# Can We Use Burstiness Mathematical Modeling To Optimize Swarm Warfare Defense Systems?

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For those of us who study bottlenecks in data flow and communication networks, we realize there are many ways of alleviating the challenges or overwhelming of such systems. Burstiness and the challenges it poses to data flow in networks, or ‘denial of service attacks’ is indeed similar, philosophically speaking, to the problems of mitigating against incoming swarms of missiles, warfighters, robotic unmanned suicide systems or the appearance of electronic decoys during a large scale attack. Since nothing is invisible, stealth technologies only allow the enemy attack to get so far, once detected, any viable attack no matter how close will rely on some form of strategy that includes swarming and overwhelming of defense systems with false positive decoy targets.

Now then, just so we are all on the same page here, let me take a moment to define terms:

(1) The Definition of Bursty: In telecommunication, the term burst transmission or data burst has the following meanings: Any relatively high-bandwidth transmission over a short period. For example, a download might use 2 Mbit/s on average, while having “peaks” bursting up to, say, 2.4 Mbit/s.

(2) The Definition of Burstiness: Burstiness is a characteristic of communications involving data that is transmitted intermittently — in bursts — rather than as a continuous stream. A burst is a transmission involving a large amount of data sent in a short time, usually triggered as a result of some threshold being reached.

(3) The Definition of Swarm in a Military Setting: Military swarming is a battlefield tactic designed to overwhelm or saturate the defenses of the principal target or objective. Military swarming is often encountered in asymmetric warfare where opposing forces are not of the same size, or capacity.

We know about other types of swarms employed by insects such as a swarm of bees overwhelming a large animal, like a bear attacking the hive to get to the honey. In warfare, it’s the same game. In Vietnam the Viet Cong employed this tactic with wave upon wave of mass attacks. Today, swarm missile volleys are considered the easiest way to decisively win a Naval Battle against another Navy.

Similarly, a ground land based system might strategically launch swarms at a US Naval vessel to overwhelm the new Aegis System, once the ship runs out of projectiles for defense it is either denied that area, or risks being hit and sunk.

Okay so, there are many mathematic algorithms used to detect the onset of burstiness in electronic networks and communication systems, and strategies to re-route data, slow down input, output or processing. If this fails it could cause temporary crash of the system, loss of data, or complete backup, which has happened in the stock markets with HFT (high frequency trading) systems (cite: 1). Of course, when life and death are on the line, it could spell disaster, case in point might be during combat operations, where the important warfighter data, targeting data are giving priority while other data such as logistics, accounting, and other nonessential takes a back seat (cite: 2).

One recent paper “Quadratic sample entropy as a measure of burstiness A study in how well Renyi entropy rate and quadratic sample entropy can capture the presence of spikes in time-series data,” by Kira Huselius Gylling. In the abstract it states:

“Studying various entropy measures, properties for different distributions, both theoretically and via simulation, in order to better find out how these measures could be used to characterise the predictability and burstiness of time series. We find that a low entropy can indicate a heavy-tailed distribution, which for time series corresponds to a high burstiness. Using a previous result that connects the quadratic sample entropy for a time series with the Renyi entropy rate of order 2, we suggest a way of detecting burstiness by comparing the quadratic sample entropy of the time series with the Renyi entropy rate of order 2 for a symmetric and a heavy-tailed distribution. “

So then, take a missile or projectile swarm headed for a US Navy warship or an Aircraft Carrier, as the swarm begins to diminish due to heavy defense, the defense system would detect a high entropy lull, if the swarm is being defeated, if the entropy or drop rate in numbers is slow to diminish, then it means the defense system must ramp up to overwhelm the swarm or expect the burstiness of the incoming swarm to challenge the system at a future higher level. However if the entropy drops of fast, then we know that round is being won and resources can now be allocated elsewhere for reloading or other potential threats.

Such swarm defense systems now act totally with artificial intelligence as things happen too fast for human decision making in the allocation or use directed decision making, so using this knowledge we can design a more robust system to challenge the out limits of swarm volleys against our warships. The US Navy has undergone surface warfare ‘war games’ testing the limits of their systems, in one of the first large exercises one Admiral volley’ed everything he had as soon as the game started, and overwhelmed the defense. Decimating the other side, they immediate stopped the wargame and had to start over.

He knew the vulnerability of their defense systems and the odds of getting through the layered defense. Today, most of those vulnerabilities have been shored up. Still in the future there will be swarms in much greater numbers to deal with, perhaps this is why I’ve prepared this article to help think of borrowing strategies and technologies from other domains to ensure an iron defense and survival. Think on this.

– Cite 1: Research Paper: “The Impact of Management Operations on the Virtualized Datacenter” by Vijayaraghavan Soundararajan and Jennifer M. Anderson. 2010 ACM 978-1-4503-0053-7/10/0.

– Cite 2: Thesis Paper: “The Benefits of a Network Tasking Order in Combat Search and Rescue Missions” by Murat Gocman. TUAF AFIT/GCE/ENG/09-01. USAF, Institute of Technology – Wright-Patterson AFB.

(1) Research Paper: “Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures” by Mung Chiang, Steven H. Low, A. Robert Calderbank, and John C. Doyle. 0018-9219. 2007 IEEE Vol. 95, No. 1.

(2) Research Paper: NRL – Naval Research Logistics: “A model for geographically distributed combat interactions of swarming naval and air forces,” by Connor MeLemore. 2016, DOI: 10.1002/nav.21720.

(3) Research Paper: Calhoun – Institutional Archive of Post Graduate Naval School, Thesis; “2003-12 Defense of the sea base – an analytical model,” by Henry S. Kim.

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