Team 2056 Page 16 of 50 Figure 4: Cumulative distribution function of a Weibull distribution We observe that the distribution had a sigmoidal shape, consis- tent with our baggage loading process. When there are few people in the plane, the time required to load baggage is relatively small since there are a lot of empty spots in the baggage bins. As the number of people increases, this time increases slowly when there still a lot of space and then rapidly as people start having to rear- range compartments to fit their luggage. As the plane reaches full capacity, the difference in time required to find space for baggage becomes minimal as most baggage bins have relatively little space left We note that the hazard rate (or failure rate) of this distribution can be given for the following expression 5) For k I we see that the failure rate is increasing. thus indicating that the frequency with which people can not find space for luggage Is Increasing 3.2.4 Queue size The initial model assumed that each processor could have an in- finitely sized queue. This makes sense for the initial processor, as
Team 2056 Page 16 of 50 Figure 4: Cumulative distribution function of a Weibull distribution We observe that the distribution had a sigmoidal shape, consistent with our baggage loading process. When there are few people in the plane, the time required to load baggage is relatively small since there are a lot of empty spots in the baggage bins. As the number of people increases, this time increases slowly when there is still a lot of space and then rapidly as people start having to rearrange compartments to fit their luggage. As the plane reaches full capacity, the difference in time required to find space for baggage becomes minimal as most baggage bins have relatively little space left. We note that the hazard rate (or failure rate) of this distribution can be given for the following expression, h(x, κ, λ) = κ λ x λ (κ−1) For κ > 1 we see that the failure rate is increasing, thus indicating that the frequency with which people can not find space for luggage is increasing. 3.2.4 Queue size The initial model assumed that each processor could have an in- finitely sized queue. This makes sense for the initial processor, as
Team 2056 Page 17 of 50 Figure 5: Model of a plane with two aisles its queue consists of the passengers lined up along the loading ramp However, for processors inside the aircraft, we must consider that actually take all processor queues but the first at a length of 2. We used a cap of 2 as it corresponded well with physical reality when considering the ratio of aisle length to passenger size 3.2.5 Planes with multiple aisles We modeled multi-aisle planes as processor sets with multiple pipelines Using this technique, planes of arbitrary sizes, topologies and en- trance points can be modeled. We describe here the technique for the modeling of a double-aisled plane, such as the Boeing 777 As in the single-aisle model, all passengers are initially queued at a single processor( see figure 5). For the double-aisled plane, this processor represents the junction point at the entry of the plane. No passengers are assigned seats at this row. From the first processor when a passenger is passed, he may move to either of two different processors. Each of these two processors begins a serial chain of processors akin to a single-aisled plane. Each passenger chooses ar aisle based on his seat assignment. As in real aircraft, certain row of the plane are widened so that a passenger can move from one aisle to the other
Team 2056 Page 17 of 50 Figure 5: Model of a plane with two aisles its queue consists of the passengers lined up along the loading ramp. However, for processors inside the aircraft, we must consider that the processor queue actually takes up physical space. Hence, we cap all processor queues but the first at a length of 2. We used a cap of 2 as it corresponded well with physical reality when considering the ratio of aisle length to passenger size. 3.2.5 Planes with multiple aisles We modeled multi-aisle planes as processor sets with multiple pipelines. Using this technique, planes of arbitrary sizes, topologies and entrance points can be modeled. We describe here the technique for the modeling of a double-aisled plane, such as the Boeing 777. As in the single-aisle model, all passengers are initially queued at a single processor (see figure 5). For the double-aisled plane, this processor represents the junction point at the entry of the plane. No passengers are assigned seats at this row. From the first processor, when a passenger is passed, he may move to either of two different processors. Each of these two processors begins a serial chain of processors akin to a single-aisled plane. Each passenger chooses an aisle based on his seat assignment. As in real aircraft, certain rows of the plane are widened so that a passenger can move from one aisle to the other