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STRUCTURE OF A QUEUING SYSTEM 453

customers in the queue at any one time and the average time a customer spends in the
queue. The major determinants of the operating characteristics for a specific queuing
situation include: the arrival rate; the service rate; the queue discipline; the calling
population.
The arrival rate is the rate at which customers arrive for service during a specified
period of time (per hour, per minute, etc.). This is typically taken as an average over
the time period. In general arrivals are assumed to be independent of each other and
to vary randomly over time. The arrival rate may be derived from empirical obser-
vation although it is more usual to assume that the arrival rate can be estimated
using a theoretical probability distribution of which the Poisson distribution is most
common.
The service rate is the average rate at which customers can be served during a
specified period of time. As with the arrival rate, the service rate is assumed to be
random.
The queue discipline refers to the order in which customers in a queue are served
and is typically an important feature in a queuing model. In many situations we
would expect this to be first-come, first served; that is, the person at the front of the
queue who has waited longest is served first; then the second person in the queue
and so on. However, other queue disciplines may be used in different situations. An
alternative discipline is last-in, first-out where the latest arrival in the queue is
served, or dealt with first. This might happen with an office clerk dealing with
incoming correspondence placed in the inbox. The item of correspondence at the
top of the pile (which came in last) may be picked up first and dealt with. You may
also operate this disciple when checking your emails – reading the most recent item
first and working down the list. A third discipline is random selection. This may
happen in an assembly line situation where an operator is assembling a piece of
equipment. The operator reaches into a box of components and selects one at
random to be used in the next assembly. Periodically the box is re-filled with more
components. Another queue discipline is scheduled service: this occurs where
customers are given a pre-determined and time-scheduled appointment for service –
as in a doctor’s or dentist’s surgery, or in a restaurant or when having your car
serviced. In this discipline customers are seen in the scheduled order regardless of
how long they have been in the queue. The final queue discipline is that where a
priority or predetermined discipline is applied. This may be appropriate, for exam-
ple, in a hospital emergency room where the most medically urgent patients are seen
first. Or in an airport check-in where first-class and business-class customers receive
priority treatment. Or where there is a pre-determined order to service, perhaps in
alphabetical order.
The calling population is the source of customers for the queuing system. Some
systems have a finite calling population; there may be 15 aircraft waiting to land at a
busy airport during the next 100 minutes for example. Other systems may have an
infinite calling population; an international retailer’s call centre for example can
reasonably be assumed to have an infinite number of potential callers over the next
hour.
Now we have an understanding of the basic terminology used in queuing theory,
let us examine the basic features of a queuing model with an example. The Dome is
a small cafeteria based in the local hospital which serves hospital visitors and
hospital staff with drinks, refreshments and light meals. The Dome operates as a
profit centre within the hospital so has to provide good food and good service to
attract customers and remain financially viable.
The Dome is concerned that the methods currently used to serve customers are
resulting in excessive waiting times. Management wants to conduct a queuing study
to help determine the best approach to reduce waiting times and improve service.

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