Performance and cost evaluation of an adaptive queuing system with customer reneging and retention: steady-state and transient analysis

Customers are often required to wait when they arrive at service facilities and see the servers are busy, or when they find other customers who arrived earlier waiting. The longer customers wait, the more dissatisfied they are likely to be and may leave the queue without receiving service (reneging). The objective of the service provider is to improve the quality of service in order to minimise the possibility of customer reneging since it increases cost and reduces revenue. Therefore, a trade-off between performance and cost should be considered when designing, planning and reducing the queues at service facilities. In this paper, we propose an adaptive queuing model with the retention of reneging customers. We derive the steady-state and transient-state performance parameters, and also discuss performance and cost evaluation. We demonstrate the utility of the model in the evaluation of waiting lines in the service industry using numerical examples.