ers around 25 minutes [5]. Inserting the numbers into the third formula, we solve for average arrival rate, λ. Solving the equation, 25 minutes = 1/(36.67 customers per minute- λ) yields λ = 36.54 customers per minute. Notice the minimal difference between service rate and arrival rate. Using λ and µ, we further calculate traffic intensity, ρ. Solving ρ = 36.54/36.67 = .997, indicating the coaster is operating at nearly full capacity. Finally, we are able to solve for the mean number of customers in line, N. N = .997/(1-.997), so N=296 customers in line. This information is critical to engineers and park management. Expecting up to 300 customers to wait in line, queues must be constructed to allow enough waiting room. Utilizing these hard numbers, Disney’s “Imagineers” are able to plan and adapt queues to accommodate expected customers. Indeed, Disney’s Hollywood studios conducted an experiment testing a new “queue-less” wait system. Rather than waiting in line, guests are split into groups and assigned a group number. Entertaining themselves in an air-conditioned tent, guests are free to enjoy their waits. Once their group number is called, guests are free to board the ride, having escaped the drudgery of waiting in a never-ending line [6]. The application of queueing theory extends beyond planning a roller coaster. The designing of restaurants, traffic lights, grocery stores, and computer jobs all employ queueing theory. Indeed, anytime individuals queue for a service, queueing theory is applicable. While the expanse of entire queueing theory cannot be covered in a short article, resources are available and easily accessible. Deeper understanding of queueing theory will take many hours of research and dedication. Yet, if you use the time you spend waiting to learn, the server of your mind will process the job of understanding with minimal waiting time. Works Cited [1] Ward, J. "How Much Time People Spend Doing Stuff In Their Lifetime.” http://www.thefactsite.com/2010/03/ how-much-time-people-spend-doing-stuff.html (2010). [2] Adan, I. & Resing, J. Queueing Theory. (Eindhoven Univ., Eindhoven, 2001). [3]"Queueing Theory Basics." http://www.eventhelix. com/realtimemantra/congestioncontrol/queueing_theory.htm (2011). [4] Tibben-Lembke, R. S. Maximum Happiness: Amusement Park Rides as Closed Queueing Networks. Management Science 1, www.business.unr.edu/faculty/trl/ summer07/MS-happiness16.pdf (2007). [5] Testa, L. “Disney California Adventure Crowd Levels.” http://touringplans.com/disney-california-adventure/crowd-levels (2002). [6] Caldwell, L. "No lines at Walt Disney World?." http:// www.gadling.com/2010/04/09/no iines-at-walt-disneyworld-theme-park-tests-new-queue-less/ (2010). Volume 4, Issue 2. 2012
Phantom Limbs BY APOORVA MYLAVARAPU
The doctor tells you to move your left hand, and you do. He tells you to reach for the pen in his hand, and you do. His grip on the pen doesn’t loosen, and you feel a sharp pang of pain shoot up your arm. Suddenly, you realize that your arm was amputated three years ago after a car accident. Then why is it that your arm extends and retracts unexpectedly? Why do you feel jolts of pain in your arm when you touch your cheek? Why do you still feel voluntary movements in your arm, years after its amputation? Approximately 98% of amputees experience a phantom limb, a sensation that an amputated limb is still present and occasionally painful. First observed in 1872, this ghostly sensation has always been a mysterious phenomenon.1 Amputations result in severed nerve endings, called traumatic neuromas, which cause tumors in the nerve tissue. These neuromas continue to send pain signals to the brain even after the limb has been removed, causing the brain to believe that the limb is still there. A study conducted by V. S. Ramachandran and William Hirstein reveals that this mysterious sensation is caused by a cross-wiring of neurons in the somatosensory cortex, the main receptive region for touch in the brain.1 Signals that are received from touch receptors in the skin pass via sensory nerves to the spinal cord. Here, connecting neurons pass the information to the thalamus and the sensory cortex in the brain. This information is highly topographic, meaning that the body is represented at different levels in the nervous system.2 Larger areas of the sensory cortex are devoted to sensations from the most sensitive areas of the body, including the hands and the lips. Less sensitive parts of the body are represented by smaller cortical regions. The somatosensory cortex, located in the parietal lobe, consists of a sensory homunculus: a map of sensory space, often connecting the legs to the arms, the arms to the face, the face to the mouth, and so on. This homunculus is dependent on how much sensory input it receives, so if a 9