A Markov Chain Model for the Analysis of Round-Robin Scheduling Scheme

In the literature of Round-Robin scheduling scheme, each job is processed, one after the another after giving a fix quantum. In case of First-come first-served, each process is executed, if the previously arrived processed is completed. Both these scheduling schemes are used in this paper as its special cases. A Markov chain model is used to compare several scheduling schemes of the class. An index measure is defined to compare the model based efficiency of different scheduling schemes. One scheduling scheme which is the mixture of FIFO and round robin is found efficient in terms of model based study. The system simulation procedure is used to derive the conclusion of the content

💡 Research Summary

**
The paper presents a probabilistic framework for evaluating and comparing CPU scheduling policies, focusing on Round‑Robin (RR) and First‑Come‑First‑Served (FIFO) as special cases of a broader class. The authors model the evolution of the ready‑queue as a discrete‑time Markov chain. Each state of the chain corresponds to the number of jobs waiting for service, and transitions are governed by two fundamental probabilities: the likelihood that a job finishes within its allocated quantum (p₁) and the likelihood that it survives the quantum and returns to the back of the queue (p₂). Under these definitions, FIFO is represented by p₁ = 1 and p₂ = 0 (a job runs to completion), while pure RR corresponds to p₁ < 1 and p₂ = 1 (every quantum forces the job to re‑enter the queue).

The transition matrix is constructed explicitly, and the stationary distribution π is obtained by solving πP = π with the normalization Σπ_i = 1. From π the authors derive key performance metrics: the expected number of jobs in the queue, average waiting time (via Little’s law), system utilization, and throughput. To compare policies, they introduce an “index measure” I = α·(throughput) − β·(average waiting time). In the experiments α and β are set to 1, making larger I values indicative of higher overall efficiency.

A novel contribution is the definition of a mixed scheduling policy that probabilistically blends FIFO and RR. A mixing parameter p∈