Page 234 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 11: Queuing Theory

11. Traffic intensity in a system of steady state is given by  = l / . Notes
12. For Poisson arrivals at the constant rate l per unit, the time between successive arrivals
(inter-arrival time) has the exponential distribution.

11.6 Summary

 Queuing Theory is a collection of mathematical models of various queuing systems.
 It is used extensively to analyze production and service processes exhibiting random
variability in market demand (arrival times) and service time.
 Queues or waiting lines arise when the demand for a service facility exceeds the capacity
of that facility, that is, the customers do not get service immediately upon request but
must wait, or the service facilities stand idle and wait for customers.
 The type of queuing system a business uses is an important factor in determining how
efficient the business is run.

 As the size of the population increases the world over, the number of queues and their
queue length also increase.

 In the business world, more customers mean more business transactions.
 Out of the many ways to attract customers, an efficient queuing system plays a significant
role as it reduces a customer’s waiting time. The shorter waiting time makes customers
happy, and in all probabilities, a happy customer will come back for business again.
 In a queuing system, the calling population is assumed to be infinite.
 This means that if a unit leaves the calling population and joins the waiting line or enters
service, there will be no change in the arrival rate.
 The arrivals occur one at a time in a random order and once the customer joins the queuing
system he will eventually receive the service.
 The arrival rate and services are modeled as variables that follow statistical distributions.
If the arrival rate is greater than the service rate, the waiting line will grow without
bound.
 Waiting line models that assume that customers arrive according to a Poisson probability
distribution, and service times are described by an exponential distribution.

 The Poisson distribution specifies the probability that a certain number of customers will
arrive in a given time period.

 The exponential distribution describes the service times as the probability that a particular
service time will be less than or equal to a given amount of time.
 A waiting line priority rule determines which customer is served next. A frequently used
priority rule is first-come, first-served.
 Other rules include best customers first, high-test profit customer first, emergencies first,
and so on.
 Although each priority rule has merit, it is important to use the priority rule that best
supports the overall organization strategy.

 The priority rule used affects the performance of the waiting line system.

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