On the other side of this forum, there is a
raging debate over the potential impact of sequestration on security lines. Unfortunately, lost in the debate is that there is a real possibility, supported by mathematical theory, that lines could get very long.
I do not work for the TSA, I do not like the TSA, I am not here to defend the TSA. I am an expert in queueing theory. Please continue reading only if you would like to understand why an 8% cut in the TSA's checkpoint capacity could result in lines that are an order of magnitude above the length they are today.
Congestion in queues is derived from variability. If people arrived on regular intervals and everyone took exactly the same amount of time to be screened, there would never be a line. However, as in most service systems, the time it takes to complete a security screening varies from person to person.
If we assume a very basic queueing model, the
M/M/1 queue, the total waiting time (i.e., time to get through security) is given by 1/(SERV_RATE-ARR_RATE), where SERV_RATE is the service rate (number of people processed per hour) and ARR_RATE is the arrival rate (number of people entering the system per hour). Thus, you can see that the waiting time does not depend linearly on the service rate, meaning an 8% decrease in the service rate does not result in an 8% increase in waiting time. In fact, as the service rate gets closer and closer to the arrival rate, waiting time gets very large.
Example: Consider a small checkpoint where 150 passengers arrive per hour, and there is screening capacity for 165 passengers per hour. Then the expected waiting time is 4 minutes (1/15 hour). Now, assume that the screening capacity is cut by 8% to 151.8 per hour. Then the expected waiting time will be 33.3 minutes (1/1.8 hour), which is over 700% increase. The key point is that depending on the arrival and service rates, an 8% cut could result in a waiting time increase that is much larger than 8%.
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