Optimizing flow rates in a queueing network with side constraints

Network Analysis;operations research

Analysis of Multiserver Retrial Queueing System: A Martingale Approach and an Algorithm of Solution

The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon arrival all servers are busy, then the customer goes to the secondary queue, orbit, and after some random time retries more and more to occupy a server. A service time of each customer is exponentially distributed random variable with parameter $\mu_1$. A time between retrials is exponentially distributed with parameter $\mu_2$ for each customer. Using a martingale approach the paper provides an analysis of this system. The paper establishes the stability condition and studies a behavior of the limiting queue-length distributions as $\mu_2$ increases to infinity. As $\mu_2\to\infty$, the paper also proves the convergence of appropriate queue-length distributions to those of the associated `usual' multiserver queueing system without retrials. An algorithm for numerical solution of the equations, associated with the limiting queue-length distribution of retrial systems, is provided.Comment: To appear in "Annals of Operations Research" 141 (2006) 19-52. Replacement corrects a small number of misprint

Importance Sampling Simulation of Population Overflow in Two-node Tandem Networks

In this paper we consider the application of importance sampling in simulations of Markovian tandem networks in order to estimate the probability of rare events, such as network population overflow. We propose a heuristic methodology to obtain a good approximation to the 'optimal' state-dependent change of measure (importance sampling distribution). Extensive experimental results on 2-node tandem networks are very encouraging, yielding asymptotically efficient estimates (with bounded relative error) where no other state-independent importance sampling techniques are known to be efficient The methodology avoids the costly optimization involved in other recently proposed approaches to approximate the 'optimal' state-dependent change of measure. Moreover, the insight drawn from the heuristic promises its applicability to larger networks and more general topologies

A Markov Chain Model Checker

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen Twente Markov Chain Checker $(E \vdash MC^2$), where properties are expressed in appropriate extensions of CTL. We illustrate the general bene ts of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of $(E \vdash MC^2$)

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"

Coupled queues with customer impatience

Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved

Modeling and analysis to improve the quality of healthcare services

For many healthcare services or medical procedures, patients have extensive risk of complication or face death when treatment is delayed. When a queue is formed in such a situation, it is very important to assess the suffering and risk faced by patients in queue and plan sufficient medical capabilities in advance to address the concerns. As the diversity of care settings increases, congestion in facilities causes many patients to unnecessarily spend extra days in intensive care facilities. Performance evaluation of current healthcare service systems using queueing theory gains more and more importance because of patient flows and systems complexity. Queueing models have been used in handsome number of healthcare studies, but the incorporation of blocking is still limited. In this research work, we study an efficient two-stage multi-class queueing network system with blocking and phase-type service time distribution to analyze such congestion processes. We also consider parallel servers at each station and first-come-first-serve non-preemptive service discipline are used to improve the performance of healthcare service systems

Fast Discrete-Event Simulation of Markovian Queueing Networks through Euler Approximation

The efficient management of large-scale queueing networks is critical for a variety of sectors, including healthcare, logistics, and customer service, where system performance has profound implications for operational effectiveness and cost management. To address this key challenge, our paper introduces simulation techniques tailored for complex, large-scale Markovian queueing networks. We develop two simulation schemes based on Euler approximation, namely the backward and forward schemes. These schemes can accommodate time-varying dynamics and are optimized for efficient implementation using vectorization. Assuming a feedforward queueing network structure, we establish that the two schemes provide stochastic upper and lower bounds for the system state, while the approximation error remains bounded over the simulation horizon. With the recommended choice of time step, we show that our approximation schemes exhibit diminishing asymptotic relative error as the system scales up, while maintaining much lower computational complexity compared to traditional discrete-event simulation and achieving speedups up to tens of thousands times. This study highlights the substantial potential of Euler approximation in simulating large-scale discrete systems