Queueing Theory Study of Round Robin versus Priority Dynamic Quantum Time Round Robin Scheduling Algorithms Maysoon A. Mohammed, Mazlina AbdulMajid Balsam A. Mustafa Faculty of Computer Systems & Software Engineering Universiti Malaysia Pahang Kunatan, Malaysia maysoon.ameir@gmail.com, mazlina@ump.edu.my, balsam@ump.edu.my Rana Fareed Ghani Department of Computer Sciences University of Technology Baghdad, Iraq ranafghany@yahoo.com Abstract — The queue size distribution and average waiting time for a time-shared system using round-robin (RR) scheduling, with and without overhead, are determined. In this study, the incoming processes are prioritized, and dynamic quantum times are assigned depending on the level of priority. With these parameters, RR versus priority dynamic quantum time round robin scheduling algorithm is analyzed to explore the effect of changing the quantum time of processes and determine the optimum context switches, turnaround time, and waiting time. Keywords— queueing theory; Round Robin; Priority Dynamic Quantum Time; quantum time; scheduling algorithms. I. INTRODUCTION In an operating system, many processes compete for the services provided by a central processing unit (CPU). The scheduling algorithm of a computer should distribute “bursts” of computer time among these processes such that the cycle time of a process is inversely related to its level of priority or importance while a reasonable cycle time is maintained for all machine processes. This type of systems may be studied using classical queueing theory. The processes of the system are the customers, and the CPU is the server. The processing time is the service length in the queueing system. II.RELATED WORK Few studies have intensively analyzed round-robin (RR) scheduling with another algorithm, and no recent investigations in this area have been conducted. Several related studies will be discussed in this section. Reference [1] presented an expression using RR queue size and average waiting time for M/M/1 to assume a fixed switching time overhead for every slice time. This expression determined the quantum size by studying a cost measure based on specific priorities of processes to decrease the process service time. Meanwhile, a sharing queueing model of multithreading web server was demonstrated by [2]. Multiple users were used in this experiment, and a single server, including a group of economic and flexible servers (Apache), and a single-speed router were used to verify and accomplish the model. Reference [3] presented an early analysis of the join-shortest-queue for farms with shared processor by using the single queue that was isolated from other queues. The arrival rate of the single queue was dependent on the number of processes at the same queue. Then, the impact of the other queues was described using the conditional arrival rates. In [4] the performance of RR was investigated by considering the process switching overhead such that an incoming process waited for all precedent processes to arrive to obtain time slices before it was assigned its queue time. III.QUEUEING THEORY Queuing theory is a highly effective method for identifying the current innovations in information technology and the mathematical learning of waiting queues. This theory is a branch of operation research (because of the need to make business decisions about the resources of the service) that analyzes the relationship between a request in the service system and the waiting time of the user in this system. The queueing theory is based on modelling, analyzing, and designing several processes that control human activities, such as telecommunications [5], reservation counters [6], and supermarkets [7]. This theory is also used to determine the sequence of computer operations (BLUM), computer performance [8], health services [9], and airport traffic [6]. In Computerized parallel and distributed systems are also based on queue models [10]. Erlang, a Danish mathematician, statistician, and engineer, introduced queueing theory when he was working on telephone network problems. This theory has been effectively applied in numerous fields, such as in traffic control [11], manufacture systems [12], inventory systems [13], communication systems [14] and computer systems (BLUM), and has yielded positive results. Queueing theory uses a set of tools to mathematically analyze the probability system for users and servers. This theory is also known as the theory of overcrowding [10]. Other fields that use queueing theory include aircrafts in traffic flow,