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# 516 Queuing

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### 516 Queuing

1. 1. Delays at DDM International Airport<br />Ryan Hess<br />Tonisha Morris<br />Sandra Nasilowski<br />Phil Sampona<br />
2. 2. Queuing Theory<br />Queuing= waiting lines <br />Orderly fashion<br />Elements of a queue<br />Arrivals that need service of some kind.<br />Service facilities that take care of the arrivals.<br />The queue, where the arrivals wait until they can be serviced.<br />
3. 3. Queuing TheoryExamples of Queuing<br />M/M/1:<br />This is the simplest queuing system to analyze. Here the arrival and service time are negative exponentially distributed (Poisson process). The system consists of only one server. This queuing system can be applied to a wide variety of problems as any system with a very large number of independent customers can be approximated as a Poisson process<br />M/D/n:<br />Here the arrival process is Poisson and the service time distribution is deterministic. The system has n servers. (e.g. a ticket booking counter with n cashiers) Here the service time can be assumed to be same for all customers)<br />G/G/n:<br />This is the most general queuing system where the arrival and service time processes are both arbitrary. The system has n servers. No analytical solution is known for this queuing system<br />
4. 4. Queuing TheoryExamples of Queuing<br />Arrivals<br />Shoppers<br />Patients<br />Customers<br />Machine breakdowns<br />Finished goods<br />Pharmaceuticals<br />Airplanes<br />Telephone calls<br />Arrivals Factors<br />Arrival distribution <br />When do new customers arrive? At random? In groups or singly?<br />Size of population from which customers are drawn <br />Is the population effectively infinite or is it small enough that each arrival means one less new customer in the future?<br />
5. 5. Queuing TheoryExamples of Queuing<br />Servers<br />Clerks<br />Doctor<br />Operating teams<br />Stock<br />Repair persons<br />Dealer<br />Pharmacy in hospital<br />Runways<br />Circuits<br />Fire fighters<br />Service factors<br />Service time distribution <br />– how long it takes to serve an arrival<br />Number of parallel channels or servers <br />how many checkout counters at the grocery store<br />How many stages of service there are<br />
6. 6. Queuing TheoryExamples of Queuing<br />The Queue<br />Checkout line<br />In waiting room<br />Waiting list<br />Back orders<br />Broken machines<br />Inventory<br />Stack in air<br />Uncompleted calls<br />Burning buildings<br />Queue factors<br />How many queues -- one or more than one?<br />Service priority among customers. <br />Possibilities include first come first served<br />
7. 7. Airport Conditions in Good Weather <br />Capacity of 120 planes per hour<br /># of arrivals = # of departures<br />3 runways in operation, 2 runways used for arrivals<br />45-60 arrivals per hour<br />Cost of Delays<br />\$350 per plane per hour for a 19 seat plane<br />\$1500 for a 150 seat plane<br />\$600 for regional jets<br />Passenger cost of waiting is \$25 per hour<br />
8. 8. Delayed flight is one arriving or departing 15 minutes past schedule<br />70% plane capacity<br /> Describe the operating conditions, average delay times (i.e. waiting times), and operational and passenger delay costs <br />What proportion of flights will be delayed?<br />
9. 9. Inclement Weather<br />In bad weather<br />2 runways for both arrival and departure<br />Capacity of 45 planes per hour<br />Severe Weather<br />10 days per year<br />1 runway for both arrivals and departures<br />Capacity of 30 planes per hour<br />
10. 10. Problem<br />Describe relevant operating conditions for these moderate and severe weather conditions and associated costs for the three types of planes. <br />proportion of flights will be delayed? <br />What would happen if an additional runway costing \$1 million was built<br />Should it be built?<br />Most efficient use of it?<br />Assuming 18 hour days and 365 operating days<br />
11. 11. RESULTS<br />MODERATE WEATHER<br />Arrival Rate: 45 – 59<br />Service Rate: 30<br />Servers: 2<br />
12. 12. Moderate Weather<br />
13. 13. Moderate Weather<br />
14. 14. Moderate Weather<br />
15. 15. Inclement Weather<br />Arrival Rate: 35 – 44<br />Service Rate: 22.5<br />Servers: 2<br />
16. 16. Inclement Weather<br />
17. 17. Inclement Weather<br />
18. 18. Inclement Weather<br />
19. 19. SEVERE INCLEMENT WEATHER<br />Arrival Rate: 20 – 29<br />Service Rate: 30<br />Servers: 1<br />
20. 20. Severe Weather<br />
21. 21. Severe Weather<br />
22. 22. Severe Weather<br />
23. 23. Costs<br />
24. 24. Recommendations<br />With the savings being nearly \$2 million per year, it is a no-brainer to add another runway.<br />The most efficient way to use the new runway would be for departures when all runways are in use.<br />During inclement weather it would be use for both arrivals and departures.<br />