Location Models For Airline Hubs Behaving as M/D/C Queues

1. Location Models For Airline Hubs Behaving as M/D/C Queues By: Shuxing Cheng Yi-Chieh Han Emile White

2. Outline • Background • Hub network: airline, communication network • Problem statement and model building • Analytical model • Difficult point • Queuing theory background • Queuing example • Kendall notation • M/D/C queue

3. Airline

4. Hubs • A hub is a node of the network that concentrates traffic from several origins and distributes it to the final destinations. • In multi-hub networks, the traffic is concentrated at a hub and sent from there to a second hub, which distributes it to the final destinations. • The benefit of hubs is that the transportation between hubs is less expensive per unit flow than the transportation between a hub and a non-hub. • As traffic levels increase, hub airports become more congested than non-hub airports, because they receive higher traffic levels.

5. Airline Hub Network

6. Model • This paper proposes models that can be used to determine the optimal hub locations in a network system. • The optimal network is one that: • Minimizes cost of the network. • Prevents high levels of congestion at particular hubs. • However, congestion at an airport is hard to model because of certain problems.

7. Problem #1 • The arrival rate of planes at the hub airport is highly variable throughout the day. • Airplanes follow a schedule, however: • Flights are often delayed at their origin airport or during the flight. • Weather conditions • Departing flights may be delayed, thus delaying the landing of arriving aircraft. • The actual arrival rate of airplanes at a hub airport is often non-deterministic.

8. Problem #2 • The service rate of aircraft varies: • In the short run, it can be assumed constant. • In the long run, there will be variation in the service times due to different causes: • Type of plane that is serviced. • Weather conditions • Passengers transfer between airplanes at hubs, thus making service times dependent upon the arrival time of other flights. • The service rates of aircraft are not identical and independently distributed (i.i.d).

9. Problem #3 • Upon arrival, airplanes must go through three processes: • Landing on a landing runway • Service at the gate • Departure through a take-off runway • The probabilistic distributions of these services are very difficult to determine. • Total time required is highly variable.

10. Solution • Due to these problems, approximation models are more useful. • We can use a peak hour analysis. • Traffic will be at it’s highest level. • We assume that average arrival rate and the service rate are both constant. • This allows us to model an airport hub as an M/D/C queuing system. • Poisson arrivals, deterministic service time D, and the number of servers, C.

11. Queuing theory • A large field within stochastic process • A mathematical tool having a direct engineering background • A lot of applications • Business analysis • Engineering system performance modeling • The next slides show several examples of different queuing theory models.

12. A queuing system model • We want • Items waiting: • Waiting time: • Items queued: r • Residence time: • Given • Arrival rate: • Service rate: • Number of servers:N

13. Multiserver queue

14. Kendall notation • A queue is denoted as Q1/Q2/Q3/Q4/Q5 Qdisc • Q1: denotes the distribution of inter arrival times to the queue • Q2: denotes the distribution of service time • Q3: denotes the number of servers • Q4: denotes the maximum number of slots in the queue • Q5: denotes the population of the system Q1, Q2 can be assigned to M or D • M: Exponential (memoryless) • D: Constant Q4, Q5 can be omitted if they are assumed to be infinity • Qdisc: the discipline that governs in which order the members of the queue are being served, it can be FCFS, LCFS, Round-Robin

15. M/D/C queue • M: Poisson distribution • D: The service time is constant • C: The number of servers • Queue discipline: FCFS • Relationship: Independence of arrival rate and service rate