Queueing System with On-Demand Number of Servers

We consider a queuing system where the number of active servers changes depending on the length of the queue. As a practical example of such system, we consider the security check queue at the airports. The number of active servers increases when the queue grows by k customers and decreases accordingly. That allows to save server resources while maintaining acceptable performance (average queuing time and its variation) for customers. We obtain a closed-form solution for the serving time, queue length and average number of servers. To validate the model we have selected the data of Dallas Fort international airport, the 8th largest in the world. Our simulation model shows a close match with analytic results. Cost savings in the number of open servers are achievable while providing acceptable waiting time for the customers.