CS 177 Winter 2006 Assignment 1

Elevator Scheduling in High-Rise Buildings

Due: Friday, February 10, 11:59 PM

Introduction

A brief history of elevators, and a tutorial on their basic operating principles, can be found at http://science.howstuffworks.com/elevator.htm/printable. In this assignment, we are specifically interested in cable-operated elevators suitable for high-rise buildings, rather than the hydraulic elevators we have on the UCR campus.

Elevators make large high-rise buildings practical by making it fast and easy to move people and goods to any floor without heavy physical work. Unfortunately, the number of elevators required grows much faster than linearly as the buildings become taller. Thus, the designers of mega-buildings starting with the World Trade Center have had to develop complex elevator systems, with large high-speed shuttle elevators feeding “sky lobbies” part way up the building, at which point passengers must transfer to smaller local elevators to reach their destination. (http://www.kone.com/en_CN/main/0,,content=38016,00.html.)

For this assignment, you will be developing a basic elevator simulation model for a medium-sized building served by one bank of elevators. In future assignments, you will modify your program to handle larger and more complex systems.

Problem Specifications

Assume that the elevator bank serves 10 floors of offices, located directly above the ground floor (which we will call floor number 0). Adjacent floors are 4 meters apart, so an elevator ride from floor i to floor j covers a distance of 4*abs(i–j) meters.

Approximately 1000 people work in these office floors (i.e., 100 per floor), most of whom follow a similar 8-hour workday with a one-hour break for lunch. Figure 3 in http://www.sal.hut.fi/Publications/pdf-files/rsii97b.pdf shows the results from a measurement study of elevator traffic as a function of time-of-day for an office building in Australia. Based on these results, we want to make sure that our elevator bank can handle the following peak traffic patterns:

Passenger Class	Entry floor	Exit floor	Morning peak rate	Lunch Hour peak rate
Inbound	0	Random: 1 – 10	12 / minute	7 / minute
Interior	Random: 1 – 10	Random: 1 – 10 (but not entry)	4 / minute	8 / minute
Outbound	Random: 1 – 10	0	2 / minute	7 / minute

In all cases, the inter-arrival time between consecutive passengers of the same class follow the exponential distribution, using the rate shown in the corresponding table entry.

Whenever an elevator stops at a floor to pick up or drop off passengers, its doors remain open for 10 seconds, plus an additional 2 seconds for every additional passenger movement beyond the first one. The elevator can carry a maximum of 10 passengers. An elevator will not stop to pick up more passengers if it is full and none of its current passengers wants to get off at that floor.

The elevator’s travel time between floors is based on an engineering study published in Elevator World. In this example, the elevator has a “maximum cruising speed” of 2.5 meters/second, but changes in speed happen gradually to avoid causing discomfort to the passengers.

Please note that these graphs contain some errors and approximations. In particular, the sign of the acceleration at time 17 seconds must be negative, not positive. More importantly, the units on the horizontal axis must be half-seconds, not seconds, or else the relationship between speed and distance during the middle “cruising” period makes no sense. After making this adjustment, and recognizing that the time axis starts at 1, not 0, we can estimate that the elevator requires approximately 8 seconds to travel 2 floors (i.e., a distance of 8 meters). Since each additional floor beyond the first two simply increases the “cruising time”, we will assume that an elevator ride from floor i to floor j requires 6.4 + 1.6 *abs(i–j) seconds.

The movement of elevators generally follows a simple pattern of alternating directions. If the elevator is currently traveling “up”, it keeps going in the same direction until it has discharged all its current passengers and there is nobody has called for the elevator from a higher floor. At that point, the elevator changes its direction of travel to “down” and follows the same policy in the opposite direction. Elevator scheduling becomes more complicated when a building contains a bank of elevators serving the same set of floors. In this case, there is (usually!) only one call button per floor, and each call is answered by the first available elevator with room for more passengers and traveling in the requested direction.

Your goal in this assignment is to determine how many elevators are required in this building, given the industry standard requirement that the average waiting time for a passenger should be less than 20 seconds, and the average trip length should be less than 2 minutes.