This weekend, huge numbers of people have been carrying out their Haj pilgrimage. But no matter how they travelled, they could be sure of one thing: being stuck in queues.
With the numbers travelling to Mecca increasing each year, and expected to top 1.8 million this year, airport and border officials are well-versed in dealing with this bane of long-distance travel. But they also know how even the slightest mishap can result in queueing chaos.
It's an apposite phrase, for even a single line of people is a manifestation of what mathematicians call a "non-linear phenomenon".
Queues have much in common with the weather in that they too can fall prey to the proverbial flap of a butterfly's wings.
This is just one of the insights that emerge from one of the lesser known but most useful branches of applied mathematics, queuing theory.
Its origins lie in a classic case of a simple problem with a solution that proved anything but: how to best design a telephone exchange. In the early 20th century, a Danish engineer named Agner Erlang had to work out how many operators would be needed to handle incoming calls efficiently. This led him to discover the most basic paradox concerning queues. Imagine that calls arrive at an average of 10 a minute. How fast should operators deal with them to prevent a backlog of irate callers? The answer seems obvious: the team must also deal with them at an average rate of 10 a minute.
But Erlang's equations revealed this just isn't good enough. They showed that merely matching the rate guarantees ever-increasing numbers of irate callers waiting to be put through.
It's the same with people queuing at supermarket checkouts and border crossings: if the rate at which people are dealt with merely matches the rate at which they join the queue, the queue will get ever longer. To avoid this, operators, cashiers and immigration officials must process people faster than they arrive.
The explanation lies in that phrase "average rate". People (and phone calls) don't arrive like clockwork. They are subject to random effects, with sudden surges of arrivals followed by none at all.
Erlang captured this effect mathematically and showed the only way to avoid being caught out is for the average processing time to exceed the rate at which people turn up.
A simple point, but one with big implications. For example, it shows managers seeking "efficiencies" in service industries face a choice. They can cut staff dealing with those using the service and face ever-increasing numbers of dissatisfied clients, or they can keep the clients happy and tolerate the sight of staff standing around "doing nothing".
If clients turn up at random, as they have an annoying habit of doing in, say, hospital casualty wards, it's impossible to avoid both dissatisfaction and "overstaffing".
Queuing theory provides insights into other long-standing issues. As every woman knows, while equality may slowly be increasing in many aspects of life, there is one where it remains as distant as ever - the need to queue for the lavatory.
Yet as every architect will tell you, the provision of restrooms is usually at least as generous for women as it is for men. So why do the queues persist? Part of the answer comes from studies that confirm the suspicions of every man: women take their time.
Indeed, international studies (don't ask) show that women take about 1.5 minutes a visit, compared with just 40 seconds for men.
But queuing theory shows this doesn't mean women face queues 2.3 times longer. By a quirk of the mathematics, the length of a queue increases according to the square of the time - leading to queues more than five times longer.
At least the solution is obvious. Provide women with at least twice as many stalls as the men get. How long it will take architects to catch on to that, though, is anyone's guess.
One way around the mathematical implications of queuing theory is to use psychology. All queuing theorists have stories of how complaints were cured by giving people either entertainment or information while they wait. One such anecdote relates how the owners of a new skyscraper in America were faced with complaints about the slowness of the lifts. This seemed to demand an expensive refit until someone suggested fitting full-length mirrors next to the lifts.
The complaints evaporated almost immediately, as people passed the time preening themselves or watching others as they waited for the same slow lifts to arrive.
Designers of theme parks have found it can actually be beneficial to keep people queuing. Research has shown visitors give higher ratings to rides they have to wait for than ones they can simply walk straight on to.
It seems the anticipation of taking the ride, and seeing it in action while you queue, builds excitement in a way instant gratification cannot.
But sometimes the answer to frustration lies in our own hands. Take, perhaps, the most notorious of all its manifestations - choosing one of several queues for the supermarket checkout, only to find the one next door is surging ahead.
As ever, the source of the trouble lies with randomness. After making our choice, there are three queues we care about: the one we're in, plus our two neighbouring queues.
Even if all the queues have the same risk of random delay, the chances that on any particular occasion we've chosen the fastest is just one in three. About 66 per cent of the time, one or other of those neighbouring queues will beat ours.
The solution? Relax. In the end it all evens out and everyone has their fair share of queuing success.
Robert Matthews is visiting reader in Science at Aston University, Birmingham, England
COMPANY%20PROFILE
%3Cp%3E%3Cstrong%3ECompany%3A%3C%2Fstrong%3E%20Eco%20Way%3Cbr%3E%3Cstrong%3EStarted%3A%3C%2Fstrong%3E%20December%202023%3Cbr%3E%3Cstrong%3EFounder%3A%3C%2Fstrong%3E%20Ivan%20Kroshnyi%3Cbr%3E%3Cstrong%3EBased%3A%3C%2Fstrong%3E%20Dubai%2C%20UAE%3Cbr%3E%3Cstrong%3EIndustry%3A%3C%2Fstrong%3E%20Electric%20vehicles%3Cbr%3E%3Cstrong%3EInvestors%3A%3C%2Fstrong%3E%20Bootstrapped%20with%20undisclosed%20funding.%20Looking%20to%20raise%20funds%20from%20outside%3Cbr%3E%3C%2Fp%3E%0A
Wicked
Director: Jon M Chu
Stars: Cynthia Erivo, Ariana Grande, Jonathan Bailey
Business Insights
- Canada and Mexico are significant energy suppliers to the US, providing the majority of oil and natural gas imports
- The introduction of tariffs could hinder the US's clean energy initiatives by raising input costs for materials like nickel
- US domestic suppliers might benefit from higher prices, but overall oil consumption is expected to decrease due to elevated costs
COMPANY PROFILE
Founders: Alhaan Ahmed, Alyina Ahmed and Maximo Tettamanzi
Total funding: Self funded
COMPANY%20PROFILE
%3Cp%3E%3Cstrong%3EName%3A%3C%2Fstrong%3E%20Floward%0D%3Cbr%3E%3Cstrong%3EBased%3A%20%3C%2Fstrong%3ERiyadh%2C%20Saudi%20Arabia%0D%3Cbr%3E%3Cstrong%3EFounders%3A%20%3C%2Fstrong%3EAbdulaziz%20Al%20Loughani%20and%20Mohamed%20Al%20Arifi%0D%3Cbr%3E%3Cstrong%3ESector%3A%20%3C%2Fstrong%3EE-commerce%0D%3Cbr%3E%3Cstrong%3ETotal%20funding%3A%20%3C%2Fstrong%3EAbout%20%24200%20million%0D%3Cbr%3E%3Cstrong%3EInvestors%3A%20%3C%2Fstrong%3EAljazira%20Capital%2C%20Rainwater%20Partners%2C%20STV%20and%20Impact46%0D%3Cbr%3E%3Cstrong%3ENumber%20of%20employees%3A%20%3C%2Fstrong%3E1%2C200%3C%2Fp%3E%0A
Living in...
This article is part of a guide on where to live in the UAE. Our reporters will profile some of the country’s most desirable districts, provide an estimate of rental prices and introduce you to some of the residents who call each area home.
How to protect yourself when air quality drops
Install an air filter in your home.
Close your windows and turn on the AC.
Shower or bath after being outside.
Wear a face mask.
Stay indoors when conditions are particularly poor.
If driving, turn your engine off when stationary.
The specs
Engine: 77.4kW all-wheel-drive dual motor
Power: 320bhp
Torque: 605Nm
Transmission: Single-speed automatic
Price: From Dh219,000
On sale: Now
Company%20Profile
%3Cp%3E%3Cstrong%3ECompany%20name%3A%3C%2Fstrong%3E%20Cargoz%3Cbr%3E%3Cstrong%3EDate%20started%3A%3C%2Fstrong%3E%20January%202022%3Cbr%3E%3Cstrong%3EFounders%3A%3C%2Fstrong%3E%20Premlal%20Pullisserry%20and%20Lijo%20Antony%3Cbr%3E%3Cstrong%3EBased%3A%3C%2Fstrong%3E%20Dubai%3Cbr%3E%3Cstrong%3ENumber%20of%20staff%3A%3C%2Fstrong%3E%2030%3Cbr%3E%3Cstrong%3EInvestment%20stage%3A%3C%2Fstrong%3E%20Seed%3C%2Fp%3E%0A
Company%20profile
%3Cp%3E%3Cstrong%3ECompany%20name%3A%3C%2Fstrong%3E%20Fasset%0D%3Cbr%3E%3Cstrong%3EStarted%3A%20%3C%2Fstrong%3E2019%0D%3Cbr%3E%3Cstrong%3EFounders%3A%3C%2Fstrong%3E%20Mohammad%20Raafi%20Hossain%2C%20Daniel%20Ahmed%0D%3Cbr%3E%3Cstrong%3EBased%3A%3C%2Fstrong%3E%20Dubai%0D%3Cbr%3E%3Cstrong%3ESector%3A%20%3C%2Fstrong%3EFinTech%0D%3Cbr%3E%3Cstrong%3EInitial%20investment%3A%3C%2Fstrong%3E%20%242.45%20million%0D%3Cbr%3E%3Cstrong%3ECurrent%20number%20of%20staff%3A%3C%2Fstrong%3E%2086%0D%3Cbr%3E%3Cstrong%3EInvestment%20stage%3A%3C%2Fstrong%3E%20Pre-series%20B%0D%3Cbr%3E%3Cstrong%3EInvestors%3A%3C%2Fstrong%3E%20Investcorp%2C%20Liberty%20City%20Ventures%2C%20Fatima%20Gobi%20Ventures%2C%20Primal%20Capital%2C%20Wealthwell%20Ventures%2C%20FHS%20Capital%2C%20VN2%20Capital%2C%20local%20family%20offices%3C%2Fp%3E%0A
The biog
Simon Nadim has completed 7,000 dives.
The hardest dive in the UAE is the German U-boat 110m down off the Fujairah coast.
As a child, he loved the documentaries of Jacques Cousteau
He also led a team that discovered the long-lost portion of the Ines oil tanker.
If you are interested in diving, he runs the XR Hub Dive Centre in Fujairah
Globalization and its Discontents Revisited
Joseph E. Stiglitz
W. W. Norton & Company
TO A LAND UNKNOWN
Director: Mahdi Fleifel
Starring: Mahmoud Bakri, Aram Sabbah, Mohammad Alsurafa
Rating: 4.5/5
HUNGARIAN GRAND PRIX RESULT
1. Sebastian Vettel, Ferrari 1:39:46.713
2. Kimi Raikkonen, Ferrari 00:00.908
3. Valtteri Bottas, Mercedes-GP 00:12.462
4. Lewis Hamilton, Mercedes-GP 00:12.885
5. Max Verstappen, Red Bull Racing 00:13.276
6. Fernando Alonso, McLaren 01:11.223
7. Carlos Sainz Jr, Toro Rosso 1 lap
8. Sergio Perez, Force India 1 lap
9. Esteban Ocon, Force India 1 lap
10. Stoffel Vandoorne, McLaren 1 lap
11. Daniil Kvyat, Toro Rosso 1 lap
12. Jolyon Palmer, Renault 1 lap
13. Kevin Magnussen, Haas 1 lap
14. Lance Stroll, Williams 1 lap
15. Pascal Wehrlein, Sauber 2 laps
16. Marcus Ericsson, Sauber 2 laps
17r. Nico Huelkenberg, Renault 3 laps
r. Paul Di Resta, Williams 10 laps
r. Romain Grosjean, Haas 50 laps
r. Daniel Ricciardo, Red Bull Racing 70 laps
I Care A Lot
Directed by: J Blakeson
Starring: Rosamund Pike, Peter Dinklage
3/5 stars
2024%20Dubai%20Marathon%20Results
%3Cp%3E%3Cstrong%3EWomen%E2%80%99s%20race%3A%3C%2Fstrong%3E%0D%3Cbr%3E1.%20Tigist%20Ketema%20(ETH)%202hrs%2016min%207sec%0D%3Cbr%3E2.%20Ruti%20Aga%20(ETH)%202%3A18%3A09%0D%3Cbr%3E3.%20Dera%20Dida%20(ETH)%202%3A19%3A29%0D%3Cbr%3EMen's%20race%3A%0D%3Cbr%3E1.%20Addisu%20Gobena%20(ETH)%202%3A05%3A01%0D%3Cbr%3E2.%20Lemi%20Dumicha%20(ETH)%202%3A05%3A20%0D%3Cbr%3E3.%20DejeneMegersa%20(ETH)%202%3A05%3A42%3C%2Fp%3E%0A
Hydrogen: Market potential
Hydrogen has an estimated $11 trillion market potential, according to Bank of America Securities and is expected to generate $2.5tn in direct revenues and $11tn of indirect infrastructure by 2050 as its production increases six-fold.
"We believe we are reaching the point of harnessing the element that comprises 90 per cent of the universe, effectively and economically,” the bank said in a recent report.
Falling costs of renewable energy and electrolysers used in green hydrogen production is one of the main catalysts for the increasingly bullish sentiment over the element.
The cost of electrolysers used in green hydrogen production has halved over the last five years and will fall to 60 to 90 per cent by the end of the decade, acceding to Haim Israel, equity strategist at Merrill Lynch. A global focus on decarbonisation and sustainability is also a big driver in its development.
THE SPECS
Engine: 6.75-litre twin-turbocharged V12 petrol engine
Power: 420kW
Torque: 780Nm
Transmission: 8-speed automatic
Price: From Dh1,350,000
On sale: Available for preorder now
COMPANY%20PROFILE
%3Cp%3E%3Cstrong%3ECompany%20name%3A%3C%2Fstrong%3E%20Revibe%20%0D%3Cbr%3E%3Cstrong%3EStarted%3A%3C%2Fstrong%3E%202022%0D%3Cbr%3E%3Cstrong%3EFounders%3A%3C%2Fstrong%3E%20Hamza%20Iraqui%20and%20Abdessamad%20Ben%20Zakour%20%0D%3Cbr%3E%3Cstrong%3EBased%3A%3C%2Fstrong%3E%20UAE%20%0D%3Cbr%3E%3Cstrong%3EIndustry%3A%3C%2Fstrong%3E%20Refurbished%20electronics%20%0D%3Cbr%3E%3Cstrong%3EFunds%20raised%20so%20far%3A%3C%2Fstrong%3E%20%2410m%20%0D%3Cbr%3E%3Cstrong%3EInvestors%3A%20%3C%2Fstrong%3EFlat6Labs%2C%20Resonance%20and%20various%20others%0D%3C%2Fp%3E%0A
COMPANY%20PROFILE
%3Cp%3E%3Cstrong%3ECompany%20name%3A%3C%2Fstrong%3E%20Klipit%3C%2Fp%3E%0A%3Cp%3E%3Cstrong%3EStarted%3A%3C%2Fstrong%3E%202022%3C%2Fp%3E%0A%3Cp%3E%3Cstrong%3EFounders%3A%3C%2Fstrong%3E%20Venkat%20Reddy%2C%20Mohammed%20Al%20Bulooki%2C%20Bilal%20Merchant%2C%20Asif%20Ahmed%2C%20Ovais%20Merchant%3C%2Fp%3E%0A%3Cp%3E%3Cstrong%3EBased%3A%3C%2Fstrong%3E%20Dubai%2C%20UAE%3C%2Fp%3E%0A%3Cp%3E%3Cstrong%3EIndustry%3A%3C%2Fstrong%3E%20Digital%20receipts%2C%20finance%2C%20blockchain%3C%2Fp%3E%0A%3Cp%3E%3Cstrong%3EFunding%3A%3C%2Fstrong%3E%20%244%20million%3C%2Fp%3E%0A%3Cp%3E%3Cstrong%3EInvestors%3A%3C%2Fstrong%3E%20Privately%2Fself-funded%3C%2Fp%3E%0A
Ways to control drones
Countries have been coming up with ways to restrict and monitor the use of non-commercial drones to keep them from trespassing on controlled areas such as airports.
"Drones vary in size and some can be as big as a small city car - so imagine the impact of one hitting an airplane. It's a huge risk, especially when commercial airliners are not designed to make or take sudden evasive manoeuvres like drones can" says Saj Ahmed, chief analyst at London-based StrategicAero Research.
New measures have now been taken to monitor drone activity, Geo-fencing technology is one.
It's a method designed to prevent drones from drifting into banned areas. The technology uses GPS location signals to stop its machines flying close to airports and other restricted zones.
The European commission has recently announced a blueprint to make drone use in low-level airspace safe, secure and environmentally friendly. This process is called “U-Space” – it covers altitudes of up to 150 metres. It is also noteworthy that that UK Civil Aviation Authority recommends drones to be flown at no higher than 400ft. “U-Space” technology will be governed by a system similar to air traffic control management, which will be automated using tools like geo-fencing.
The UAE has drawn serious measures to ensure users register their devices under strict new laws. Authorities have urged that users must obtain approval in advance before flying the drones, non registered drone use in Dubai will result in a fine of up to twenty thousand dirhams under a new resolution approved by Sheikh Hamdan bin Mohammed, Crown Prince of Dubai.
Mr Ahmad suggest that "Hefty fines running into hundreds of thousands of dollars need to compensate for the cost of airport disruption and flight diversions to lengthy jail spells, confiscation of travel rights and use of drones for a lengthy period" must be enforced in order to reduce airport intrusion.
Kanguva
Director: Siva
Stars: Suriya, Bobby Deol, Disha Patani, Yogi Babu, Redin Kingsley
Company%20Profile
%3Cp%3E%3Cstrong%3ECompany%20name%3A%20%3C%2Fstrong%3ENamara%0D%3Cbr%3E%3Cstrong%3EStarted%3A%20%3C%2Fstrong%3EJune%202022%0D%3Cbr%3E%3Cstrong%3EFounder%3A%20%3C%2Fstrong%3EMohammed%20Alnamara%0D%3Cbr%3E%3Cstrong%3EBased%3A%20%3C%2Fstrong%3EDubai%20%0D%3Cbr%3E%3Cstrong%3ESector%3A%20%3C%2Fstrong%3EMicrofinance%0D%3Cbr%3E%3Cstrong%3ECurrent%20number%20of%20staff%3A%20%3C%2Fstrong%3E16%0D%3Cbr%3E%3Cstrong%3EInvestment%20stage%3A%20%3C%2Fstrong%3ESeries%20A%0D%3Cbr%3E%3Cstrong%3EInvestors%3A%20%3C%2Fstrong%3EFamily%20offices%0D%3Cbr%3E%3C%2Fp%3E%0A
The Sand Castle
Director: Matty Brown
Stars: Nadine Labaki, Ziad Bakri, Zain Al Rafeea, Riman Al Rafeea
Rating: 2.5/5
Electoral College Victory
Trump has so far secured 295 Electoral College votes, according to the Associated Press, exceeding the 270 needed to win. Only Nevada and Arizona remain to be called, and both swing states are leaning Republican. Trump swept all five remaining swing states, North Carolina, Georgia, Pennsylvania, Michigan and Wisconsin, sealing his path to victory and giving him a strong mandate.
Popular Vote Tally
The count is ongoing, but Trump currently leads with nearly 51 per cent of the popular vote to Harris’s 47.6 per cent. Trump has over 72.2 million votes, while Harris trails with approximately 67.4 million.
'The Batman'
Stars:Robert Pattinson
Director:Matt Reeves
Rating: 5/5
SNAPSHOT
While Huawei did launch the first smartphone with a 50MP image sensor in its P40 series in 2020, Oppo in 2014 introduced the Find 7, which was capable of taking 50MP images: this was done using a combination of a 13MP sensor and software that resulted in shots seemingly taken from a 50MP camera.
Brief scores
Barcelona 2
Pique 36', Alena 87'
Villarreal 0
Ticket prices
- Golden circle - Dh995
- Floor Standing - Dh495
- Lower Bowl Platinum - Dh95
- Lower Bowl premium - Dh795
- Lower Bowl Plus - Dh695
- Lower Bowl Standard- Dh595
- Upper Bowl Premium - Dh395
- Upper Bowl standard - Dh295
