Show and(or) Tell – Queuing in traffic jams

<> on May 27, 2011 in Los Angeles, United States.

The operations course encourages “Show and Tell”, which is an opportunity for students to share their observations from everyday life and how it relates to concepts of operations we have learnt in class. The purpose is to keep a curious mind to identify the items in our daily life that may be relevant to operations. Professor Wei had chosen 3 students to share their observations with the rest of the class today, our very last operations management class of the term. Marcus, a Canadian engineer explained how his father had acquired a business and turned it around through operational transformation. His presentation was clear, about operations and fairly intuitive for someone with a background in operations. The only downside was that maybe it would have been a bit difficult for operations gazelles to understand given that it wasn’t exactly an everyday life problem.

Next, Carol, a Spanish engineer presented a project from her previous job where she had implemented kaizen in her work area. I am not sure I completely understood the problem being explained although it seemed to be very close to projects at my previous job. Carol’s presentation was like watching Masterchef America while Marcus’s presentation was more like Masterchef Australia. Why? Go figure! Not surprisingly, Carol won the show because the MBA program as I’d mentioned before is a perfect simulation of the real world where the American version has at least 2-3 times the viewership than the Australian one has. Now, there was a third presenter, which was me but I can’t be my own judge. All I can say is that it was just a regular everyday life problem – Traffic Jams.

I thought traffic jams were great examples of queuing, which we had learnt to analyse in class earlier during the term. Here’s a little history about why I chose to explain this and how it relates to my operations course. Ever since I’ve been living in Barcelona, I’ve mostly been a pedestrian which means I have more time to look around, watch vehicles pass by and think about them. But every now and then (50 metres), I stopped for a traffic light. Stopping for a traffic light can be more annoying when yore sitting in a bus and end up in endlessly waiting for the bus to start moving since people mostly adhere to traffic rules here in Barcelona. Also, since people follow lane discipline here unlike in India, it gets even more frustrating. When I was having a conversation with Wei about queuing one evening, I had an ‘aha’ moment and realised that maybe after all, the system in India was actually the sub-optimal one.

In unregulated traffic (like in India) every player acts in his/ her self interest and the market takes care of itself by efficiently interspersing cars, bikes and auto rickshaws (Heijunka?) leading to higher utilisation of infrastructure (close to a 100%) creating a bottleneck. This leads to traffic jams. On the other hand, in Barcelona, most of the road infrastructure is under-utilised and a constant flow is maintained due to regulation of traffic by traffic signals. Yet, sometimes, we end up in jams. After some research, I discovered that jams occur even when there isn’t an apparent bottleneck in the system and such jams are called phantom traffic jams. These jams occur due to variability in the individual driver behaviour that results in a greater collective variability on the road. This results in the formation of queues and waits in these queues.

This makes perfect sense based on the formula we learnt for the mean waiting time in a queue –

\mathbb E(W_q) \approx \left( \frac{\rho}{1-\rho} \right) \left( \frac{c_a^2+c_s^2}{2}\right) \tau
Ca and Cs are functions of standard deviation in arrival and service rates in a queue. The standard deviation is essentially a measure of variability in the driver behaviour and as variability increases, waiting time increases. QED. Also, another important concept to note is that the higher the capacity utilisation, greater is the variability and hence it is by design that roads in Barcelona are made to be under-utilised through regulation. Now, how do we regulate variability?    This might be a separate blogpost in itself but the inspiration for this would surely be my classmates who had several ideas today and I am so proud of them – zoning by speed, creation of express ways, driver less cars, etc. This is a start.

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