Consider a queueing system with a fixed number n = 5 of parallel servers fed by a single q...

Consider a queueing system with a fixed number n = 5 of parallel servers fed by a single queue. Customers arrive with interarrival times that are exponentially distributed with mean 5 (all times are in minutes). An arriving customer finding an idle server will go directly into service, choosing the leftmost idle server if there are several, while an arrival finding all servers busy joins the end of the queue. When a customer (initially) enters service, her service requirement is distributed uniformly between a = 2 and b = 2.8, but upon completion of her initial service, she may be “dissatisfied” with her service, which occurs with probability p = 0.2. If the service was satisfactory, the customer simply leaves the system, but if her service was not satisfactory, she will require further service. The determination as to whether a service was satisfactory is to be made when the service is completed. If an unsatisfactory service is completed and there are no other customers waiting in the queue, the dissatisfied customer immediately begins another service time at her same server. On the other hand, if there is a queue when an unsatisfactory service is completed, the dissatisfied customer must join the queue (according to one of two options, described below), and the server takes the first person from the queue to serve next. Each time a customer reenters service, her service time and probability of being dissatisfied are lower; specifically, a customer who has already had i (unsatisfactory) services has a next service time that is distributed uniformly between a/(i + 1) and b/(i + 1), and her probability of being dissatisfied with this next service is p/(i + 1). Theoretically, there is no upper limit on the number of times a given customer will have to be served to be finally satisfied.

There are two possible rules concerning what to do with a dissatisfied customer when other people are waiting in queue; the program is to be written so that respecifying a single input parameter will change the rule from (i) to (ii):

(i) A customer who has just finished an unsatisfactory service joins the end of the queue.

(ii) A customer who has just finished an unsatisfactory service rejoins the queue so that the next person taken from the (front of the) queue will be the customer who has already had the largest number of services; the rule is FIFO in case of ties. This rule is in the interest of both equity and efficiency, since customers with a long history of unsatisfactory service tend to require shorter service and also tend to be more likely to be satisfied with their next service.

Initially the system is empty and idle, and the simulation is to run for exactly 480 minutes. Compute the average and maximum total time in system [including all the delay(s) in queue and service time(s) of a customer], and the number of satisfied customers who leave the system during the simulation. Also compute the average and maximum length of the queue, and the time-average and maximum number of servers that were busy. Use stream 1 for interarrivals, stream 2 for all service times, and stream 3 to determine whether each service was satisfactory.