Question: A service facility consists of two servers in series (tandem), each with its own FIFO queue (see Figure 8.63). A customer completing service at server 1 proceeds to server 2, and a customer completing service at server 2 leaves the facility. Assume that the interarrival times of customers to server 1 are exponentially distributed with mean of 1 min. Service times of customers at server 1 are exponentially distributed with a mean of 0.7 min, and at server 2 they are exponentially distributed with a mean of 0.9 min:

a. Run the simulation for 1000 min and estimate for each server the expected average waiting time in the queue for a customer and the expected utilization.

b. Suppose that there is a travel time from the exit of server 1 to the arrival to queue 2 (or server 2). Assume that this travel time is distributed uniformly between 0 and 2 min. Modify the simulation model and run it again to obtain the same performance measures as in part (a). (Hint: You can add an Activity block to simulate this travel time. A uniform distribution can be used to simulate the time.)

c. Suppose that no queuing is allowed for server 2.

That is, if a customer completing service at server 1 sees that server 2 is idle, the customer proceeds directly to server 2, as before. However, a customer completing service at server 1 when server 2 is busy with another customer must stay at server 1 until server 2 gets done; this is called blocking. When a customer is blocked from entering server 2, the customer receives no additional service from server 1 but prevents server 1 from taking the first customer, if any, from queue 1. Furthermore, new customers may arrive to queue 1 during a period of blocking. Modify the simulation model and rerun it to obtain the same performance measures as in part (a).