Queuing Theory
QUEUING THEORY
INTRODUCTION
Waiting lines 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 is based on mathematical theories and deals with the problems arising due to flow of customers towards the service facility
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 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,
INTRODUCTION
Waiting lines 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 is based on mathematical theories and deals with the problems arising due to flow of customers towards the service facility
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 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,