Queuing theory is the mathematical study of waiting lines which are the most frequently encountered problems in everyday life. For example, queue at a cafeteria, library, bank, etc.
Common to all of these cases are the arrivals of objects requiring service and the attendant delays when the service mechanism is busy. Waiting lines cannot be eliminated completely, but suitable techniques can be used to reduce the waiting time of an object in the system. A long waiting line may result in loss of customers to an organization. Waiting time can be reduced by providing additional service facilities, but it may result in an increase in the idle time of the service mechanism.
The waiting line models help the management in balancing between the
cost associated with waiting and the cost of providing service. Thus,
queuing or waiting line models can be applied in such situations where
decisions have to be taken to minimize the waiting time with minimum
The present section focuses on the standard vocabulary of Waiting Line Models (Queuing Theory).
It is a suitable model used to represent a service oriented problem, where customers arrive randomly to receive some service, the service time being also a random variable.
The statistical pattern of the arrival can be indicated through the probability distribution of the number of the arrivals in an interval.
The time taken by a server to complete service is known as service time.
It is a mechanism through which service is offered.
It is the order in which the members of the queue are offered service.
It is a probabilistic phenomenon where the number of arrivals in an interval of length t follows a Poisson distribution with parameter λt, where λ is the rate of arrival.
A group of items waiting to receive service, including those receiving the service, is known as queue.
Time spent by a customer in the queue before being served.
It is the total time spent by a customer in the system. It can be calculated as follows:
Waiting time in the system = Waiting time in queue + Service time
Number of persons in the system at any time.
The number of customers in the queue per unit of time.
The average time for which the system remains idle.
It is the first in first out queue discipline.
If more than one customer enter the system at an arrival event, it
is known as bulk arrivals.
Please note that bulk arrivals are not embodied in the models of the subsequent sections.