Measures of Performance for Queuing Systems

Performance measures for queuing systems are used to assess how well the system is performing and to identify areas for improvement. Some common performance indicators for queuing systems are:

• Utilization: The percentage of time spent by the server serving customers. A high utilization rate indicates that the server is being used effectively, whereas a low utilization rate indicates that the server is being underutilized.
• Average waiting time: The amount of time customers spend waiting in line to be served. A long waiting time may indicate a system bottleneck, whereas a short waiting time indicates that the system is running efficiently.
• An average number of customers in the system: The average number of customers in the system, including those being served as well as those waiting in line. A high number of customers in the system may indicate that there is a high demand for service, whereas a low number indicates that the system is running efficiently.
• An average number of customers in line: The average number of customers in line to be served. A large number of customers in the queue may indicate that the system is unable to meet the demand for service, whereas a small number indicates that the system is operating efficiently.
• Throughput: The rate at which the system serves customers. A high throughput indicates that the system is running efficiently, whereas a low throughput may indicate that the system has a bottleneck.
• The steady-state probability distribution of the system: provides the likelihood of finding a certain number of customers in the system at any given time.
• Waiting time probability distribution: indicates the likelihood that a customer will have to wait for a certain amount of time before being served.
• Response time or cycle time: Response time, also known as cycle time, is the total amount of time a customer spends in the system from arrival to departure.

These performance measures are not all applicable to every system; the most common and important are determined by the queueing model used to represent the system and the performance objectives.

In general, there is no fixed set of processes that run on systems; thus, measuring the exact processing requirements of processes is impossible. We can, however, measure the distributions of CPU bursts and I/O bursts over the course of a process and derive a mathematical formula that identifies the probability of a specific CPU burst. The arrival rate of processes in the system can be approximated in the same way. The development of queuing theory, a branch of mathematics, resulted from the use of mathematical models for evaluating the performance of various systems. 

The fundamental model of queuing theories is the same as the model of a computer system. Each computer system is represented as a collection of servers such as CPUs and I/O devices, each with its own queue. The article focuses on discussing the Queuing System in Operating System.

The following topics will be discussed here:

1. Components of Queuing System
2. Number of Servers
3. Measures of Performance for Queuing Systems
4. Notation for Queues
5. Queue Discipline
6. Queuing Models

Let’s start discussing each of these topics in detail.