Queueing Theory

Queueing theory is used in service oriented organization, machine repair shop, in case of semifinished products waiting for finishing operation. The main objective is to maintain the capability for service at levels sufficient to keep
the waiting time to certain acceptable average levels.

Characteristic of Queueing Model

Arrival Pattern of Clients

In most of the cases random arrival is observed which is best described by Poisson’s process. If the arrivals are governed by Poisson’s process then the time between arrivals is exponentially distributed.

Service Discipline

It tells about the ways in which the customers are being served in the system.

• – First come first serve
• – Last in, first out
• – Service in random order

Number of Servers and Service Channels

• – Single channel, single server
• – Single channel, multiple server
• – Multiple channel, single server
• – Multiple channel, multiple server

Service Pattern

There is no standard probability distribution for service process. Infact, in many cases actual data is used for describing the service time. However, if the service times are exponentially distributed, then the model becomes simple.

Calling population

The entire sample of customers from which a few visit the service facility is known as calling population.

Remember

The size of calling population can be finite or infinite.

Customer Behavior

• – Balking: If queue is very long, customer decides not to enter the queue.
• – Reneging: Customer leave the queue without queue without getting the service.
• – Jockeying: When customer switches the queue, called jockeying.
• – Collision: In this case several customers may collaborate and only one of them may stand in the queue.
  Here the queue length may be small, but service time for an individual may be more.