Waiting Lines and Queuing Theory Models - Essay Example

Business Waiting lines and queuing theory models d: July 16, Waiting lines and queuing theory models A queuing model can be referred to as a system which comprises one or more than one server that offers distinctive services to the customers. Generally, the arriving customers attempt to join one or more than one queue facing the servers, if they are found to be busy. The queuing models have evidently been very useful for applications in different practical areas. This may include the production, the communication as well as the inventory systems.

The queuing system can be characterized by several elements namely, arrival procedure of customers, queue discipline, service mechanism and the behavior of customer. (Systems Modelling and Simulation) Firstly, the arrival procedure consists of portraying the way of arrival used by the customers to the system. The arrivals might derive from one or numerous sources known as the calling population that can be unlimited or limited. For instance, machines which are fixed in amount and fail at random.

The general assumption comprises independent inter arrival times with simple distribution. In practical circumstances customers arrive in accordance with Poisson stream. The arrival of customers might concern one customer at a time or customers in batches. In case of batches, the checking of documents of passengers at the border is one such example. (Systems Modelling and Simulation) Secondly, the queue discipline refers to the rule used by the server to select the subsequent customer as soon as the service of the existing customer is completed by the server.

They may be served in the batches or one by one. There are three types of common queue disciplines which are widely used. The first one being FIFO is referred to the situation where the customers get served on the basis of first-in first-out. The second one being LIFO deals with the circumstances wherein customers get served in a manner of last-in first-out. Next, according to the priority, the customers get served on the grounds of the importance they possess as well as the services required by them.

(Queuing models and some fundamental relations) Thirdly, in the service mechanism the amount of servers specifies the service mechanism. In this case each server possesses its separate queue or a familiar queue as well as the probability distribution of the service time of the customer. (Queuing models and some fundamental relations) Generally, it is assumed that the time taken for the services consist of inter arrival times, sovereign and indistinguishably distributed. For instance, the service times can be exponential or conclusively distributed.

Moreover, the service times can depend on the length of queue. An example of this could be the machine processing rates increasing in system of production when the jobs to be progressed become very large. (Queuing models and some fundamental relations) Moreover, the behavior of the customer is very essential characteristic. Some of the customers might be willing to wait for a long period of time. Conversely, other might not be patient and would decide to leave after a short time. For instance, in the situation of call centers most of the customers would hang up, if they are made to wait for a long span of time.

(Systems Modelling and Simulation) References “Queuing models and some fundamental relations”. www.win.tue.nl. n.d. Web. 16 July. 2011. “Systems Modelling and Simulation”. www.cs.utexas.edu. School Of Mechanical, Manufacturing & Medical Engineering. n.d. Web. 16 July. 2011.