The optimal management of a queueing system with controlling arrivals

This article considers the optimal management problem of a finite capacity M/H-2/1 queueing system, in which the unreliable server operates the F-policy. When the number of customers in the system reaches its capacity K (K < infinity), no further arriving customers are allowed to enter the system until a certain number of customers who are already in the system have been served so that the number of customers in the system decreases to a predetermined threshold F (0 <= F <= K - 1). At that time, the server needs to take an exponential startup time and allow customers to enter the system. The F-policy investigates the most common issue of controlling arrival to a queueing system and a startup time is required before allowing customers to enter the system. This system is useful in many potential applications for wireless communication networks, transportation service systems, and production systems. Some important performance measures are derived. A cost model, developed to determine the optimal capacity K, the optimal threshold F, the optimal setup rate, and the optimal repair rate at a minimum cost, is also studied.