Classroom Note: A note on calculating steady state results for an M/M/k queuing system when the ratio of the arrival rate to the service rate is large (original) (raw)
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The-Application-of-Queuing-Analysis-in-modeling-Optimal-Service-level.pdf
Queues are common scenario faced in the modern day Banks and other financial Institutions. Queuing theory is the mathematical study of waiting lines; this can also be applicable queues in the banking system. This study examine the queuing system at Guarantee Trust Bank (GTB), putting into consideration the waiting time spend by Customers, Service time spend by a Customer and the average cost a customer loses while in queue and the service cost of each server in order to optimize the system. The First Come First Serve (FCFS) Multi-Server queuing model was used to model the queuing process. The waiting time was assumed to follow a Poisson distribution while the service rate follows an Exponential distribution. This study adopted a case study approach by randomly administering questionnaires, interviews and observation of the participants. The data were collected at the GTB cash deposit unit for four days period. The data collected were analyzed using TORA optimization window based software as well as standard queuing formula. The results of the analysis showed that the average queue length, waiting time of customer with a minimum Total Cost that utilize the system is by using five Servers against the present server level of Three Servers which incur a high total cost to both the Customers and the system.
Trends in the Mathematics of Queuing Systems
In this article, we study the trends in queuing system mathematics (mathematical study of waiting lines) from its inception in 1909 to date. The aim is to educate on how advances in system engineering and operations research are transforming study trends in terms of scholarly contributions (historical evolution), problems formulation, analytic techniques, modeling and results. To achieve this objective, articles on this field of operations research are studied and general trends uncovered and made easily understandable for educational purposes. In the end, we came out with deductions that trends in the mathematics of queuing systems depend to a large extend on developments in operation systems and engineering. What makes this paper most interesting is the understanding that queuing problems are fast becoming pure stochastic (diffusion) problems. This understanding is made more elaborated and easily understandable for a wide variety of audience.
Queuing Theory in today's world-An Overview
When all is said in done we don't prefer to hold up. Be that as it may, decrease of the holding up time for the most part requires additional speculations. To choose whether or not to contribute, it is essential to know the impact of the speculation on the holding up time. So we require models and strategies to investigate such circumstances. In this course we treat various basic queueing models. Consideration is paid to techniques for the examination of these models, furthermore to uses of queueing models. Essential application regions of queueing models are creation frameworks, transportation and stocking frameworks, correspondence frameworks and data handling frameworks. Queueing models are especially helpful for the outline of these framework regarding design, limits and control.
QUEUING THEORY AND IT'S IMPACT ON VARIOUS APPLICATIONS - A REVIEW
Waiting is an intimate dimension of our daily lives. Everyone has experienced waiting in line at the traffic control of daily life of human like telecommunications, reservation counter, super market, big bazaar, Picture Cinema hall ticket window and also to determining the sequence of computer operations, computer performance, health services, airport traffic, and airline ticket sales like any number of other places. Queuing theory is the mathematical study of waiting lines and it is very useful to define Modern information technologies require innovations that are based on modelling, analyzing, designing to deals with. Queuing theory is used widely in engineering and industry for analysis and modelling of processes that involve waiting lines. Applications of queuing theory is increased day by day in the fields of banking sector, healthcare, traffic control, computer Parallel System and Distributed system are also have the base of Queue models. This paper is an attempt to analyze the instances of use of queuing theory in various applications and benefits acquired from the same. Keywords- queue, queuing theory, queuing system, queuing theory applications.
International Journal of Science and Research (IJSR)
The ultimate objective of the analysis of queuing systems is to understand the behaviour of their underlying process so that informed and intelligent decisions can be made by the management. The application of queuing concepts is an attempt to minimize cost through minimization of inefficiency and delays in a system. Various methods of solving queuing problems have been proposed. In this study we have explored single –server Markovian queuing model with both interarrival and service times following exponential distribution with parameters and , respectively, and unlimited queue size with FIFO queuing discipline and unlimited customer population. We apply this model to catering data and estimate parameters for the same. A sensitivity analysis is the carried out to evaluate stability of the system.
Waiting on a queue is not usually interesting, but reduction in this waiting time usually requires planning and extra investments. Queuing theory was developed to study the queuing phenomenon in the commerce, telephone traffic, transportation, etc [Cooper (1981), ]. The rising population and health-need due to adverse environmental conditions have led to escalating waiting times and congestion in hospital Emergency Departments (ED). It is universally acknowledged that a hospital should treat its patients, especially those in need of critical care, in timely manner. Incidentally, this is not achieved in practice particularly in government owned health institutions because of high demand and limited resources in these hospitals. In this paper, we develop the equations of steady state probabilities. Example from a out-patient department of a clinic was presented to demonstrate how the various parameters of the model influence the behavior of the system.