Problem:
A queueing system has two servers (A and B) in series, and two types of customers (1 and 2). Customers that arrive to the system have their types determined immediately upon arrival.
An arriving customer is classified as type 1 with probability However, an arriving customer may balk, that is, may not actually join the system, if the queue at server A is too long. Specifically, assume that if an arriving customer finds m (m greater than or equal to 0) other customers already in the queue for A, he will join the system with probability 1/(m+1), regardless of the type (1 or 2) of customer he may be. Thus, for example, an arriving customer finding nobody else in the queue for A (i.e., m = 0) will join the system for sure [probability = 1/(0+1) = 1], whereas an arriving customer finding 5 others in the queue for A will join the system with probability 1/6. All customers are served by A. (If A is busy when a customer arrives, the customer joins a First-In-First-Out (FIFO) queue.) Upon completing service at A, type 1 customers leave the system, while type 2 customers are served by B. (If B is busy, type 2 customers wait in a First-In-First-Out (FIFO) queue.) Assume that there is only one person serving at each server (A and B). Also, 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 at server A (regardless of customer type) = 0.8 minute.
• Mean service time at server B = 1.2 minutes.
Initally the system is empty and idle, and is to run till 1000 customers (of either type and including those that balked) have left the system.
Problem Situation. We are concerned about the utilisation of the two servers, and we wish that these servers are better utilised, while at the same time, we do not want them to be over-utilised.
a) Build a simulation model in SIMUL8 to model this process. Find the average total time each type of customer spends in the system, as well as the number of balks. Also, find the maximum length of each queue, and both server utilisations.
b) Suppose the mean service time of the servers can be changed in the following ways: mean service time at server A = 0.7 minute, mean service time at server B = 1.4 minutes; and mean service time at server A = 0.6, mean service time at server B = 1.8 minutes, Experiment with the simulation model you built in a) to address the problem situation described above. Each trial should contain at least 10 runs. Results of statistical analysis, computer outputs should be included in your report. Use the number u as your initial random seed. A managerial report is NOT needed.