Page 113 - DCAP601_SIMULATION_AND_MODELING

Unit 7: Simulation of Queuing System (I)

A conveyor just long enough to hold only 5 bundles would not do, because this is only the Notes
average number of bundles. On the other hand, we ask the question : What is the maximum
number of bundles that can build up on the conveyor? Theoretically the answer is an infinite
number. For design purposes, however, we can use formula (4-18), and then by setting a reasonable
limit on the probability figure we can evaluate n as follows:

Suppose we build the conveyor so that 99 per cent of the time it is sufficient to hold the bundles
waiting to be baled. Thus the probability of having more than n bundles being in the system is
(5/6) = .01,
n+1
and yields
n = 24.26

Thus if the conveyor is made 24 × 1.5 = 36 meters long, with 99 per cent assurance we can say that
it is long enough. This would be an acceptable risk.
Beginning from the time of birth (generally concerning an approximately 9-month period from
the instant of commencement) until death (an entire life-time – whether concise, wide-ranging
or in between) and at many moments along the way human beings frequently discover themselves
waiting for things, events, circumstances, etc. A foremost topic of Applied Mathematics that
deals with this event of waiting is known as Queuing Theory. Using the word “Queue”, which
is more ordinary in British than American English and means “a line up” or “to form a line”, a
closely consistent body of mathematical theory has been developed to explain this ordinary
human activity – theory applicable to normal economic activity. Practical applications can be
made to the event of customers in anticipation of the delivery of goods/services, in addition to
goods-in-process approaching to be finished goods.
Queuing Theory occurs from the use of powerful mathematical analysis to notionally explain
production processes together with statistical/probabilistic methods to report for changeable
dynamic outlines within the stages of a creative process. The problem to be met - that occasioned
the growth of such theory - is simply entitled “congestion”, what happens when a system does
not function easily or proficiently.
Here the reader is invited to summon up his/her own multiple common examples for the
application of the hypothetical concepts that pursue. The claim for solutions to congestion problems
occurs all across the board of the worldwide economy, in addition to the course of every day
living. The origination of the official study of Queuing Theory is accredited to A. K. Erlang, a
Danish telephone engineer who in the 1920’s was endeavoring to predict telephone call service.
As discussed above Queuing Theory observes the progress of consumers (people) pursuing
obtainable services, in addition to goods-in- process (things) obtaining the status of completed
goods (whether capital or consumer goods). There are three regions of focus: Arrivals, Queue,
Service Facility - each of which is further subdivided by a multiplicity of logical detail. A single
process may include more than one stage/station, if the person/product passes through a series
of Service Facilities; and it may also have more than one actual Queue/channel/ waiting-line
leading to the following Service Facility(ies).
The first region of focal point considers Arrivals - entries into a productive organization. (Please
note down that the theory pertains equally to customers and goods-in-process). The number of
Arrivals is important (limited - few/many; or unlimited - probably infinite). The outline of
arrival may confess of a tight/loose agenda (so many per time period) or completely randomly
Arrivals. The behavior of the Arrivals may include quiet, patient people, stable/unstable objects,
argumentative children/adults, etc. Therefore the first region of worry is the nature and number
of the object(s) entering the process.
Secondly, concentration is drawn to the Queue/Waiting-Line itself, which once recognized
could have a limited (few or many) or unlimited inhabitants. Of greater significance is the

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