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The other side of queuing

In “No Lines, No Waiting” (August), Kevin McManus illustrates the value of queuing analysis in everyday situations. As a frequent traveler, I can relate, and many service interactions can benefit from time studies/queuing analysis to shorten customer waiting times. However, this one-sided view of the impact of queuing analysis ignores that most analyses feature a certain trade-off.

For example, in queuing systems, the number of customers in a system equals the arrival rate multiplied by the average time a customer spends in the system. From this, the average time that a customer waits is a function of both the arrival rate and the processing rate of the system. Which parts of the equation can we control? The arrival rate? Perhaps. The processing rate? More likely. So a trade-off emerges based on the levers we can use to influence the overall time the customer spends in the system.

Therefore, the service provider can hire more servers or make the current servers work faster. The trade-off is the cost of hiring workers vs. customer satisfaction vis-à-vis waiting times. Arguably, the cost of the worker is much easier to calculate than the cost associated with the customer’s waiting time.

My introduction to industrial engineering course uses an example of a fast-food restaurant. As the manager of the restaurant, I want to reduce the wait for patrons, especially during the lunch rush. Higher throughput implies happier customers and, perhaps, higher revenue.

However, I cannot hire a disproportional number of servers. Workers come at a cost and tend to be inflexible. I cannot hire someone just for a two-hour lunch shift. Moreover, the logistics of the operation may not let me employ these additional servers effectively. Given these restrictions, the optimal solution cannot eliminate waiting time, nor should it from a cost-effectiveness perspective.

With many (if not all) concepts in industrial engineering, cost/benefit analyses can help determine the correct course of action. In queuing analysis, while waiting customers may not be the happiest, prohibitively high costs and operational logistics force waiting times to occur.

Take a lesson from Disney World’s playbook. Patrons there tend to enjoy waiting in the queue because adequate distractions are offered.

Marcial Lapp
Department of Industrial and Operations Engineering
University of Michigan
Ann Arbor, Mich.

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