Examining the Performance of a Distributed System Through the Application of Queuing Theory

The paper studies the performance of a distributed computing system using Markov chains and queuing theory. The system under study possesses a buffer capacity of N and M servers. Service time is distributed exponentially. Customers entering the system in a Poisson flow consist of a random number of tasks ranging from 1 to K. The probability that a customer contains k tasks is \(b_k\) , and the normalization condition is satisfied: \(\sum _{k=1} ^{K} b_{k} = 1\) . Each individual task is serviced on a separate server. The order of service is determined by the FIFO principle. The paper describes a system using a Markov chain and provides formulas for calculating its performance characteristics. It compares the performance characteristics computed analytically to those obtained from a real distributed computing system.