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Published in Sunderesh S. Heragu, Facilities Design, 2022
As the name implies, queuing theory involves the study of queues or waiting lines. Unlike many other modeling methods, it is not process specific and can be used to model any dynamic system in which discrete events alter the state of the system. Queuing theory can be used to study any manufacturing or service system where a queue buildup occurs over time. Thus, the system can be an airport, a walk-in medical clinic, fast-food restaurant, or a machine shop. In an airport, we see queues forming when departing airplanes wait for clearance from air traffic control to take off. Similarly, in a walk-in medical clinic, customers wait their turn for consultation with medical staff, and in a fast-food restaurant, customers wait to place an order and to pick up their order. Jobs wait to be machined on an automated lathe in a machine shop. In this chapter, we will focus on the application of queuing theory to manufacturing environments. Queuing theory can be used to answer the following questions with respect to a given system: What is the expected number of parts waiting in a queue?What is the expected time a part spends waiting in a queue?What is the probability that a machine will be idle?What is the probability of a queue being filled?
EPMS for Business Process Analysis
Published in Vivek Kale, Enterprise Process Management Systems, 2018
The field of queueing theory has developed a taxonomy to describe systems based on their arrival process, service process, and number of servers, written as arrival/service/number servers. The basic notation, widely used in queueing theory, is composed of three symbols separated by forward slashes. The values for the symbols are: M for Poisson or exponential distributionsD for deterministic (constant) distributionsE for Erlang distributionsG for general distributions (any arbitrary distribution)GI for general independent in the case of arrival rates
Queueing In Transportation Systems
Published in Dušan Teodorović, The Routledge Handbook of Transportation, 2015
Dušan Teodorović, Ranko Nedeljković
Queueing theory helps us to evaluate levels of service and operational performance of the systems. The average waiting time a customer spends in a queue, and the average number of customers in a queue, represent the usual metrics for the level of service. Utilization of the service facility has been frequently used as a metric for the system’s operational performance. Planners and designers use queueing theory techniques in various design stages of the future service facility (calculation of the number of lanes at intersection, the estimation of the length of left-turning bays, calculation of the size of the check-in area at the airport, calculation of the required number of parking spaces, etc.). In essence, the analysts use queueing theory techniques to answer the following questions: What is the operational efficiency of the observed queueing system? What is the level of service offered to the clients? Should transportation capacity be increased in response to expected demand?
Robust capacity planning for sterilisation department of a hospital
Published in International Journal of Production Research, 2023
Another approach widely utilised for the capacity planning of healthcare services is queuing theory; readers are referred to Fomundam and Herrmann (2007) for a review. Queuing theory is a mathematical field of the study aiming to find performance measures of a queuing system. As an example, built-in queuing formulas can be utilised to find the capacity of appointment-driven health centres aiming to meet certain performance targets (Creemers and Lambrecht 2009). Hulshof et al. (2013) also use queuing formulas to compute the optimum number of patients to be served in elective patient admission and resource allocation for hospitals with uncertain treatment paths and number of arrivals. They consider several queues with time-dependent resource levels. Similarly, Cochran and Roche (Cochran and Roche 2009) utilise queuing theory to investigate the impact of various capacity design alternatives in a hospital emergency department. The main disadvantage of queuing theory is that most of the built-in formulations for the queue's performance measures are non-linear and require the arrival and service processes to follow certain distributions such as exponential.
Three-moment approximation for the mean queue time of a GI/G/1 queue
Published in IISE Transactions, 2018
Kan Wu, Sandeep Srivathsan, Yichi Shen
Queueing theory is an analytical tool that can be used in the performance evaluation of a wide range of real-life systems, such as manufacturing and communication systems. In this article, our focus is on single-server queues, which are the fundamental building blocks of those practical systems. Figure 1 shows the structure of a general single-server queue. Jobs arrive from outside and require service from server S. Under the First-In-First-Out policy, a job has to wait in the queue until the previous jobs have finished their service (if any). Denote the arrival time of the nth job as An and the time it starts to receive service as Dn. Then the queue time of the nth customer is Wn = Dn − An and the mean queue time is