Queuing System Or Process
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Input Process (cont.):
Input to the queuing system refers to the pattern of arrival of customers at the service facility.
The input process is described by the following characteristics:
nature of arrivals, capacity of the system and behavior of the customers.
(a) Size of arrivals:
- The size of arrivals to the service system is greatly depends on the nature of size of the population, this may be infinite or finite.
- The arrival pattern can be more clearly described in terms of probabilities and consequently the probability distribution for inter- arrival times i.e. the time between two successive arrivals or the distribution of number of customers arriving in unit time must be defined.
- customers arrive in Poisson or Completely random fashion.
- In fact there are many more arrival patterns are available but for simplicity,only Poisson arrivals are considered.
(b) Inter-arrival time:
- The period between the arrivals of individual customers may be constant or may be scattered in some distribution fashion.
- Most queuing models assume that the some inter-arrival time distraction applies for all customers throughout the period of study.
- It is true that in most situations that service time is a random variable with the same distribution for all arrivals, but cases occur where there are clearly two or more classes of customers such as a machine waiting for repair with a different service time distribution.
- Service time may be constant or random variable.
- Service time Negative exponential distribution and Erlang or Gamma distribution. Poisson distribution and negative exponential distribution curves.
(a) Capacity of the service system
(b) Customer behaviour
- In queuing context the capacity refers to the space available for the arrivals to wait before taken to service.
- The space available may be limited or unlimited.
- When the space is limited, length of waiting line crosses a certain limit; no further units or arrivals are permitted to enter the system till some waiting space becomes vacant. This type of system is known as system with finite capacity and it has its effect on the arrival pattern of the system,
- The length of the queue or the waiting time of a customer or the idle time of the service facility mostly depends on the behaviour of the customer.