, we discuss some particular cases. Finally, numerical results of the proposed model have been derived

Analysis of a Queueing Model with MAP Arrivals and Heterogeneous Phase-Type Group Services

Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. These two sectors cover everything we deal with on a day-to-day basis. Queues in which the services are offered in blocks (or groups or batches) are well established in the literature and have a wide variety of applications in practice. In this paper, we look at one such queueing model in which the arrivals occur according to a Markovian arrival process and the services are offered in batches of varying sizes from 1 to a finite pre-determined constant, say, b. The service times are assumed to be of phase type with representation depending on the size of the group. Thus, the distributions considered are heterogeneous from both the representation and rate points of view. The model can be studied as a G I/M/1-type queue or as a QBD-model. The model is analyzed in steady state by establishing results including on the rate matrix and the waiting time distribution and providing a number of illustrative examples

MAP/PH/1 systems with group service: performance analysis under different admission strategies

2015 - 2016Recent advances in wireless communication networks led to possibility of multi-rate transmission of information. The queueing theory represents a valid tool to study how the performances of such communication systems can be improved, and to give proper solutions. Modeling a multi-rate transmission system, in terms of queueing theory, means that a particular discipline has to be considered: a group of requests from users can be processed simultaneously in parallel and processing of the whole group is supposed finished if processing of all individual requests belonging to this group is over. In order to model this typology of telecommunication systems, some particular assumption can be made on arrivals, which occur by a Markovian arrival process, and on service time and length of admission period, which are regulated by phase type distributions. Thus, in this thesis MAP/PH/1 queueing systems have been considered, with and without retrial to take into account all possible behaviours of the customers. The main goal of the research activity presented in this work is to introduce novel admission strategies for the described systems, in order to give a major contribute to the current performance analysys, in particular as regard the choice of the optimal length of admission period and optimal size of the groups. Dynamics of such systems are described by multidimensional Markov chains. Ergodicity condition for these Markov chains have been derived, stationary probability distribution of the states have been computed, formulas for the main performance measures of the system have been attained. Essential advantages of the proposed customer’s service disciplines have been numerically illustrated. [edited by author]I recenti progressi ottenuti per le reti di comunicazione wireless, permettono la trasmissione multi-frequenza delle informazioni. La teoria delle code rappresenta un valido strumento per studiare come le performance di tali sistemi di comunicazione possano essere migliorate, e individuare opportune soluzioni. In termini di teoria delle code, modellare un sistema di trasmissione multi-frequenza significa considerare una determinata disciplina: un gruppo di richieste da parte di utenti possono essere processate simultaneamente in parallelo, e il processo dell’intero gruppo risulta completato se tutte le richieste appartenenti a tale gruppo sono espletate. Al fine di modellare tale tipologia di sistemi di telecomunicazione, si possono definire particolari assunzioni sugli arrivi, determinati da processi di arrivo Markoviani, e sul tempo di servizio e lunghezza del periodo di ammissione, regolati da distribuzioni di tipo a fasi. Pertanto, in tale lavoro di tesi sono stati considerati sistemi a coda di tipo MAP/PH/1, con e senza retrial per considerare tutti i possibili comportamenti degli utenti. Il principale obiettivo dell’attivita` di ricerca presentata in tale lavoro `e introdurre nuove strategie di ammissione per i sistemi descritti, al fine di fornire un maggior contributo alle attuali analisi sulle performance, in particolare relativamente alla scelta della lunghezza ottimale del periodo di ammissione e la dimensione ottimale dei gruppi. Le dinamiche di tali sistemi sono descritte da catene di Markov multidimensionali. `E stata ricavata la condizione di ergodicit`a per tali catene di Markov, `e stata calcolata la distribuzione delle probabilita` stazionarie degli stati, e sono state ottenute le formule per le misure dei principali parametri prestazionali del sistema. I principali vantaggi delle discipline di servizio proposte sono state illustrate numericamente. [a cura dell'autore]XXIX n.s

Coupling and monotonicity of queueing processes

The main purpose of this work is to give a survey of main monotonicity properties of queueing processes based on the coupling method. The literature on this topic is quite extensive, and we do not consider all aspects of this topic. Our more concrete goal is to select the most interesting basic monotonicity results and give simple and elegant proofs. Also we give a few new (or revised) proofs of a few important monotonicity properties for the queue-size and workload processes both in single-server and multi- server systems. The paper is organized as follows. In Section 1, the basic notions and results on coupling method are given. Section 2 contains known coupling results for renewal processes with focus on construction of synchronized renewal instants for a superposition of independent renewal processes. In Section 3, we present basic monotonicity results for the queue-size and workload processes. We consider both discrete-and continuous-time queueing systems with single and multi servers. Less known results on monotonicity of queueing processes with dependent service times and interarrival times are also presented. Section 4 is devoted to monotonicity of general Jackson-type queueing networks with Markovian routing. This section is based on the notable paper [17]. Finally, Section 5 contains elements of stability analysis of regenerative queues and networks, where coupling and monotonicity results play a crucial role to establish minimal suficient stability conditions. Besides, we present some new monotonicity results for tandem networks

An integrated approach to solving retrial queue complexity

Retrial queues have been proposed in literature as a means of managing lost traffic in wireless cellular networks. However, the retrial queue system has led to a more complex Markovic process in network analysis. This complexity is further worsened by the addition of handover prioritization. In this paper, a solution that can minimize this complexity has been studied. The solution involves an integration of computational and analytical modeling techniques. The work was simulated and tested in Matlab/Simulink with guard channels as a handover prioritization scheme. Further evaluations were carried out on the effect of blocking probability (PB) as a quality of service (QoS) parameter. Numerical results obtained from the integrated approach show that the retrial queue reduces the PB for all requests (new and handover). The result obtained from this paper simplifies the solution to the complexity found in retrial queue systems. Furthermore, it was also deduced that reduced retrial rate with corresponding increase in the retrial queue size improves the network quality without an increase in system complexity.Keywords: Markov, retrial, probability, network, traffi