Arrival Process

Definition: The Arrival Process is the first element of the queuing structure that relates to the information about the arrival of the population in the system, whether they come individually or in groups. Also, at what time intervals people come and are there a finite population of customers or infinite population.

The general structure of the queuing system is shown below:

general structure of queuing system

Following are the bases on which the arrival from the input population can be classified:

Arrival process

  1. According to the Source: The source of customers coming for the queuing system can be finite as well as infinite. For example, people of a city are the potential customers for a big bazaar in the city. Hence, the population is large and is said to be infinite. Whereas in the industrial or business perspective the population cannot be infinite, it is finite. Let’s say there are 10 machines that require repair and maintenance, hence, for a maintenance crew, the population of machinery is finite.
  2. According to Numbers: This means, a customer can either arrive for a service singly or in groups. The example of individual arrival is, a customer visiting the beautician or a student going to the library counter. The customers also arrive in groups, such as a family going to a restaurant, bulk or batch arrivals, etc.
  3. According to time: Also, the time intervals at which customers arrive in the queuing system is taken into the consideration. The customer may arrive in the system at known time intervals or in a random way. Thus, the customer arriving at the regular/known time intervals is categorized as deterministic models.Sometimes, the arrival of the customers is uncertain and hence, customers reaching the system per unit time might be described by a probability distribution. However, arrival might follow any pattern, but is generally assumed that arrivals are Poisson Distributed.

Thus, all the information related to the number of the population arriving in the system at different time intervals is taken care of while designing the queue structure.

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