MINI-CASE :

The city of Hong Kong has a dense population with limited land suitable for housing. As a result, building trends have been toward taller apartment units, with many in excess of 140 m. With water resource management a large concern for city planners, the design of efficient building water supply systems is very important. A key component of the design process is estimating the maximum total simultaneous water demand in such buildings so that engineers can limit the water supply failure rate to less than 1%. The challenge for city engineers is to balance the cost of the water supply system with its reliability. A variety of methods have been used to estimate the maximum load. They typically involve using the flow rate of each water fixture, the number of water fixtures in a building, and an estimated parameter that captures the probability that all of the fixtures are in use simultaneously. These "fixture-unit" methods were initially developed in the mid-1900s, and were parameterized with empirical data from medium-rise housing. Hong Kong engineers were concerned that the methods might not be suitable for high-rise buildings.

To address this concern, the engineers conducted a survey of close to 600 households to find out the typical daily usage patterns of various water consuming appliances for each family member. Combining this with sampled flow rates and flow duration for each of the appliances, they were able to construct probabilitv distributions for each of these sources of variation. The engineers then used this information as input to a Monte Carlo simulation, which was used to construct a cumulative risk profile for the peak water load on the system. The simulation predicted a peak load of only 50%-60% of that computed by the "fixture-unit" method, and implied a much lower cost for the high-rise buildings' water supply system. These findings were thought to be useful in updating the methodology for computing water demand in high-rise residential construction and were seen to be a step forward in balancing cost with water supply reliabilitv.

Discussion
As a result of technological change and the emergence of new societal needs, engineers must constantly review and update design processes. In this mini-case, increases in the height of apartment towers and the need to better manage natural resources were the driving forces behind consideration of new design parameters for load estimation for sizing water plants and piping systems. The design parameters developed vears previously for low-rise or medium-rise buildings were not considered appropriate for the very highrise housing common in Hong Kong. Also, the need to manage fresh water consumption through the use of efficient water supply systems was considered necessary. The process of estimating overall peak water needs started with studying the individual components of an aparnnent water system-the typical domestic appliances one would find in an apartment.

By collecting data on the water consumption of each appliance, and then by sampling appliance usage patterns by time of day, day of week, and by time of year, the engineers were able to build up a profile for water usage patterns. The sampling allowed them to establish probability distributions for the number of users served by a particular appliance, the flow rate of an appliance, its operating time and the hourly use of the appliance. Using this as their basic unit of analysis, they could then build up a model of an apartment system by specifying its size, and how the individual components interacted.

For many engineering projects, system-level behaviour can be difficult to predict, even if there is a good model of how individual components behave. For example, in this mini-case, older peak water consumption models assumed that all appliances in the same washroom could be in use simultaneously. A more realistic assumption, validated by the interview results, was that only one could be in use at a time. While the older model might have been more mathematically tractable, the model developed in this mini-case allowed for more complex and realistic interactions. As a result, the engineers were able to produce a predictive model that met the needs of technological change and societal need.

Questions
1. Many projects can be implemented without an initial simulation study. Name a few examples, and explain why decisions about their acceptability can be made without a simulation study.

2. What are the characteristics of projects where simulation makes sense? Provide several examples of this type of project.

3. Simulations can help with evaluating different design alternatives, including the possibility of pinpointing potential problems. Can you think of other benefits provided by a simulation?

4. The output of a single simulation trial is a random variable. What is the problem with using only one trial for the purposes of decision making?

5. Ji-Ye is evaluating a proposal to build a plant that will cost 7670 000 000. A consultant has offered her a simulation that was developed to model the performance of a similar plant in the United States. If she wanted to use the American simulation, what considerations would she need to make for its application in a Chinese setting? How might she judge how much to spend on the simulation?