A polling model with reneging at polling instants

In this paper we consider a single-server, cyclic polling system with switch-over times and Poisson arrivals. The service disciplines that are discussed, are exhaustive and gated service. The novel contribution of the present paper is that we consider reneging of customers at polling instants. In more detail, whenever the server starts or ends a visit to a queue, part of the customers waiting in each queue leave the system before having received service. The probability that a certain customer leaves the queue, depends on the queue in which the customer is waiting, and on the location of the server. We show that this system can be analysed by introducing customer subtypes, depending on their arrival periods, and keeping track of the moment when they abandon the system. In order to determine waiting time distributions, we regard the system as a polling model with varying arrival rates, and apply a generalised version of the distributional form of Little’s law. The marginal queue length distribution can be found by conditioning on the state of the system (position of the server, and whether it is serving or switching)

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"

Tandem queues with impatient customers for blood screening procedures

We study a blood testing procedure for detecting viruses like HIV, HBV and HCV. In this procedure, blood samples go through two screening steps. The first test is ELISA (antibody Enzyme Linked Immuno-Sorbent Assay). The portions of blood which are found not contaminated in this first phase are tested in groups through PCR (Polymerase Chain Reaction). The ELISA test is less sensitive than the PCR test and the PCR tests are considerably more expensive. We model the two test phases of blood samples as services in two queues in series; service in the second queue is in batches, as PCR tests are done in groups. The fact that blood can only be used for transfusions until a certain expiration date leads, in the tandem queue, to the feature of customer impatience. Since the first queue basically is an infinite server queue, we mainly focus on the second queue, which in its most general form is an S-server M=G[k;K]=S + G queue, with batches of sizes which are bounded by k and K. Our objective is to maximize the expected profit of the system, which is composed of the amount earned for items which pass the test (and before their patience runs out), minus costs. This is done by an appropriate choice of the decision variables, namely, the batch sizes and the number of servers at the second service station. As will be seen, even the simplest version of the batch queue, the M=M[k;K]=1 + M queue, already gives rise to serious analytical complications for any batch size larger than 1. These complications are discussed in detail. In view of the fact that we aim to solve realistic optimization problems for blood screening procedures, these analytical complications force us to take recourse to either a numerical approach or approximations. We present a numerical solution for the queue length distribution in theM=M[k;K]=S+M queue and then formulate and solve several optimization problems. The power-series algorithm, which is a numerical-analytic method, is also discussed

On a 2-class polling model with reneging and ki -limited service

The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-018-2915-yThis paper analyzes a 2-class, single-server polling model operating under a ki-limited service discipline with class-dependent switchover times. Arrivals to each class are assumed to follow a Poisson process with phase-type distributed service times. Within each queue, customers are impatient and renege (i.e., abandon the queue) if the time before entry into service exceeds an exponentially distributed patience time. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the per-class waiting time distributions are computed via the use of matrix analytic techniques. The impacts of reneging and choice of service time distribution are investigated through a series of numerical experiments, with a particular focus on the determination of (k1,k2) which minimizes a cost function involving the expected time a customer spends waiting in the queue and an additional penalty cost should reneging take place.Natural Sciences and Engineering Research Council of Canada through its Discovery Grants program || (#RGPIN-2016-03685) Postgraduate Scholarship-Doctoral progra