Optimum cost analysis for an Geo/Geo/c/N feedback queue under synchronous working vacations and impatient customers

This paper concerns the cost optimisation analysis of a discrete-time finite-capacity multiserver queueing system with Bernoulli feedback, synchronous multiple and single working vacations, balking, and reneging during both busy and working vacation periods. A reneged customer can be retained in the system by employing certain persuasive mechanism for completion of service. Using recursive method, the explicit expressions for the stationary state probabilities are obtained. Various system performance measures are presented. Further, a cost model is formulated. Then, the optimization of the model is carried out using quadratic fit search method (QFSM). Finally, the impact of various system parameters on the performance measures of the queueing system is shown numerically.</p

Performance and economic evaluation of differentiated multiple vacation queueing system with feedback and balked customers

The present paper deals with a single server feedback queueing system under two differentiated multiple vacations and balked customers. It is assumed that the service times of the two vacation types are exponentially distributed with different means. The steady-state probabilities of the model are obtained. Some important performance measures of the system are derived. Then, a cost model is developed. Further, a numerical study is presented

Analysis of some batch arrival queueing systems with balking, reneging, random breakdowns, fluctuating modes of service and Bernoulli schedulled server vacations.

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without service upon the absence of the server; especially due to vacation is quite a natural phenomenon. We study this reneging behaviour in a queueing process with a single server in the context of Markovian and non-Markovian service time distribution. Arrivals are in batches while each customer can take the decision to renege independently. The non-Markovian model is further extended considering service time to follow a Gamma distribution and arrivals are due to Geometric distribution. The closed-form solutions are derived in all the cases. Among other causes of service interruptions, one prime cause is breakdowns. We consider breakdowns to occur both in idle and working state of the server. In this queueing system the transient and steady state analysis are both investigated. Applying the supplementary variable technique, we obtain the probability generating function of queue size at random epoch for the different states of the system and also derive some performance measures like probability of server‟s idle time, utilization factor, mean queue length and mean waiting time. The effect of the parameters on some of the main performance measures is illustrated by numerical examples to validate the analytical results obtained in the study. The Mathematica 10 software has been used to provide the numerical results and presentation of the effects of some performance measures through plots and graphs

A Utility-Driven Multi-Queue Admission Control Solution for Network Slicing

38th IEEE International Conference on Computer Communications (IEEE INFOCOM 2019)The combination of recent emerging technologies such as network function virtualization (NFV) and network programmability (SDN) gave birth to the Network Slicing revolution. 5G networks consist of multi-tenant infrastructures capable of offering leased network “slices” to new customers (e.g., vertical industries) enabling a new telecom business model: Slice-as-a-Service (SlaaS). In this paper, we aim i) to study the slicing admission control problem by means of a multi-queuing system for heterogeneous tenant requests, ii) to derive its statistical behavior model, and iii) to provide a utility-based admission control optimization. Our results analyze the capability of the proposed SlaaS system to be approximately Markovian and evaluate its performance as compared to legacy solutions.This work has been partially funded by the European Union Horizon-2020 Projects 5G-MoNArch and 5G-Transformer under Grant Agreements 761445 and 761536 as well as by the Network for the Promotion of Young Scientists (TU-Nachwuchsring), TU Kaiserslautern with individual funding

Entropy Maximisation and Queues With or Without Balking. An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks.

An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks Keywords: Queues, Balking, Maximum Entropy (ME) Principle, Global Balance (GB), Queue Length Distribution (QLD), Generalised Geometric (GGeo), Generalised Exponential (GE), Generalised Discrete Half Normal (GdHN), Congestion Management, Packet Dropping Policy (PDP) Generalisations to links between discrete least biased (i.e. maximum entropy (ME)) distribution inferences and Markov chains are conjectured towards the performance modelling, analysis and prediction of general, single server queues with or without arrival balking. New ME solutions, namely the generalised discrete Half Normal (GdHN) and truncated GdHN (GdHNT) distributions are characterised, subject to appropriate mean value constraints, for inferences of stationary discrete state probability distributions. Moreover, a closed form global balance (GB) solution is derived for the queue length distribution (QLD) of the M/GE/1/K queue subject to extended Morse balking, characterised by a Poisson prospective arrival process, i.i.d. generalised exponential (GE) service times and finite capacity, K. In this context, based on comprehensive numerical experimentation, the latter GB solution is conjectured to be a special case of the GdHNT ME distribution. ii Owing to the appropriate operational properties of the M/GE/1/K queue subject to extended Morse balking, this queueing system is applied as an ME performance model of Internet Protocol (IP)-based communication network nodes featuring static or dynamic packet dropping congestion management schemes. A performance evaluation study in terms of the model’s delay is carried out. Subsequently, the QLD’s of the GE/GE/1/K censored queue subject to extended Morse balking under three different composite batch balking and batch blocking policies are solved via the technique of GB. Following comprehensive numerical experimentation, the latter QLD’s are also conjectured to be special cases of the GdHNT. Limitations of this work and open problems which have arisen are included after the conclusion

A class of multi-server queueing systems with unreliable servers: Models and application.

Where queueing systems with unreliable servers are concerned, most research that has been done focuses on one-server systems or systems with a Poisson arrival process and exponential service time. However, in some situations we need to consider non-exponential service time or service rate changes with the number of available servers. These are the queueing systems that are discussed in this thesis, none of which has ever been discussed in the literature. Since the phase type distribution is more general than the exponential distribution and captures most features of a general distribution, the phase type distributed service time is considered in unreliable queueing systems such as M/PH/n and M/PH/n/c. For the M/PH/n queueing system with unreliable servers, the mathematical model, stability condition analysis, stationary distribution calculation, computer programs and examples are all presented. For the M/PH/n/c queueing system with server failures, a finite birth-and-death mathematical model is built and the stationary distribution and performance evaluation measurements are calculated. Computer programs are developed and an example is given to demonstrate the application of this queueing system. (Abstract shortened by UMI.)Dept. of Industrial and Manufacturing Systems Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .Y375. Source: Masters Abstracts International, Volume: 43-01, page: 0295. Adviser: Attahiru S. Alfa. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

Modelling deadlock in queueing systems

Motivated by the needs of Aneurin Bevan University Health Board, this thesis ex- plores three themes: the phenomenon of deadlock in queueing systems, the develop- ment of discrete event simulation software, and applying modelling to the evaluation of the effects of a new healthcare intervention, Stay Well Plans, for older people in Gwent. When customers in a restricted queueing network become mutually blocked, and all possible movement ceases, that system becomes deadlocked. This thesis novelly investigates deadlock. A graph theoretical method of detecting deadlock in discrete event simulations is given, analytical models of deadlocking systems are built, and these are used to investigate the effect of system parameters on the expected time until reaching deadlock. Furthermore a deadlock resolution procedure is proposed. An open source discrete event simulation software, Ciw, is developed. This software is designed and developed using best practice principles. Furthermore it permits the use of best practice, such as reproducibility, in simulation modelling. Ciw is used for the modelling of a healthcare system, in order to evaluate the effect of Stay Well Plans. During the development of these models, a number of techniques are employed to overcome the difficulties of lack of data. Insightful results from these models are obtained, indicating a shift in demand from residential care services to community care services

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment