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Basic Elements of Queuing Model

The basic elements of a queuing model depend on the following factors :


(a)                             Arrival s distribution. Customers arrive and join in the queue according to a probability distribution. The arrival may be single or bulk.


(b)                            Service-time distribution. The service offered by- the server also follows a probability distribution. The server(s) may offer single or bulk services e.g., one man barber shop, a computer with parallel processing.


(c)                             Design of service facility. The services can be offered by the servers in a series, parallel or network stations. A facility comprise a number 6f series stations through which the customer many pass for service is called 'Tandem queues'. Waiting lines may or may not be allowed between the stations. Similarly parallel queue and network queue are defined.


(d)                            Service discipline/Queue discipline. There are three types of discipline e.g.,


FIFO - First In First Out

LIFO - Last In First Out

SIRO - Service in Random Order


'Stack' IS an example of LIFO and selling tickets in a bus is an example of SIRO. Sometimes FIFO is referred as GO (i.e., General Discipline).


Also there is priority service which is two types.

Preemptive. The customers of high priority are given service over the low priority customer.


Non-preemptive. A customer of low priority is served before a high priority customer.


(e) Queue Size. Generally it is referred as length of the queue or line length. Queue size may be finite or infinite (i.e., a very large queue). Queue size along with the server(s) form the capacity of the system.


(j) Calling Population. It is also called calling source. Customers join in the queue from a

source is known as calling population which may be finite or infinite (i.e., a very large number). To reserve a ticket in a railway reservation counter, customers may come from anywhere of a city. Then the population of the city forms the calling population which can be considered as infinite.


(g) Human behaviour. In a queuing system three types of human behaviours are observed.


Jockeying - If one queue is shorter than one join from a larger queue to it.

Balking - If the length of the queue is large, one decides not to enter into it.

Reneging - When a person becomes tired i.e .. loses patience on standing on a queue, the person leaves the queue.