We often need to use public toilets when we attend events at public spaces such as stadiums. In the District of Columbia and few other US states, all single-occupancy restrooms open to public must be designated gender-neutral, designated with gender-neutral language.^[1] A few other states in the US have similar laws. In most states and municipalities in the US, building codes and regulations require gender-specific designations for bathrooms and fixtures used in restrooms, ruling out gender-neutral or unisex restrooms.

The issues of gender, discrimination, and bathroom use is an ongoing cultural and political debate. In this question, you should leave aside the debate and your own biases/beliefs about gender and bathroom use. You are expected to analyze a practical problem, confined to the current practices, policies, and laws.

In the absence of spaces designed for gender-neutral use, public has only two choices: womens or mens bathrooms. In New York City, the public laws prior to 2005 required that womens restrooms in a building or facility should occupy equal floor space as the mens restrooms, e.g., 25 square meters for each. Is this fair? The answer depends on how you measure fairness and the answer is clearly No! when you consider the average waiting times to use the public restrooms.

In 2005, New York City passed a law requiring that all new or significantly renovated places of public assembly have two womens toilet fixtures for every one devoted to men to have the same flushing capacity for both genders or to achieve the potty parity. Please read the article New Ballpark Statistic: Stadiums Toilet Ratio at https://nyti.ms/34dmWS0 for more information.

One of the readers of The New York Times posted the following comment on the website:

Has anyone actually collected reliable data and done the math on this issue? There has to be an (undoubtedly complex) algorithm that addresses both the likely male/female ratio of users against the average time and frequency of use.

Answer the questions below for a queueing system that serves two market segments with two designated types of servers., i.e., Segment A is served by only Type A servers and Segment B is served by only Type B servers. In the article, Segment A corresponds to users of womens restrooms and Segment B corresponds of users of mens bathrooms.

1. (4 points) Consider the building laws prior to 2005 in New York City. At a National Football League match at a stadium in New York City, why might the length of restroom queues for

Segment A be longer than those of Segment B? Explain clearly. Your answer should discuss all

possible factors affecting the wait times in queues such as the arrival rates, service times, service capacity, utilization, and variability. Read the article carefully before answering the question.

2. Suppose Segment A spends on average twice as long to complete their service (this excludes the wait time in line) than Segment B. In the public restroom context, suppose an individual in Segment B occupies a Type B restroom stall for an average of 2 minutes and an individual in Segment A occupies a Type A restroom stall for an average of 4 minutes. Assume that the segments are of the same size and the same number of individuals in each segment arrive on average (5.4 people per minute) to each type of restroom. For simplicity, assume all restrooms/stalls are identical and are designed for single occupancy.
   • (2 points) What is the minimum number of stalls needed to serve the demand of Segment A, i.e., to avoid infinite waiting times in queues? When the minimum number of stalls is installed, what is the resulting average wait time in queue for Segment A?
   • (2 points) What is the minimum number of stalls needed to serve the demand of Segment B, i.e. to avoid infinite waiting times in queues? When the minimum number of stalls is installed, what is the resulting average wait time in queue for Segment B?
   • (2 points) Is there potty parity (parity in average wait time in line) across the segments when the minimum number of stalls is used to meet the demand of each segment? What is the resulting flushing capacity ratio of Segment A to Segment B? Is a 2:1 ratio stipulated in the article sufficient to achieve potty parity?
3. (2 points) Consider the average arrival rates and average service times provided in part (b). How many restroom stalls of Type A and Type B should be available at the facility for the average wait time in the queue to be less than 2 minutes for each segment?
4. (3 points) In addition to changing flushing capacity, what do you recommend to building designers, architects and policy makers to reduce wait times for restrooms in public spaces such as stadiums? Discuss the pros and cons of your recommendation.

NOTE: Your answer needs to be professional, thoughtful, and insightful to decision makers. Refrain from using insensitive, discriminatory, and/or sexist language or making recommendations to individuals in only one segment. Do not forget that the same stadium may be used for several different events and events dont necessarily attract the same ratios of Segment A and Segment B individuals. For instance, a particular type of event may attract more Segment A individuals than Segment B or vice versa. In addition, the ratios of segments may change over time and across events.