TRAFFIC JAM! A Mathematical Model to Solve Nairobi’s Traffic Dilemma

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TRAFFIC JAM!

A Mathematical Model to Solve Nairobi’s Traffic Dilemma

IOMBA: BUSINESS MATHEMATICS November 13, 2007

Marina Krawczyk, John Karuri, Joshua Choi &

Laureen Reagan

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This paper is the result of a collaborative effort between the 4 members of the Group as shown in the cover page. The group was interested in looking for a practical solution to an existing problem. While we considered many areas we could address using a mathematical model as learned in class, we unanimously agreed that of all the issues we were considering, resolving the serious congestion problem in Nairobi, the capital city of Kenya would have the most profound impact, directly benefiting close to 3 million people.

We set out to address the congestion problem using mathematical models as learnt during the Business Mathematics course for the IOMBA program. As a group, we tried various models to see which would be most suitable to solve our puzzle. Using the forecasting method to find out the likely growth trends of both the population and the number of vehicles in Nairobi, we established that if the problem is not addressed, congestion would grow exponentially leading to a possible gridlock in the city, in effect translating to millions of shillings in lost man- hours, not to mention a huge cost on environment as a result of increased carbon emissions from idling vehicles. We then used the sensitivity analysis method to identify the most ideal intervention point. Having identified that a decrease in vehicle delay time would have the highest impact, we then used a simple simulation model to look at different alternative options and their impact. We have used simple data to illustrate our model. However, our request for the most current data from Nairobi City Council was not honored. We are however confident that this results can be replicated using live data with similar results to those of our findings.

This paper lays out in detail the methodology used and the results we arrived at. In the end it lays out the key managerial decisions we recommend, namely, first, to build 2 by-pass roads to divert vehicles from the Central Business District that have no business there in the long- run, and, second, in the short run, to replace the current existing circles (roundabouts) with what we have established to be more efficient ramps at major intersections. We have also suggested other policy recommendations worth being pursued pursuant to research on their practicality and impact.

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2.0 BACKGROUND

Nairobi, home to between 3 and 4 million inhabitants, is the Capital city of Kenya and the most populous city in East Africa. The city is counted as one of the most prominent cities in Africa both politically and financially, and is listed by the World Cities Study Group and Network as amongst the most prominent social centres in the world¹. It is one of the busiest cities in Africa and hosts one of the largest Stock Exchange Markets in Africa behind the Johannesburg Stock Exchange. Nairobi is also host to one of the four United Nations Secretariats, the only one in a developing country. It also plays host to major Transnational Companies regional offices, the world’s major airlines gateway hub to the continent and one of the busiest airports in Africa,² diplomatic missions as well as other financial and Non- Governmental organizations.

Despite Nairobi’s rising star status in Africa the city suffers from a debilitating condition that will only worsen as the economic condition of the people improves; gridlock in the Central Business District and the roads leading to it. The city’s 306 kilometers of arterial roadways are intolerably clogged with carbon spewing vehicles transporting both goods and people sometimes chaotically and other times at a snails pace throughout the city.

Nairobi’s roads were planned over a half century ago for a population of only half a million.

Since then the increasing population has overstretched the services of the whole city, most significantly the roads.³ Even though less than one-tenth of Nairobi's three million citizens own cars traffic has expanded, some estimates say by 300 percent in a decade.

The costs are high both on and individual and social level for the people of Nairobi. Not only are the number of road traffic accidents substantially on the rise but a recent survey indicated that traffic jams were costing Nairobi drivers as much as 50 million shillings ($746,000) a day through increased fuel consumption, mechanical damage and pollution⁴. It is not surprising that millions of Kenyans are believed to be suffering from diseases related to pollution since it is known that leaded gasoline combustion contributes to pollution in urban areas with high traffic densities and results in serious health risks to the urban dwellers. Crops

1 Taylor, P.J., Leading World Cities: Empirical Evaluations of Urban Nodes in Multiple Networks, Urban Studies 42 (9), 2005, ppgs 1593-1608

2 Kenya Airports Authority website, http://www.kenyaairports.com/jkia/IndexJkia.php Accessed on November 13, 2007.

3 AAK chairman Gideon Mulyungi said in a speech. http://www.reuters.com/article/latestCrisis/idUSL2192250 last accessed November 8, 2007

4 http://www.reuters.com/article/latestCrisis/idUSL2192250 last accessed November 8, 2007

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grown close to heavily trafficked roads especially when those roads become congested by idling vehicles accumulate atmospheric lead deposits on the foliage leading to dangerous levels of lead in the plants and soil.⁵

2.1 Map of Kenya showing major roads

Source : Kenya Roads Board

5 http://www.uneca.org/csd/CSD4_Report_of_African_Atmosphere_and_Air_Pollution.htm last accessed Nov 8, 2007

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2.2 Complexity of the Problem

Nairobi’s traffic problems are compounded by several complex elements. First there is only one major road, the Uhuru Highway that runs through the city and is punctuated by a string of roundabouts that often function less as traffic regulators than as traffic traps. There are only four major paths leading to the Central Business District, namely, Uhuru highway, Landhies Road, Murang’a Road and Waiyaki way. The city’s business activities are centralized into the downtown area causing large numbers of people to need to commute into and out of one central location at peak hours during the day (ie 6:30AM – 8:30AM and 4:30PM – 7:30PM).

The congestion does not end on these roads but spills over into the adjoining streets that then flow in and out of residential areas. This is compounded by the fact that damaged roads have gone un-repaired due to mismanagement of resources meant for road maintenance and corruption within the government. It is estimated that 57 percent of the road network is currently in disrepair.

The highway is used not only by commuters but also by heavy trucks transiting to all parts of the country. Public transport is 80 percent composed of private buses called Matatus that are considered one of the major causes of congestion. Matatus are known for weaving wildly from lane to lane at breakneck speeds and for creating traffic chaos by dropping off and picking up passengers anywhere including the middle of the street. They are also known to run in poor mechanical condition and to hold profits made by picking up the most passengers per shift to be a higher priority than obeying traffic laws.

Traffic lights and traffic laws are generally unheeded by all vehicles on the roadway. The Police are known to be more interested in bribes than in managing traffic jams and often overrule lights causing further traffic jams and preventing people from following traffic lights in the future. City traffic is the worst on Friday evenings, especially close to pay day and also after rains.

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2.3 Street Map of Nairobi

Source : Yahoo Travel

2.4 The way ahead

Experts indicate that Nairobi's problems are not insurmountable and in many cases not as complex as other traffic congested cities. Plans to overcome Nairobi's congestion began over 30 years ago and including bypasses, overpasses and 14 "missing links" to avoid long detours.

However these plans never materialized on the ground. The reason, experts say was due to systematic corruption during the 24-year rule of former President Daniel Arap Moi. Foreign donor funding essential for building new roads, dried up due to Kenya’s reputation for corruption and misuse of public funds. By the end of the Moi presidency only 20 percent of the country's roads were in adequate condition⁶.

It is clear that Nairobi’s traffic problems are greatly impacted by political dimensions that may require a long period of time to address. Permanent solutions to Nairobi’s traffic problems will require cost and time intensive plans which depend almost entirely on complete transparency from the government. Political and regulatory measures will have to be implemented in order to ensure success. Instead what our group seeks to identify is one or two elements that will have the most profound affect on improving traffic in Nairobi and will

6 http://www.reuters.com/article/latestCrisis/idUSL2192250 last accessed November 8, 2007

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serve as a short term solution until the government can address their problems and implement a longer lasting and more permanent solution.

3.0 METHODOLOGY

In order to choose a methodology to improve the increasingly chaotic traffic situation in Nairobi, it is important to consider what kind of model is relevant to the question being asked.

“The optimality of a model must be weighted with respect to the task, according to a current mode of thinking.” ⁷ After evaluating different methods and possible actions to offer a simple and concrete solution to Nairobi, the group has identified Sensitivity Analysis as the main methodology to be used in this analysis.

Due to administrative constraints within Kenya, it is unlikely that the government of Nairobi will be able to rapidly implement major infrastructural changes. This is the primary reason why the group considered it necessary to find one or two simple and doable solutions that will have the greatest impact and can be easily implemented by the city government of Nairobi.

The group decided to implement a sensitivity analysis using the “spider” chart in order to identify the most sensitive variables. The objective was to identify the variables with greatest positive impact, that if changed would have greater chance to improve the traffic situation in Nairobi.

Sensitivity analysis examines how model outputs vary with changes in model inputs. If changing a model input variable changes the model output then the model is considered to be sensitive. Output variability can be qualitative or quantitative depending on the different sources of variation in the inputs.⁸ In this way the most affected element in a scenario can be defined. Modeling practice requires an evaluation of the confidence in the model, possibly assessing the uncertainties associated with the modeling process and with the outcome of the model itself. Sensitivity Analysis offers valid tools for characterizing the uncertainty associated with a model.⁹

7 Saltelli, Andrea. Global Sensitivity Analysis: An Introduction. Retrieved online from:

http://sensitivity-analysis.jrc.ec.europa.eu/tutorial/index.asp, on November 6, 2007. p. 36

8 Saltelli, Andrea. Global Sensitivity Analysis: An Introduction. Retrieved online from:

http://sensitivity-analysis.jrc.ec.europa.eu/tutorial/index.asp, on November 6, 2007. 27

9 Saltelli, Andrea. Global Sensitivity Analysis: An Introduction. Retrieved online from: http://sensitivity- analysis.jrc.ec.europa.eu/tutorial/index.asp, on November 6, 2007. p.28

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There are several possible applications of Sensitivity Analysis; however this paper will use the methodology in order to discover the factors that mostly contribute to the output variability. In this way, the variable that most affect traffic congestion in Nairobi will be identified, and the group will provide an informed decision on how to deal with it in order to reduce traffic congestion in Nairobi.

Our team also used forecasting as a methodology to explore this problem but found the results to be less informative. We have included these results as an appendix (Appendix A).

4.0 ANALYSIS

The group defined the congestion as ‘average commuting hour’ in order to describe the traffic problem in Nairobi in mathematical way. <Table 1> shows five variables resulting in congestion.

We extracted the data of 1997 and 2006 from various sources, and the other data was hypothesized¹⁰. The group developed a formula that describes the relationship between the six variables in average commuting hour based on the data of 1997 and 2006, and apply the formula to all the cases.

The formula used to calculate average commuting hours is:

Average Commuting Hour = (No. of Public Transportation/1000)*1/3 + (No. of Car/10000)*0.5 +(Population/100000)*0.2-(∆No. of Main Road)*0.8-(∆No. of Accessible Road)*0.1

The formula is based on hypothesis that:

1) 1,000 units of public transportation increase 1/3 min.

2) 10,000 units of car increase 2 min.

3) 100,000 units of population increase 0.2 min.

4) 1 unit increase of M. Road decreases 0.8 min.

5) 1 unit increases of Accessible Road decreases 0.1 min

10 John Howe and Deborah Bryceson, Poverty and Urban Transport in East Africa: Review of Research and Dutch Donor Experience, International Institute for Infrastructural, Hydraulic and Environmental Engineering, A report prepared for the World Bank, December 2000 and http://www-

wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2006/01/17/000160016_20060117095837/Rendered/INDE X/34061.txt

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When you see the commuting hour of the year 2002, you can recognize the considerable decrease from the previous year. It is the only year that experiences the decrease of congestion, whereas the following year, 2003, the average commuting hour increased significantly. The group decided to set the first goal to decrease the commuting hour at the level of year 2002.

In order to find out which variables are the most sensitive to congestion, and the most influential to the decrease of the average commuting hour of year 2002, the group used the spider chart.

To make a spider chart, we have to define a variation range. In this case, it would be the year from 1997 to 2006. The standard point is the data at the year of 2002 (because we set up the goal to decrease the average commuting hour at the level of year 2002.) We can see each variable’s respective impact on the average commuting hour by making spider chart.

<Graph 1> is the spider chart which represents the sensitivity of each variable to the congestion. As the graph shows, the most sensitive variables are the number of cars and the number of accessible roads. The one is the variable resulting in congestion; the other is the one resolving the congestion.

In this spider chart, we can assume that the solution is to control the growth of the number of cars, and build as many accessible roads as possible.

98.3 97.0

92.9 81.8

48.9 60.1

52.1 47.8

41.6 38.0

Average Commuting Hour (Min.)

1,084 1,079

1,079 1,065

1,032 890

874 877

869 850

No. of Accessible Road

306 303

300 300

300 295

301 303

303 300

No. of Main

2,880,820 2,796,913

2,734,030 2,677,797

2,474,858 2,310,792

2,196,570 2,122,290

2,017,386 1,973,959

Population of Nairobi

1,783,840 1,748,863

1,649,871 1,473,099

1,133,153 921,262

787,404 764,470

714,458 649,507

No. of Car

18,922 19,190

19,000 18,270

18,757 18,390

18,208 18,579

18,215 17,650

No. of Public Trans.

2006 2005

2004 2003

2002 2001

2000 1999

1998 1997

98.3 97.0

92.9 81.8

48.9 60.1

52.1 47.8

41.6 38.0

1,084 1,079

1,079 1,065

1,032 890

874 877

869 850

306 303

300 300

300 295

301 303

303 300

No. of Main

2,880,820 2,796,913

2,734,030 2,677,797

2,474,858 2,310,792

2,196,570 2,122,290

2,017,386 1,973,959

1,783,840 1,748,863

1,649,871 1,473,099

1,133,153 921,262

787,404 764,470

714,458 649,507

No. of Car

18,922 19,190

19,000 18,270

18,757 18,390

18,208 18,579

18,215 17,650

2006 2005

2004 2003

2002 2001

2000 1999

1998 1997

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<Graph 1> Y-axis = calculated sensitivity figures, X-axis = Years

Now, the group is going to propose the solution for the traffic problem in Nairobi by using simulation method based on the results of forecasting and sensitivity analysis.

5.0 APPLICATION OF RESULTS

In order to reduce the congestion, we recommend that the City Council of Nairobi to either increase the number of roads in the city or reduce the number of cars in the city centre. With the Kenyan economy growing at an average annual rate of 5% over the last 5 years, and most of this growth being concentrated in Nairobi, the number of vehicles on the roads is more likely to increase in the coming years rather than decrease and any government intervention on this front will have negative repercussions. Thus the only viable option is to increase the number of roads and or more lanes on the existing ones.

In increasing the number of roads, the emphasis should be laid on first ensuring that vehicles with no business in the City Centre are diverted out of the Central Business District. To do so, at least two by-pass roads are needed, one in the south of Nairobi that diverts vehicles destined for the west of the capital and a second on the north of the city that would divert the traffic destined to and from the agriculturally rich central Kenya. Currently, the only road that joins the port city of Mombasa and the western and central parts of the country joins Uhuru highway from the South of the city thus adding to the problems of the already congested street. This road serves as the only port entry not only for Kenya but also for the landlocked

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

No. of Public Trans. vehicles

No. of Cars

No. of Main Roads

No. of Accessible Roads

Commuting Hours

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Uganda, Rwanda and Congo to the west of the country. The railway line leading to these countries has been in disuse for a number of years now meaning all the land transport transits on this road. These by-passes will thus reduce the amount of vehicles by a factor of about 20% in our estimates. It is imperative to note that this number is comprised almost entirely of heavy load trucks and buses destined for the places mentioned. This therefore not only slows down the traffic but is a heavy burden on the fabric of the roads themselves making it expensive to maintain them in good conditions.

Construction of the by-pass roads will need a number of resources such as availability of land on which they will be built on, huge capital outlays and the political goodwill of the policy makers. To address the matter in the short term, we have looked at the possible impact on increasing the flow of the vehicles at the circles (roundabouts) which are common at all the major entry points to the CBD from the 4 highways. Using a simple simulation software downloaded from the internet (http://www.paramics-online.com/demo_download.php), we have looked at two scenarios of either leaving the circles as they are or having ramps at each of the nodes. The simulation results (as shown below) are clearly in favor of ramps over circles.

However, this does not say anything about the cost element of such a change in road design.

It only gives a more short term solution that the City may as well look at to immediately address the continuing congestion problem.

Our analysis supports the following:

a) That a minimum of two by-pass 2-lane roads be built to circumvent the Central Business District area

b) That to address the problem in the immediate foreseeable future, the City may also consider replacing the inefficient circles with the more efficient ramps

While suggesting the above options, we are aware there are other policy options that the government may consider. We have not included them in the scope of this paper but mention them here for possible consideration:

• Move the capital city from its current location to another smaller city with better planning, such as Isiolo

• Introduce road taxes for users during peak hours

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• Limit the number of vehicles entering the city centre by increasing and encouraging through fiscal means the use of commuter trains

• Introduce a 24-hour working shifts in the city so that the peak hours are redistributed during the day

• Open a well planned financial centre outside Nairobi, say in Naivasha, and encourage the private sector to invest there

5.1 Simulation

Measure of Effectiveness Existing

By-

pass Ramp

VMT: Major Highways 300 596 401

VMT: Joining Roads 200 334 287

VMT: Total 500 930 688

VHT: Major Highways 200 123 154

VHT: Joining Roads 100 57 74

VHT: Total 300 180 228

Delay (VHT): Major Highways

100 62 78

Delay (VHT): Joining Roads 100 57 72

Delay (VHT): Total 200 119 150

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VMT Vehicle miles time

VHT Vehicle hour time

From the above table, which shows the average of 10 runs on the simulation model, we see that that the total delay time reduces by a 46% if a by-pass road is built and when a ramp built, by 25% over the existing condition. Thus both methods will increase efficiency, though our favored solution is to have the by-pass roads.

This simulation is run using simple data for illustration purposes only.

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6.0 References

1. Taylor, P.J., Leading World Cities: Empirical Evaluations of Urban Nodes in Multiple Networks, Urban Studies 42 (9), 2005

2. Kenya Airports Authority website, http://www.kenyaairports.com/jkia/IndexJkia.php 3. AAK chairman Gideon Mulyungi said in a speech.

http://www.reuters.com/article/latestCrisis/idUSL2192250 4. http://www.reuters.com/article/latestCrisis/idUSL2192250

5. http://www.uneca.org/csd/CSD4_Report_of_African_Atmosphere_and_Air_Pollution.ht m

6. http://www.reuters.com/article/latestCrisis/idUSL2192250

7. Saltelli, Andrea. Global Sensitivity Analysis: An Introduction. Retrieved online from:

http://sensitivity-analysis.jrc.ec.europa.eu/tutorial/index.asp,

8. John Howe and Deborah Bryceson, Poverty and Urban Transport in East Africa: Review of Research and Dutch Donor Experience, International Institute for Infrastructural, Hydraulic and Environmental Engineering, A report prepared for the World Bank, December 2000

9. http://www-

wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2006/01/17/000160016_20060 117095837/Rendered/INDEX/34061.txt

10. http://www.paramics-online.com/demo_download.php

11. http://ops.fhwa.dot.gov/trafficanalysistools/tat_vol3/sectapp_g.htm 12. Brunel University. West London. Retrieved from:

http://people.brunel.ac.uk/~mastjjb/jeb/or/forecast.html

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7.0 APPENDIX A: Forecasting

As a way to start our research, the group decided to use forecasting to estimate what would happen by the year 2010 in Nairobi, Kenya if nothing changed. The methodology of forecasting is intended to estimate in unknown situations at some future point in time. The idea behind it is that “if we can predict what the future will be like we can modify our behavior now to be in a better position, than we otherwise would have been, when the future arrives”¹¹. As a result, the group identified as necessary to start by using forecasting in order to understand the magnitude of the problem being analyzed and to come up with an appropriate solution in order for Nairobi to achieve a better position in the years to come.

Forecasting is a well know and useful method for different studies; however, since the results of forecasting in this case did not provide relevant information, the group decided to include this methodology only as an appendix with the purpose of showing the progression of the work.

Forecasting Nairobi by the year 2010

99.8 99.6

98.9 101.4

1,081 1,082

1,081 1,081

304 304

304 303

No. of Main Road

2,832,759 2,823,146

2,842,371 2,803,921

1,754,286 1,754,924

1,753,409 1,727,524

No. of Car

19,030 19,003

19,050 19,038

2010 2009

2008 2007

99.8 99.6

98.9 101.4

1,081 1,082

1,081 1,081

304 304

304 303

No. of Main Road

2,832,759 2,823,146

2,842,371 2,803,921

1,754,286 1,754,924

1,753,409 1,727,524

No. of Car

19,030 19,003

19,050 19,038

2010 2009

2008 2007

The group defined the congestion as ‘average commuting hour’ in order to describe the traffic problem in Nairobi in a mathematical way. <Table 1> shows six variables resulting in congestion. The three variables on the top are the ones that would increase the average commuting hour, while the other three on the bottom are the ones decreasing the average commuting hour.

11 Brunel University. West London. Retrieved from: http://people.brunel.ac.uk/~mastjjb/jeb/or/forecast.html , on November 09 2007.

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The data of 1997 and 2006 were given by several governmental organizations of Kenya, and the other data was hypothesized. The group found a formula, which represents the relation between six variables and average commuting hour based on the data of 1997 and 2006, and apply the formula to all the cases.

The formula is:

Average Commuting Hour = (No. of Public Transportation/1000)*1/3 + (No. of Car/10000)*0.5 +(Population/100000)*0.2-(∆ Parking Capacity./1000)*0.1-(∆No. of Main Road)*0.8-(∆No. of Accessible Road)*0.1

The formula is based on hypothesis that :

1) 1,000 units of public transportation increase 1/3 min 2) 10,000 units of car increase 2 min

3) 100,000 units of population increase 0.2 min 4) 1 unit increase of M. Road decreases 0.8 min

5) 1 unit increases of Accessible Road decreases 0.1 min.

The group forecasted what will happen by the year 2010 if nothing changed as we explained before. The group used ‘Moving Average’ for forecasting. <Table 2> shows the results forecasted by moving average, and <Graph 1> shows the results of moving average method.

99.8 99.6

98.9 101.5

1,081 1,082

1,081 1,081

304 304

304 303

No. of Main Road

74,101 74,211

74,037 74,054

Parking Capacity in the city center

2,832,759 2,823,146

2,842,371 2,803,921

1,754,286 1,754,924

1,753,409 1,727,524

No. of Car

19,030 19,003

19,050 19,038

2010 2009

2008 2007

99.8 99.6

98.9 101.5

1,081 1,082

1,081 1,081

304 304

304 303

No. of Main Road

74,101 74,211

74,037 74,054

Parking Capacity in the city center

2,832,759 2,823,146

2,842,371 2,803,921

1,754,286 1,754,924

1,753,409 1,727,524

No. of Car

19,030 19,003

19,050 19,038

2010 2009

2008 2007

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Moving Average - No. of T ransportation

17,500 18,000 18,500 19,000 19,500

1 2 3 4 5 6 7 8 9 10

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Moving Average - No. of T ransportation

17,500 18,000 18,500 19,000 19,500

1 2 3 4 5 6 7 8 9 10

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Moving Average - No. of Car

0 500,000 1,000,000 1,500,000 2,000,000

1 2 3 4 5 6 7 8 9 10

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Moving Average - No. of Car

0 500,000 1,000,000 1,500,000 2,000,000

1 2 3 4 5 6 7 8 9 10

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Moving Average - Population of Nairobi

0 1,000,000 2,000,000 3,000,000 4,000,000

1 2 3 4 5 6 7 8 9 10

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Moving Average - No. of Road

285 290 295 300 305 310

1 2 3 4 5 6 7 8 9 10

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

M oving Average - No. of Accessible Roads

0 200 400 600 800 1,000 1,200

1 2 3 4 5 6 7 8 9 10

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Real Curve Forecasted curve

As we can see in the table 2 and graph 1, the traffic in Nairobi will get worse. (Even though forecasting by moving average is a bit more far from the reality. – Since moving average method uses the average of the past period for forecasting, the result of forecasting of some variables such as the population and number of car of year 2007 shows the slight decrease from the previous year. However, as the economic growth continues, the population and the number of car are increasing in reality.) When you see the commuting hour of the year 2002, you can recognize the considerable decrease from the previous year. It is the only year that experiences the decrease of congestion, and the next year, average commuting hour went up high. The group decided to set the first goal to decrease the commuting hour at the level of year 2002.

In order to find out which variables are the most sensitive to congestion, and the most influential to the decrease of the average commuting hour of year 2002, the group used the spider chart.

TRAFFIC JAM! A Mathematical Model to Solve Nairobi’s Traffic Dilemma

TRAFFIC JAM!

A Mathematical Model to Solve Nairobi’s Traffic Dilemma

IOMBA: BUSINESS MATHEMATICS November 13, 2007

Marina Krawczyk, John Karuri, Joshua Choi &

Laureen Reagan

TABLE OF CONTENTS