Workloads and waiting times in single-server systems with multiple customer classes

One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions

Sojourn times in the M/G/1M/G/1 queue with deterministic feedback

In this paper we consider an M/G/1 queueing model, in which each customer is fed back a fixed number of times. For the case of negative exponentially distributed service times at each visit, we determine the Laplace-Stieltjes transform of the joint distribution of the sojourn times of the consecutive visits. As a by-result, we obtain the (transform of the) total sojourn time distribution; it can be related to the sojourn time distribution in the M/D/l queue with processor sharing. For the case of generally distributed service times at each visit, a set of linear equations is derived, from which the mean sojourn times per visit can be calculated

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"

Discrete Time Analysis of Multi-Queue Systems with Multiple Departure Streams in Material Handling and Production under Different Service Rules

In this work, we present a modelling approach in order to depict service rules holistically. The developed model is called multi-queue system with multiple departure streams (MQSMDS). The MQSMDS is modelled as a discrete time Markov chain. On the basis of a numerical study, the system characteristics are evaluated. The results of this work enable a rapid and low-cost analysis of material handling and production systems as well as a fast and easy identification of suitable service rules

Approximations for the waiting-time distribution in an M/P H/c priority queue

We investigate the use of priority mechanisms when assigning service engineers to customers as a tool for service differentiation. To this end, we analyze a non-preemptive M/PH/c priority queue with various customer classes. For this queue, we present various accurate and fast methods to estimate the first two moments of the waiting time per class given that all servers are occupied. These waiting time moments allow us to approximate the overall waiting time distribution per class. We subsequently apply these methods to real-life data in a case study

Queues with regular variation

X+173hlm.;24c