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How Do Queues Form?

I am sure you have been frustrated waiting in line to receive service. People who work in customer service receive a disproportional amount of responsibility for this frustration. I think everyone should do a customer service job at least once in their life.

I would like to introduce queuing theory to frame the phenomenon of queues as a mathematical rather than a management or competence problem (even though this may be true in certain cases). In addition to customer service, queuing theory can also be applied to improve manufacturing or any process in supply chain management.

Two primary factors contribute to queues:

Arrival rate - the rate at which customers or requests arrive at the queue. Not only is the rate of arrival important but the variance of rate is important. Arrival is typically much more unpredictable than service rate. Understanding the probability distribution will help you manage arrivals significantly. Arrival rates may be actively manipulated through demand management incentives to make them more predictable and/or spread out. Offering a discount during off-peak hours is an example of this.

Service rate - the rate at which customers or requests are served and leave the queue. There are different ways the service rates can improve. Investment in tools and skills can shorten the service time. Increasing the number of service providers will also increase the service rate. Reducing errors or segmenting services into different service lines or dividing a service into multiple steps in a sequence may also improve service rates.

The primary goal of queuing theory is the balancing of these two rates. However, because resources are limited and have different impacts on the queue, additional concepts/metrics should be considered to manage a queue. Here are some examples:

  • Queue length: the number of customers or requests waiting in the queue.

  • Utilization: the proportion of time a server is busy serving customers or requests.

  • Response time: the time a customer or request spends in the queue and being served

  • Throughput: the rate at which customers or requests are being serviced and leaving the system.

There are general preferences for each of these metrics but there are also other considerations. For example, shorter queue lengths are typically preferred but the response time (time spent waiting) is generally more important than the queue length. A high utilization shows that resources are maximized but it does not necessarily translate to better throughput and may also increase employee burnout. Alternatively, providing other value-added services in a queue may be more cost-effective than shortening response time (a tactic used by theme parks and well-known hotpot restaurant Hai Di Lao). In conclusion, queue management is a balancing act, and focusing on any one metric will not provide optimal results.

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