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Transportist: The Ubiquity of Queueing
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One of the things I like to do is find methods from the Transport community that can be exported to other fields. It often feels like we are a net importer of ideas, and surely we are, just as all other fields, because the number of ideas outside our field is much greater than the number of ideas generated by our field.
However the transport community has generated important ideas in the area of equilibrium and discrete choice that are now used more broadly. Queueing is another one of those (although arguably, much of this emerged out of telecommunications), where many of the core concepts are transport and spatially based.
Wikipedia writes “Queueing theory is the mathematical study of waiting lines, or queues.” A queueing process typically involves entities (e.g., customers) arriving at a service center, waiting in a queue, and receiving service from one or more servers.
Queueing processes can be observed in many natural systems, as organisms often have to wait in line to access resources or perform tasks. Here are some examples of queueing processes in nature (co-authored with GPT-4), and suggests many applications which may not have been systematically analysed with the tools at hand:
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Ant colonies: Ants are known to form queues when foraging for food or transporting resources back to their nests. They often follow pheromone trails, which help them maintain an orderly queue while minimizing the chances of getting lost. This queueing behavior enables ants to efficiently exploit food sources and distribute resources within the colony.
Honeybees: Honeybees exhibit queueing behavior when they return to the hive after foraging for nectar or pollen. Upon returning to the hive, forager bees wait in line to transfer their collected resources to the "receiver" bees, who store it within the hive. This queueing process helps regulate the flow of resources and maintains an efficient and organized system for storing and processing food.
Bird migration: During migration, some bird species form queues or "rafts" while waiting for optimal weather conditions or resting opportunities. For example, shorebirds often gather at stopover sites during their long-distance migrations, forming a queue to take turns resting and feeding. This queuing behavior allows birds to conserve energy and reduce competition for limited resources.
Fish spawning: Some fish species exhibit queueing behavior during their spawning migrations, as they navigate upstream to spawn. Fish may gather at specific locations, waiting in line for their turn to pass through narrow passages, barriers, or other obstacles. This queueing behavior helps ensure that all individuals have an opportunity to reach their spawning grounds.
Territorial behavior: In some animal species, individuals may queue for access to limited resources or territories. For example, some male animals, such as elephant seals or deer, establish a dominance hierarchy and queue for access to mating opportunities. Similarly, some bird species establish a hierarchy for access to prime nesting sites or feeding territories. This queueing behavior helps maintain social order and reduce conflict within the population.
Social interactions in animal groups: In animal groups, such as schools of fish, flocks of birds, or herds of mammals, individuals often queue to access resources or follow leaders. This queueing behavior can be crucial for maintaining group cohesion, avoiding predation, and efficiently exploiting resources. Studying the queueing dynamics of social interactions in animal groups can provide insights into the principles of collective behavior and help inform the management and conservation of wildlife populations.
Ecological succession: The process of ecological succession, during which communities of organisms change over time in response to environmental conditions, can be viewed as a queueing problem. Species "wait in line" to colonize an area, establish themselves, and potentially be replaced by other species as the environment changes. Factors such as the availability of resources, the rate of environmental change, and interspecies interactions influence the efficiency of this process. Understanding the queueing dynamics of ecological succession can provide insights into the principles of ecosystem development and inform conservation and restoration efforts.
Predator-prey dynamics: In ecosystems, predator-prey interactions can be considered as queueing problems. For instance, predators "wait in line" for prey to become available, while prey species try to minimize their risk of predation by adopting various strategies (e.g., camouflage, group behavior). The efficiency of the predator-prey interactions depends on factors such as the availability of prey, the hunting success of predators, and the overall dynamics of the ecosystem. Studying these queueing processes can provide insights into the stability and sustainability of ecosystems and inform conservation strategies.
Resource competition in ecosystems: In ecosystems, various species compete for limited resources such as food, water, or nesting sites. This competition can be viewed as a queueing problem, with species "waiting in line" for access to these resources. Studying the queueing dynamics of resource competition can provide insights into the stability and resilience of ecosystems and help inform conservation and management strategies.
Proteins walking: Some proteins, such as kinesin and dynein, "walk" along cellular structures like microtubules to transport cargo within cells. These motor proteins can exhibit queueing behavior as they compete for limited binding sites on the microtubules. This competition can lead to traffic jams and affect the overall efficiency of intracellular transport. Studying this queueing process can provide insights into the molecular mechanisms underlying cellular transport and inform the development of targeted drug delivery systems or nanoscale machines.
Membrane transport in cells: In biological cells, transport across cellular membranes can be viewed as a queueing process. Molecules "wait in line" to pass through transport proteins or channels embedded in the membrane. Factors such as the concentration of molecules, the number and type of transport proteins, and the rate of transport influence the efficiency of this process. Studying the queueing dynamics of membrane transport can provide insights into the regulation of cellular processes and contribute to the development of drug delivery strategies or treatments for various diseases.
Protein folding: The process of protein folding, during which amino acid chains fold into their functional three-dimensional structures, can be considered a queueing problem. The folding process involves a series of conformational changes, with amino acids "waiting in line" to assume their correct positions in the final structure. Factors such as the amino acid sequence, molecular interactions, and environmental conditions influence the efficiency of this process. Studying the queueing dynamics of protein folding can provide insights into the principles of molecular biology and contribute to the development of therapies for diseases related to protein misfolding, such as Alzheimer's disease and Parkinson's disease.
Virus load: The viral load, or the number of virus particles in an infected organism, can be thought of as a queueing problem in the context of the host immune system. The immune system continually works to eliminate viral particles, while the virus replicates to maintain or increase its numbers. The queueing behavior in this context can be thought of as the competition between the immune system's ability to clear the virus and the rate at which the virus replicates. Understanding this queueing process can help researchers develop more effective antiviral treatments and vaccination strategies, as well as better understand the dynamics of viral infections.
Photosynthesis in plants: In the process of photosynthesis, plants convert light energy into chemical energy. During this process, the photosystems within the chloroplasts of plant cells absorb photons, which can be considered as a queueing problem. The photosystems must process the incoming photons efficiently, taking into account factors such as the number of available reaction centers, the rate of photon absorption, and the rate of energy transfer. Understanding this queueing process can provide insights into the fundamental principles of photosynthesis and inform the development of more efficient solar energy technologies.
DNA replication and transcription: During the process of DNA replication and transcription, various enzymes, such as DNA polymerase and RNA polymerase, must "wait in line" to access specific sites on the DNA molecule. The rate at which these enzymes can bind to the DNA and process the genetic information can be considered a queueing problem. Understanding this queueing process can provide insights into the fundamental mechanisms of gene expression and regulation, and inform the development of gene therapies and other medical interventions.
Neuronal signaling: In the context of neuronal signaling, neurotransmitters can be thought of as queueing for available receptor sites on the post-synaptic neuron. When an action potential reaches the synaptic cleft, neurotransmitters are released and bind to specific receptors, initiating a response in the post-synaptic neuron. This process can be considered a queueing problem, as the rate of neurotransmitter release, the number of available receptors, and the rate of receptor binding all play a role in determining the efficiency of synaptic transmission. Understanding this queueing process can provide insights into the principles of neuronal communication and inform the development of treatments for neurological disorders.
Enzyme-substrate interactions: In biological systems, enzymes catalyze chemical reactions by binding to specific substrate molecules. The process of enzyme-substrate interaction can be considered a queueing problem, as substrate molecules "wait in line" to bind with enzyme molecules. Factors such as enzyme and substrate concentrations, reaction rates, and the availability of active sites influence the efficiency of these interactions. Understanding this queueing process can provide insights into biochemical reaction kinetics and inform the development of drug therapies or biotechnological applications.
Cellular resource allocation: In living cells, various biological processes compete for limited resources, such as energy, nutrients, and molecular building blocks. This competition can be considered a queueing problem, as different processes "wait in line" for the resources they need to function. By studying the queueing dynamics of cellular resource allocation, researchers can gain insights into the regulation and efficiency of cellular processes and develop strategies for targeted therapeutic interventions.
Astrophysical processes: In the context of astrophysics, various processes can be considered as queueing problems. For example, stars forming in dense molecular clouds can be thought of as "waiting in line" for the available gas and dust to collapse under gravity and ignite nuclear fusion. Factors such as the density of the cloud, the availability of gas and dust, and the rate of star formation play a role in determining the efficiency of this process. Studying the queueing dynamics of star formation can provide insights into the life cycles of stars and the evolution of galaxies.
Stochastic processes in physics: In physics, stochastic processes such as radioactive decay, molecular diffusion, or random walks can be considered queueing problems. Particles or molecules "wait in line" to undergo a specific event (e.g., decay, collision) based on probabilities and time scales. Understanding the queueing dynamics of stochastic processes can provide insights into the behavior of various physical systems, from the atomic scale to the macroscopic level.
Crystal growth: The process of crystal growth can be considered a queueing problem, as atoms, ions, or molecules "wait in line" to join the crystalline structure. Factors such as the concentration of building blocks, temperature, and the rate of nucleation and growth determine the efficiency of this process. Studying the queueing dynamics of crystal growth can provide insights into the principles of crystallography and materials science and help develop advanced materials and manufacturing techniques.
Electron binding processes: In atomic and molecular systems, electrons can be thought of as queueing for available energy levels or orbitals. According to the Pauli Exclusion Principle, no two electrons can occupy the same quantum state simultaneously, so electrons fill available energy levels in a queue-like manner. This queueing behavior determines the chemical properties of atoms and molecules and plays a crucial role in processes such as chemical bonding, absorption/emission of light, and electrical conductivity. Understanding this electron queueing process can provide insights into the fundamental principles of chemistry and materials science.
Particle collisions in high-energy physics: In high-energy physics experiments, such as those conducted at particle accelerators, particles "wait in line" to collide with one another at extremely high speeds. Factors such as the number of particles, the rate of collisions, and the energy involved in the collisions determine the efficiency of this process. Studying the queueing dynamics of particle collisions can provide insights into the fundamental principles of particle physics and the nature of the building blocks of the universe.
Atmospheric processes: Atmospheric processes, such as the formation and dissipation of clouds, can be considered queueing problems. Water vapor in the atmosphere "waits in line" to condense into cloud droplets or ice crystals, depending on factors such as temperature, humidity, and the presence of cloud condensation nuclei. Conversely, when clouds dissipate, water droplets or ice crystals must "wait in line" to evaporate or sublimate back into water vapor. Understanding these queueing processes can help researchers develop more accurate weather and climate models.
Rainfall and river systems: Rainfall can be thought of as a queueing process in the context of river systems and water resource management. As rain falls on a catchment area, it must be absorbed by the soil or flow into rivers and streams. The capacity of the soil and river systems to absorb or transport water can be considered analogous to queueing, with rainwater "waiting in line" to be processed. Understanding this queueing process can help researchers predict and manage the impacts of extreme rainfall events, such as floods or droughts.
Geological processes: Earth's geological processes, such as sedimentation, erosion, and the formation of rock layers, can be considered queueing problems. For example, sediment particles in a river or ocean environment "wait in line" to be deposited, forming layers over time. Factors such as the rate of sedimentation, the capacity of the depositional environment, and the influence of other geological processes (e.g., tectonic activity) all play a role in determining the efficiency of sediment accumulation. Understanding these queueing processes can provide insights into Earth's geological history and inform the exploration of natural resources.
Sand going through funnels/channels: When sand particles flow through a narrow funnel or channel, they can exhibit queueing behavior similar to other granular materials. As the particles encounter the bottleneck, they form a queue, taking turns to pass through the narrow opening. The queueing process can lead to intermittent flow patterns and jamming, depending on factors such as the size and shape of the particles, the width of the bottleneck, and external forces. Studying this queueing behavior can help us understand the fundamental principles of granular flow and develop more efficient industrial processes involving granular materials.
Tectonic plate movement: The movement of Earth's tectonic plates can be viewed as a queueing process, as plates "wait in line" to move, interact, or change due to the forces and processes occurring within the Earth's mantle. Factors such as the rate of mantle convection, plate velocities, and the type of plate boundary interactions (convergent, divergent, or transform) influence the efficiency of this process. Understanding the queueing dynamics of tectonic plate movement can provide insights into the processes that shape Earth's surface and inform the study of natural hazards, such as earthquakes and volcanic eruptions.
Volcanic formation: Modeling the formation of a volcanic chain like Hawaii as a queueing process would be unconventional, but it could be an interesting way to represent the sequence of events involved in the formation of these chains.
In the case of a volcanic chain, you could consider the volcanic activity as a "customer" that arrives at different locations along the chain, and the mantle plume or the hotspot as the "server" that generates the volcanic activity. To model the formation of the Hawaiian volcanic chain as a queueing process, you might make the following assumptions:
The volcanic activity at a particular location is the "server" that provides the volcanic service.
The hotspot or mantle plume is the "customer" that arrives at different locations along the chain.
The queue represents the locations along the chain where the hotspot or mantle plume arrives, with the volcanic activity at each location "serving" the hotspot or mantle plume in sequence.
The arrival rate of the hotspot or mantle plume could be modeled as the rate at which the tectonic plate moves over the hotspot, causing it to "arrive" at new locations where volcanic islands form.
The service rate of the volcanic activity at a specific location could be modeled as the rate at which the volcanic activity decreases or ceases altogether once the hotspot moves away from that location.
With these assumptions, you could potentially model the formation of the Hawaiian Islands as a queueing process where the hotspot or mantle plume is the "customer" that moves along the chain and is "served" by the volcanic activity at each location.
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