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

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Résumé

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.

Mots-clés

Queue networks; M/M/K model; PSO algorithm; intermittent servers; servers down; corrective maintenance; aborting; operational costs.