Question

1. Consider a batch manufacturing process in which a machine processes jobs in batches of three units. The process starts only when there are three or more jobs in the buffer in front of the machine. Otherwise, the machine stays idle until the batch is completed. Assume that job interarrival times are uniformly distributed between 2 and 8 hours, and batch service times are uniformly distributed between 5 and 15 hours.

Assuming the system is initially empty, simulate the system manually for three batch service completions and calculate the following statistics:

• Average number of jobs in the buffer (excluding the batch being served)
• Probability distribution of number of jobs in the buffer (excluding the batch being served)
• Machine utilization
• Average job waiting time (time in buffer)
• Average job system time (total time in the system, including processing time)
• System throughput (number of departing jobs per unit time)

Approach: After each arrival, schedule the next interarrival time, and when each batch goes into service, schedule its service completion time. To obtain these quantities, use your calculator to generate a sequence of random numbers (these are equally likely between 0 and 1, and statistically independent of each other). Then transform these numbers as follows:

1. To generate the next random interarrival time, A, generate the next random number U from your calculator, and set A¼ 2þ6U.
2. To generate the next random batch service time, B, generate the next random number U from your calculator, and set B¼ 5þ10U.

If you cannot use random numbers from your calculator, use instead deterministic interarrival times, A ¼ 5 (the average of 2 and 8), and deterministic service times B ¼ 10 (the average of 5 and 15).

Answer 1