Performance Assessment of Queuing Networks with Intermittently Accessible Servers, Failed Servers, Corrective Maintenance, Feedback, and Customer Abandonment

The aim of this work is to evaluate the performance of M/M/K (K > 2) multiserver queuing networks with intermittently accessible servers, failed servers, corrective maintenance, feedback and client dropouts. We first studied the two-server heterogeneous M/M/2 model, in which Server 1 is considered to be subject to outages with corrective maintenance or repair, and Server 2 is intermittently accessible, i.e. accessibility is possible but sometimes interrupted. Using the Geometric Matrix Method (GMM), we obtained the equilibrium equations of the system, and solving them by substitution enabled us to obtain the steady-state probabilities. Using these probabilities, we obtained measures of system performance. In a second step, we extended the M/M/2 model to include avariable number of servers (M/M/K (K > 2) model). As this model is more complex to analyze numerically, we used the algorithmic method. Firstly, we used the PSO algorithm to minimize operational costs by dynamically adjusting the arrival rate λ, the service rate μ and the number of servers K. Secondly, we used the PSO algorithm to minimize the average waiting time and the abandonment rate in order to maximize customer satisfaction.This will benefit both the operator and the customer.