Module D.docx

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University of Guelph
Food Agricultural and Resource Economics
FARE 3310
Jamie Gruman

Module D: The Waiting-Line Model Queuing Theory Queuing theory- body of knowledge about waiting lines Waiting lines (queue)- items or people in a line awaiting service -useful in both manufacturing and service areas -analysis of queues in terms of waiting-line length, average waiting time and other factors helps us to understand service systems (such as bank teller stations) -useful in both manufacturing and service areas Characteristics of Waiting-Line 1. Arrivals or inputs to the system: these have characteristics such as population size, behavior and statistical distribution 2. Queue discipline or the waiting line itself: characteristics of the queue include whether it is limited or unlimited in length and the discipline of people or items in it 3. the service facility: its characteristics include its design and the statistical distribution of service times Arrival Characteristics the input source that generates arrivals or customers for a service system has three major characteristics: 1. size of the arrival population Unlimited or infinite population- queue in which a virtually unlimited number of people or items could request the services, or in which the number of customers or arrivals on hand at any given moment is a very small portion of potential arrivals Limited or finite population- a queue in which there are only a limited number of potential users of the service 2. pattern of arrivals (statistical distribution) Poisson distribution- discrete probability distribution that often describes the arrival rate in queuing theory P(x)-probability x arrivals -average arrival rate P(X)= x-number of arrivals per unit of time e-2.7183 (which is the base of natural logarithms) 3. behavior of arrivals -most queuing models assume arriving customer is patient customer (people/machines that wait in line until they are served and don’t switch between lines) -balk customers- refuse to join waiting line because it is too long to suit their needs/interests -reneging customers- enter queue but th
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