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Queuing theory is very important for ordering in a system. Queuing theory is the mathematical study of waiting time and queue length (Mwangi et al., 2015) (Onoja et al., 2018). Queues consist of customers, objects, or information. The need of queue formation arises when there are limited resources (Olaniyi et al., 2019). The queue contains three parts (Babicheva et al., 2015):
Arrival-Process-> It contains the total number of users/customers in the queue and their arrival pattern.
Service-Process-> It contains how the services are given to the users and how the users exit from the system.
Queue-> It contains the actual number of users depending upon its capacity.
The queuing system is influenced by the large waiting lines. The main issue in queuing theory is waiting. The queuing theory is designed in such a way that customers do not have to wait long for services (Suyama et al., 2018). The customers arrive in the system to receive the services by servers. This service is in between arrival of customers and the start of service in the queue. The queuing system depends on:
Queuing has various applications in the field of: logistics-management, distribution-management, etc.
Characteristics of Queuing Model
Following are the characteristics (Parimala, 2008) of queuing model:
The arrival rate actually determines how the user/customer arrive in a queue. The customers may arrive in groups or individually at random intervals of time.
Service Rate calculates the resources needed to start the service and how long the service will take. The service rate also calculates the number of available resources and whether the servers are in series or parallel.
Response time is the time taken by the server to generate first response /reply of user request. It is the total time taken by user request to get the system initially after entering the queue.
Waiting time is the total amount of time taken by the customers to wait in the queue as per the availability of space in the queue.
The total number of customers who can enter the system may be finite/infinite.
Kendell Notation (Felix et al., 2018) used in Queuing Model
Kendell notation is written as following: A/S/c/B/N/D~ (Khomonenko et al., 2016)
A is also called inter arrival time. It is the time between arrival of two customers. Poisson distribution is used for A as the probability distribution.
S is also called service time. It is the time taken to service the customer after it leaves the queue.
c is the total-number of servers in the queuing system/M/1 model has one server and M/M/k model has multiple server in the queuing system
B specifies the (number of customers) being serviced in the queue.
N is the total (number of customers) who can enter the queue.
D is the queuing discipline such as FIFO or priority.
Figure 1. Representation of queuing system
Figure 1 shows the queuing system. The customers may arrive individually or in groups, these customers are then placed in queue. The customers are given services to the system using the queuing discipline.