Queuing Theory (Waiting Line Models)
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.
Queuing Theory Definitions
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
investment cost.
Basic Terminology: Queuing theory (Waiting Line Models)
The present section focuses on the standard vocabulary of Waiting Line Models (Queuing Theory).
Queuing Model
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.
Arrival
The statistical pattern of the arrival can be indicated through the probability distribution of the number of the arrivals in an interval.
Service Time
The time taken by a server to complete service is known as service time.
Server
It is a mechanism through which service is offered.
Queue Discipline
It is the order in which the members of the queue are offered service.
Poisson Process
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.
Queue
A group of items waiting to receive service, including those receiving the service, is known as queue.
Waiting time in queue
Time spent by a customer in the queue before being served.
Waiting time in the system
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
Queue length
Number of persons in the system at any time.
Average length of line
The number of customers in the queue per unit of time.
Average idle time
The average time for which the system remains idle.
FIFO
It is the first in first out queue discipline.
Bulk Arrivals
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.
