Waiting lines at a self service fast food joint, buying tickets at the theatre, long lines at the bank are all instances to which the queuing theory can be applied. A queue is said to occur when the rate at which the demand arises exceeds the rate at which service is being provided.
It is the quantitative technique which consists of constructing mathematical models for various types of queuing systems. Mathematical models are constructed so that queue lengths and waiting times can be predicted which helps in balancing the cost of service and the cost associated with customers waiting for service.
Research started by Agner Krarup Notation for describing the Erlang of Denmark in 1903 when he characteristics of a queuing model created models to describe the was first suggested by David.G Copenhagen Telephone Exchange. Kendall in 1953. The A/B/C notation is used in all standard modern works of queuing theory.
Input Process or Arrival Pattern Service Mechanism or Service Pattern Queue Discipline Customer’s Behaviour System Capacity Transient and Steady States
Customers arrive in random fashion. The time duration between each customers’ arrival is known as inter arrival time. We assume it to follow Poisson Distribution. Customer Inter arrival Mean Arrival Rate Rate Customer Arrival Rate
Number of servers and speed of service to be considered. The time taken by a server to service a customer is known as Service Time. Service Rate Mean Service Rate
FIFO- First in First out FCFS- First Come First Serve LIFO-Last in First out SIRO- Service in Random order
Balking- When a customer leaves the queue because it is too long, has no time to wait, no space to stand etc. Reneging- When a customer leaves the queue because of his impatience. Priorities- When a customer is served based on priority and not time of arrival. Jockeying- When a customer shifts from one queue to another.
Maximum number of customers that can be accommodated in the queue. Assumed to be of infinite capacity.
When the operating characteristics are dependent on time, it is said to be a transient system. When the operating characteristics are independent of time, it is said to be a steady state.