## A Survey on Queueing Systems with Mathematical Models and Applications

Read this paper on waiting line analysis and queues. It provides a good survey of the theory and uses of this type of analysis. Pay particular attention to sections 1 through 3. How might these models be used to balance firm costs with different levels of customer satisfaction?

### 5. Performance Measures in Queueing System

#### 5.1. Performance Measures

Performance measures refer to the service quality as seen by the customers. There are different nature and design of the queueing models and so are the measures the performance. The main objective of proposing a queueing model is to provide the better service in minimum cost and minimum waiting time. Validity of these performances can be checked by means of simulation. There are some performance measures in the analysis of queueing models as follows:

(i) Distribution of the waiting and the sojourn times: Time spent by a customer in a queue is calculated in two categories. The first is the waiting time before starting to receive the service and the second is the sojourn time which includes the waiting time plus the service time.

(ii) Distribution of the number of customers: In a single server queueing system, there will be one customer receiving the service whereas in multiple server queueing system, there could be the customers equal to the number of servers receiving the service. Number of customers in a queueing system refers to the customers including or excluding the one or all the service.

(iii) Distribution of amount of work: It is the sum of service times of the waiting customers and the residual service time of the customers in service. Residual service time signifies the time that a new arrival waits until being served in a non-empty queue.

(iv) Distribution of busy period: When customers arrive to the server for the service, the server becomes busy. Busy period of a server is the time during which server is working continuously. While calculating the performance measures, we are interested in mean performance like the mean waiting time and the mean queue length.