INE $332$ SYSTEMS MODELING $$ HOMEWORK $1$

Save this document as yourname$\_$lastname$\_$lab$3.$docx after filling in your answers. Submit it along with your two Arena model files on Learn by $17$:$00$ on Friday, April $5.$

Question $1.$ Construct an Arena simulation model of a bank that has a single teller. Customers arrive to the bank according a Poisson process with rate $10$ customers per hour. The teller serves the customers one by one according to first$-$come$-$first$-$served $($FCFS$)$ service discipline. The time to serve a customer has triangular distribution with minimum $3$ minutes, mode $5$ minutes, and maximum $8$ minutes. Save your model as yourname$\_$lastname$\_$mm$1.$doe. Run the model for a replication of $1,000$ hours. Fill in the following table.

average waiting time in queue

teller utilization

Question $2.$ Consider a very small factory which consists of a machining station and an inspection station. Jobs arrive randomly to the system with exponentially distributed interarrival times with mean $1$ hour. The machining station processes jobs one by one with service times uniformly distributed between $39$ and $45$ minutes. Jobs that complete machining are inspected by a single inspector one by one. Inspection takes a uniformly distributed amount of time between $45$ and $51$ minutes. $90\%$ of inspected jobs are found satisfactory and sent to the warehouse while $10\%$ have to go back to the machining station to restart the whole process. Construct an Arena simulation model of this system and save it as yourname$\_$lastname$\_$inspection.doe. Run the model for $1,000$ hours without a warm$-$up period and fill in the following table.

average waiting time in machining queue

average queue length at machining

average waiting time in inspection queue

average queue length at inspection

utilization of machining station

utilization of inspection unit

number of parts sent to warehouse

number of parts sent back to machining