Navigating Complexity in Queue Management: Slightly serious insights from the Motor Vehicle Licence Renewal Office

Queue management at the motor vehicle licence renewal office offers a window into a realm of complexity that extends far beyond the waiting room. Exploring priority queuing and weighted fair queuing (WFQ), we uncover a world of probabilistic models, dynamic rules, and real-world applications that challenge conventional wisdom.

Upon arrival, patrons encounter priority queuing, where elderly individuals receive absolute precedence to accommodate potential mobility challenges. While this prioritisation addresses (quite reasonably!) the needs of a vulnerable group, it can lead to excessively prolonged waits for others, depending on the arrival rate of elderly patrons and the dynamics of the queue. Consideration of different objective functions for various demographics, including the young and old, could unveil alternative optimal solutions.

Actuaries are used to implicitly allowing for objective functions that aim to minimise mean squared errors, but this isn’t the only possibility. Aside from different penalties for waiting times for all participants, explicitly considering different costs to different groups of individuals makes it more interesting.

In contrast to absolute priority queuing, WFQ introduces a probabilistic element, ensuring that even low-priority individuals have a chance of being served at every point in time. The weights can be tuned for those different groups, still achieving prioritisation for the elderly. While wait times for low-priority customers will still be longer than priority customers, they remain finite, underscoring the equitable nature of this approach. I can imagine an algorithm where the weight depends on the wait – the longer the duration of the existing wait the more an individual is prioritised.

The network packets to which WFQ most commonly applies probability aren’t conscious, and therefore their experience of the wait isn’t important. For humans, the conscious experience of knowing that you don’t have to wait until every individual in a priority group is served before you might make the wait more palatable. I’m not a fan of gamification; overall this seems to have result in evil outcomes, greedily addictive algorithms and a worse society overall. However, the introduction of a little randomness and the possibility of a serendipitous early shot at renewing a licence might be a net positive.

Beyond the motor vehicle licence renewal office, the principles of queue management find relevance in diverse fields, including insurance companies. By leveraging similar concepts, insurers can prioritise claims payment or customer service based on factors like severity or urgency, but also explicit objective functions to optimise for target response times within particular bands, aiming for prompt resolution while maintaining fairness and efficiency. Sometimes the maths will demonstrate that based on demand and supply of support calls, failing these objectives is inevitable. Modelling can determine how often that may occur and then you can weigh up the costs of more call centre agents with the unappealing customer experiences.

These waiting processes should ring bells from prior study of queuing processes, of exponential, poisson, negative binomial and gamma distributions. These provide a mathematical framework for understanding and optimising queue management, revealing the hidden complexities behind seemingly simple processes. While you may not think about claims processes as queuing processes, there are some surprising linkages there too.

For me, delving into the dynamics of network switching provided some fun insights. In network architecture, switches play a critical role in directing data packets efficiently across networks. However, the limited capacity of switches can lead to packet loss during times of congestion. Buffers within switches temporarily store packets to alleviate congestion, but if overwhelmed, they are forced to drop packets, resulting in packet loss and network underperformance.

A smarter (yet initially counterintuitive step) is to apply Random Early Detection (RED), a mechanism that deliberately drops packets in anticipation of the switch being overwhelmed. Under RED, these strategically dropped packets provide information to network endpoints to manage the speed of transmission to prevent larger problems down the line. To an extent, this can can be likened to passengers on an overbooked flight being paid to take a different flight. However, unlike RED, this approach does not alert endpoints or other passengers to slow transmission rates, highlighting the unique challenges and solutions in network management.

While queue management may appear remote from your regular work, some exploration might be worth the time spent. By embracing probabilistic models, dynamic rules, and real-world applications, we may see a way to apply our skills in new areas, or even learn from the significant advancements in network modelling in our financial services world.