SKEDSOFT

Introduction:

Queuing model is the another part of operation research or management which is directly related to costumer and service intraction.in other words it is related to directly with arriving and servicing unit of any firm.

Queuing models and Kendall's notation:

The basic queuing model is shown in. It can be used to model, e.g., machines or operators processing orders or communication equipment processing information. Among others, a queuing model is characterized by:

 The arrival process of customers:

Usually we assume that the interarrival times are independent and have a common distribution. In many practical situations customers arrive according to a Poisson stream (i.e. exponential interarrival times). Customers may arrive one by one, or in batches..

The behaviour of customers:

Customers may be patient and willing to wait (for a long time). Or customers may be impatient and leave after a while. For example, in call centers, customers will hang up when they have to wait too long before an operator is available, and they possibly try again after a while.

The service times:

Usually we assume that the service times are independent and identically distributed, and that they are independent of the interarrival times. For example, the service times can be deterministic or exponentially distributed. It can also occur that service times are dependent of the queue length.

The service discipline:

Customers can be served one by one or in batches. We have many possibilities for

the order in which they enter service. We mention:

{ first come first served, i.e. in order of arrival;

{ random order;

{ last come first served (e.g. in a computer stack or a shunt buffer in a production line); priorities (e.g. rush orders first, shortest processing time first);

{ processor sharing (in computers that equally divide their processing power over all jobs in the system).

The service capacity:

There may be a single server or a group of servers helping the customers.

The waiting room:

        There can be limitations with respect to the number of customers in the system.  Kendall introduced a shorthand notation to characterize a range of these queuing models.

       It is a three-part code a=b=c. The first letter species the interarrival time distribution and the second one the service time distribution.