Performance optimization of distributed-system models with unreliable servers

Models of distributed systems with servers subject to breakdown and repair are investigated for optimization of performance measures. The optimization problems are the cost minimization, response time minimization, and throughput maximization. The system is modeled by a preemptive-resume priority queuing network. The mean-value analysis algorithm is applied to derive a relationship between the multiprogramming level and performance measure formulas. Based on this relationship the Lagrange multiplier technique is applied to carry out the optimization of performance measures. Optimal service rates are obtained that reach a target throughput while minimizing the total cost. Servers are also treated individually in order to minimize the mean response time of a particular server in the system in order to find the optimal service rates which minimize the response time of a particular server while reaching a target throughput. Formulas are derived for determining the maximum throughput of the system; unfortunately, it has no closed-form solution. However, it can be solved using the binary search and insert value method. Numerical examples illustrate the solutions