A queueing system has two service stations (A and B) in series, with one service staff at each station, and two types of customers (1 and 2). Customers arriving to the system have their types determined immediately upon their arrival. An arriving customer is classified as type 1 with probability 0.6. However, an arriving customer may balk, i.e., may not actually join the system, if the queue for station A is too long. Specifically, assume that if an arriving customer finds m (m 0) other customers already in the queue for A, if the customer is of type 1, he will join the system with probability 1(m + 1), while if the customer is of type 2, he will join the system with probability 1/(2m + 1). Thus, for example, an arrival finding nobody else in the queue for A (i.e., m = 0) will join the system for sure [probability = 1/(0 + 1) = 1] whether the arrival is a type 1 or type 2 customer, whereas an arrival finding 5 others in the queue for A will join the system with probability 1/6 if the arrival is a type 1 customer and with probability 1/11 if the arrival is a type 2 customer. All customers are served by A. (If service staff at station A is busy when a customer arrives, the customer joins a FIFO queue.) Upon completing service at A, type 1 customers leave the system, while type 2 customers are served by B. (If the service staff at station B is busy, type 2 customers wait in a FIFO queue.) Assume that all interarrival and service times are exponentially distributed, with the following parameters: Mean interarrival time (for any customer type) = 1 minute; Mean service time of service staff at station A (regardless of customer type) = 0.8 minute; Mean service time of service staff at station B = 1.2 minutes. Initially the system is empty and idle, and is to run until 1000 customers (of either type) have entered and left the system. Problem Situation: The management of the queueing system wants the average total time spent by the two types of customers in the system to be as short as possible, with particular consideration on the average time spent in the system by type 2 customers who tend to be in the system longer. He is thinking of employing an additional service staff, but is undecided where he should place the staff, at station A or B. If the service staff is placed at station A, his service time is exponential with a mean of 0.8 minute, while if the service staff is placed at station B, his service time is exponential with a mean of 1.2 minutes. Although the average service time of the additional service staff is shorter if placed at station A, but it costs an additional 5000 per annum to management for the additional staff to be placed at station A than at station B.