This is a team assignment.

Purpose

Practice the following important architecture skills:

• Constructing and analyzing a queuing model

Overview

In this assignment, you will construct a queuing model related to SCUFS.

Specifics

• Construct a queuing model of managing vehicles attempting to enter a SCUFS highway at a given entrance at rush hour
• Assume that the system processes entering vehicles as follows:
  1. Verify that the vehicle is equipped with working SCUFS equipment [assume that 5% of vehicles fail this verification and leave the system at this point]
  2. Determine the type of vehicle [assume 70% of entering vehicles are cars, 29% are trucks and 1% are emergency vehicles]
  3. For cars: assign the car to a traffic opening
  4. For cars: accelerate the car into its assigned traffic opening
  5. For trucks: assign the truck to a large traffic opening
  6. For trucks: accelerate the truck into its assigned traffic opening
  7. For emergency vehicles: create an immediate traffic opening by slowing down approaching traffic
  8. For emergency vehicles: accelerate the vehicle into the new traffic opening

Deliverables

• Draw a queuing network whose queues provide the functionality of the system processes listed above
• Make (and of course, document) an assumption about the number of servers available at each queue. Remember that some heavily-used freeway interchanges have double entrance ramps.
• Estimate the average service time for each of the queues.
• Estimate the arrival rate at the first queue. 
• From your queuing network, your service time estimates, and your arrival rate, compute
  • The average residence time at each queue
  • The average arrival rate at each queue except the first one, whose arrival rate you estimated earlier
  • The average time in the system
  • The average number of vehicles in the system

• Turnitin.com does not accept Excel spreadsheets. Use the class drop box to submit your spreadsheet.

Notes and assumptions

• There are several valid ways to model the functionality above as a queuing network. Your queues could correspond one-for-one with the system processes listed, but they do not have to.
• It's probably a bit unrealistic, but for simplicity assume that all service times are independent and exponential. That means you can use the formulas for M/M/1 and M/M/n queues that are implemented by the macros in the spreadsheet we looked at in week 7.
• Remember: normally when a vehicle "exits" the entrance-management system, it is still in SCUFS, but traveling on the highway rather than trying to enter it.
• You are not expected to be traffic engineers; try to avoid blatantly bad assumptions about traffic, but don't waste time trying to make your model too realistic. Contact me if you are unsure about what "too realistic" might be.
• For lots of background information, see the Stallings Queuing Analysis paper