Optimal staffing policy for queuing systems with cyclic demands : waiting cost approach

Although the lost profit from lost business is quite difficult to estimate for the queuing systems with cyclic demands, this paper presents a creative and effective approach to formulate waiting cost including balking loss and reneging loss. The balking probability is defined as the balking index θ1 multiplying by the expected queue length Lq and the reneging probability is defined as the reneging index θ2 multiplying by the expected waiting time in queue Wq. Using the estimation of waiting cost allows decision maker to have the capability of determining the optimal number of servers for each planning period by minimizing the total cost including the service cost and the waiting cost.