A single server Markovian queuing system with limited buffer and reverse balking

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived

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

A survey of the machine interference problem

This paper surveys the research published on the machine interference problem since the 1985 review by Stecke & Aronson. After introducing the basic model, we discuss the literature along several dimensions. We then note how research has evolved since the 1985 review, including a trend towards the modelling of stochastic (rather than deterministic) systems and the corresponding use of more advanced queuing methods for analysis. We conclude with some suggestions for areas holding particular promise for future studies.Natural Sciences and Engineering Research Council (NSERC) Discovery Grant 238294-200

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

Analysis of Military Entry Control Point Queueing

Military Entry Control Facilities (ECFs) are unique service queues that are constrained by space, receive high peak traffic flow, and have a customer base that must receive service. Due to complexity of the interactions within the system, simulations provide input that would be impractical for quantitative experimentation. Our research examines relationships within the ECF in order to develop insights that could lead to more efficient daily operations. We focus the research on interactions that generate a queue length that would interfere with traffic flow surrounding the base. Examining the interactions between multiple arrival rates and service times as well as the layout and model of the ECF we establish criterion for Officers in Charge (OICs) to make changes within the constraints of the ECF to their operations to better serve the customers and prevent ECF traffic from interfering with the community outside the military base

Queueing Network Modeling Patterns for Reliable and Unreliable Publish/Subscribe Protocols

International audienceMobile Internet of Things (IoT) applications are typically deployed on resource-constrained devices with intermittent network connectivity. To support the deployment of such applications, the Publish/Subscribe (pub/sub) interaction paradigm is often employed, as it decouples mobile peers in time and space. Furthermore, pub/sub middleware protocols and APIs consider the Things' hardware limitations and support the development of effective applications by providing Quality of Service (QoS) features. These features aim to enable developers to tune an application by switching different levels of response times and delivery success rates. However, the profusion of pub/sub middleware protocols coupled with intermittent network connectivity result in non-trivial application tuning. In this paper, we model the performance of middleware protocols found in IoT, which are classified within the pub/sub interaction paradigm-both reliable and unreliable underlying network layers are considered. We model reliable and unreliable protocols, by considering QoS semantics for data validity, buffer capacities as well as the intermittent availability of peers. Finally, we perform statistical analysis by varying these QoS semantics, demonstrating their significant effect on the rate of successful interactions. We showcase the application of our analysis in concrete scenarios relating to Traffic Information Management systems, that integrate both reliable and unreliable participants. The consequent PerfMP performance modeling pattern may be tailored for a variety of deployments, in order to control fine-grained QoS policies

Essays on Service Information, Retrials and Global Supply Chain Sourcing

In many service settings, customers have to join the queue without being fully aware of the parameters of the service provider (for e.g., customers at check-out counters may not know the true service rate prior to joining). In such blind queues\u27\u27, customers typically make their decisions based on the limited information about the service provider\u27s operational parameters from past experiences, reviews, etc. In the first essay, we analyze a firm serving customers who make decisions under arbitrary beliefs about the service parameters. We show, while revealing the service information to customers improves revenues under certain customer beliefs, it may however destroy consumer welfare or social welfare. When consumers can self-organize the timing of service visits, they may avoid long queues and choose to retry later. In the second essay, we study an observable queue in which consumers make rational join, balk and (costly) retry decisions. Retrial attempts could be costly due to factors such as transportation costs, retrial hassle and visit fees. We characterize the equilibrium under such retrial behavior, and study its welfare effects. With the additional option to retry, consumer welfare could worsen compared to the welfare in a system without retrials. Surprisingly, self-interested consumers retry too little (in equilibrium compared to the socially optimal policy) when the retrial cost is low, and retry too much when the retrial cost is high. We also explore the impact of myopic consumers who may not have the flexibility to retry. In the third essay, we propose a comprehensive model framework for global sourcing location decision process. For decades, off-shoring of manufacturing to China and other low-cost countries was a no-brainer decision for many U.S. companies. In recent years, however, this trend is being challenged by some companies to re-shore manufacturing back to the U.S., or to near-shore manufacturing to Mexico. Our model framework incorporates perspectives over the entire life cycle of a product, i.e., product design, manufacturing and delivering, and after-sale service support, and we use it to test the validity of various competing theories on global sourcing. We also provide numerical examples to support our findings from the model

Modelling activities at a neurological rehabilitation unit

A queuing model is developed for the neurological rehabilitation unit at Rookwood Hospital in Cardiff. Arrivals at the queuing system are represented by patient referrals and service is represented by patient length of stay (typically five months). Since there are often delays to discharge, length of stay is partitioned into two parts: admission until date ready for discharge (modelled by Coxian phase-type distribution) and date ready for discharge until ultimate discharge (modelled by exponential distribution). The attributes of patients (such as age, gender, diagnosis etc) are taken into account since they affect these distributions. A computer program has been developed to solve this multi-server (21 bed) queuing system to produce steady-state probabilities and various performance measures. However, early on in the project it became apparent that the intensity of treatment received by patients has an effect on the time, from admission, until they are ready for discharge. That is, the service rates of the Coxian distribution are dependent on the amount of therapy received over time. This directly relates to the amount of treatment allocated in the weekly timetables. For the physiotherapy department, these take about eight hours to produce each week by hand. In order to ask the valuable what-if questions that relate to treatment intensity, it is therefore necessary to produce an automated scheduling program that replicates the manual assignment of therapy. The quality of timetables produced using this program was, in fact, considerably better than its alternative and so replaced the by-hand approach. Other benefits are more clinical time (since less employee input is required)and a convenient output of data and performance measures that are required for audit purposes. Once the model is constructed a number of relevant hypothetical scenarios are considered. Such as, what if delays to discharge are reduced by 50%? Also, through the scheduling program, the effect of changes to the composition of staff or therapy sessions can be evaluated, for example, what if the number of therapists is increased by one third? The effects of such measures are analysed by studying performance measures (such as throughput and occupancy) and the associated costs