1. Assume a system with two processors in series where each processor has an unlimited queue in front of it; also assume FIFO queue disciplines for both servers. We need to collect data on individual entity total time in queues (total of queue time for processor 1 and queue time for processor 2; does not include processing times). Show how using Arena to collect the total queue time for each entity and place the total queue time in each entity's attribute aTotalqueueTime. (Do not be concerned about times between arrivals for the CREATE module or the delay times for each processor.)
2. You have collected time between customers arriving at Krispy Kreme Donut Shop. Would you expect the exponential distribution to apply? Why? What might you do before performing a distribution fit to examine the appropriateness of the exponential as a distribution that might fit the data?
3. A single processor has processing times coming from a NORM(30,5) distribution where time units are minutes. Items arrive with EXPO(40) minutes between arrivals. Every arrival is processed.
a. What is the expected utilization of the server?
b. Will the expected utilization change if we change queue discipline from FIFO to something else such as LIFO or shortest processing time? Why?
c. If the resource is subject to failures with up times that are NORM(200,50) and down times that are NORM(40,5) and the resource failure operating in PREEMPT mode, will the queue be explosive? Why?
4. The modeling of the number of passengers on an aircraft in problem 5-11 required that we initialize the limit on number of arrivals to a variable having a positive number and then we change that variable to have a value from the UNIF(250,360) distribution after the simulation begins. Explain why this approach in modeling the limit on arrivals was necessary rather than to just place UNIF(240,350) in the CREATE module's Limit on Arrivals window.
5. When an entity enters the system, its processing time is determined and it is this time that will be used in a process module just a bit later when the entity is in the resource to be processed. If there are 5 or more entities in queue at the time of entry, the processing time(Delay time) comes from UNIF(10,20) minutes; otherwise it comes from UNIF(15,30) minutes. Arrivals have EXPO(20) minutes between arrivals. Model in Arena.