Available online at www.sciencedirect.com
Simulation Modelling Practice and Theory 16 (2008) 315–328
www.elsevier.com/locate/simpat
A queueing model of maritime traffic in Bosporus Straits
Dimitrios Mavrakis, Nikolaos Kontinakis *
Energy Policy and Development Centre (KEPA), National and Kapodistrian University of Athens,
KEPA Building Panepistimiopolis, 157 84 Athens, Greece
Received 26 July 2005; received in revised form 20 August 2007; accepted 28 November 2007
Available online 5 December 2007
Abstract
The Bosporus Straits are among the most crowded and potentially dangerous, waterways in the world traversing urban
areas of over 12 million people. Their narrow and winding shape, along with strong surface and counter deep water sea
currents hinders the navigation. In this article, a queuing model of maritime traffic in the Bosporus Straits is presented.
Physical characteristics of the waterway and applied maritime regulations are integrated into the model. In a number
of scenarios, simulation of the traffic, based on a set of historical data, is performed and the corresponding results are
presented.
Ó 2007 Elsevier B.V. All rights reserved.
Keywords: Bosporus Straits; Maritime traffic; Simulation; Traffic scenarios
1. Introduction
1.1. Straits description
The Straits comprised of the Bosporus Straits, the Dardanelles Straits, and the Sea of Marmara, form a
water route of great strategic and economic importance between the Black Sea and the Mediterranean. The
Bosporus Straits lies between the Black Sea to the North, and the Sea of Marmara to the South. Bosporus
is approximately 31 km long, with an average width of 1500 m and it is only 700 m wide at its narrowest point.
It has many sharp turns, some of them more than 45° while a constant surface current directed from the Black
Sea to the Sea of Marmara and a deep water counter current further hinder navigation (see Fig. 1). This narrow channel is one of the busiest waterways in the world. An average of 50 000 vessels transit the Bosporus
annually, along with hundreds of passenger, fishing, and leisure crafts, which daily cross the Bosporus from
one side to the other [15,16].
*
Corresponding author. Tel.: +30 210 727 5835; fax: +30 210 727 5828.
E-mail addresses: [email protected] (D. Mavrakis), [email protected] (N. Kontinakis).
1569-190X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.simpat.2007.11.013
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Fig. 1. Bosporus Straits’ geography.
Bosporus traverses through the city of Istanbul, an urban area of over 12 million people. Moreover, Istanbul is declared a ‘‘World Heritage City” by UNESCO and a maritime accident near its centre might have negative repercussions to some of the world’s most important monuments [15].
1.2. Traffic regulations in the Straits
The passage of vessels in and through the Straits is governed by the 1936 Montreux Convention. According
to that, all merchant vessels enjoy, in principle, complete freedom of passage and navigation by day and night,
without being subject to any ‘formalities’ except for sanitary controls and optional towage and pilotage
services.
In 1994, Turkey declaring its concerns for the safety of navigation and the protection of its coastal population and environment, introduced the ‘‘Maritime Traffic Regulations for the Turkish Straits and the Marmara Region”. It also established ‘‘Traffic Separation Schemes” (TSS) in the Straits, which follow a
corresponding IMO scheme. To ensure the transit of vessels that, assumingly, cannot comply with the TSS,
the Turkish Regulations contain a number of provisions that suspend two-way traffic or nighttime traffic
for large tankers, regulate traffic to maintain a safe distance between vessels, etc. [3,4,16]. These provisions
are especially strict for the larger tankers or vessels carrying dangerous cargo, resulting to waiting times in
the Straits entrances of up to a week (as by the end of 2002 or 2004) [13].
1.3. Traffic statistics
The passage statistics in the Bosporus Straits are given in Figs. 2 and 3 in terms of yearly number of passages for the years 1995–2000 (both directions) and daily per month average number of passages for the years
1996–2000 (both directions) [9,16].
80000
60000
46954
49952
50942
49304
47906
48079
1996
1997
1998
1999
2000
40000
20000
0
1995
Fig. 2. Number of yearly passages through Bosporus Straits for 1995–2000.
D. Mavrakis, N. Kontinakis / Simulation Modelling Practice and Theory 16 (2008) 315–328
800
731 723
647
700
674
317
707 698
693 686 704
640
610
579
600
500
400
1
2
3
4
5
6
7
8
9
10
11
12
Fig. 3. Daily per month average number of passages for 1996–2000.
In addition, the following relevant statistics were taken [5,9]:
Bosporus is closed for an average of 480 h/year due to bad weather.
Bosporus is closed for an average of 30 h/year due to accidents or brake-downs of transiting vessels.
2. Maritime traffic simulation
An approach that has produced many interesting results with regard to the maritime traffic in the Straits, is
the analytical solution of a set of differential equations [6–9]. A system of equations is used to model the physical characteristics of the Straits, the vessels motion and manoeuvring, sea currents, etc. and its solution provides estimates of parameters like the accident probability and the manoeuvring performance of vessels.
In [5], a discrete-event traffic model of the Straits has been developed that relates the average number of
waiting vessels and the average waiting time in the Straits’ entrances to the mean arrival rate of vessels.
In the current article, the second methodology is followed. The aim is the development of a model that is
able to queue arriving vessels and schedule their transit taking into account a number of their attributes and
the regulations that apply to the transit of vessels through the Straits. A number of scenarios demonstrate certain aspects of the model [5,10].
The proposed approach focuses on the statistical parameters of the traffic and allows for the measurement
of the average delay and system throughput parameters while considering safety as a quantity whose expected
level has been evaluated during the maritime traffic control system design phase and has been incorporated in
the selected safety regulations. In this approach, vessels are considered as moving points, navigating without
deviations in a pre-defined route with constant speed and zero probability of accident. Consequently, the accident occurrences are treated as events which affect only the availability of the system, thus the only needed
value is the mean time that the Straits are not available to traffic due to accidents. Moreover, the set of maritime traffic regulations is considered as being well-defined and applicable, with no exceptions and invariably,
to all arriving vessels.
2.1. Queuing model of the Straits
The model consists of two identical flows, one for northbound and a second for southbound traffic. Arriving vessels are placed in the respective waiting list, which is then sorted so that all passenger-related vessels can
enter the Straits first, followed by the general cargo vessels and leaving last vessels that carry dangerous cargo.
In the first occasion, the first vessel in the list enters the Straits and the list is refreshed (pop-up scheme). After
a pre-defined amount of time that is determined by its speed, the vessel exits the Straits and, thus, the simulation system (Fig. 4).
A sequencer is used to determine, for both directions, whether a vessel waiting in the Straits’ entrance can
enter in the respective direction. This applies in situations that involve either only one direction (e.g. holding a
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Fig. 4. Bosporus Straits model.
vessel from entering the Straits until a safety distance has been secured) or both directions of traffic (e.g. suspending two-way traffic for passage of large tankers).
An event graph for this model is shown in Fig. 5 [1]. Upon a vessel’s arrival, the sequencer checks the waterway status with regard to the traffic regulations and if every constraint is met, the vessel enters the waterway.
Otherwise, the waiting list is updated and the entrance is postponed for the appropriate time. Upon a vessel’s
entrance, the sequencer variables are updated and new potential entrance times for both directions are calculated. A transit list that maintains all currently transiting vessels is updated. When a vessel exits the Straits and
the simulation system, the transit list is updated. An independent event for closing of the waterway due to
severe weather conditions is provided. This event is also used for the closing of the waterway due to accidents
or mechanical problems of the transiting vessels or other occurrences (e.g. construction works). A second independent event is provided to demark the daytime and nighttime periods of every simulation day based on a set
of sunrise/sunset data [14].
The model has been developed in ANSI C, following the bibliography regarding queueing model simulation
[1]. In order to efficiently model maritime traffic, the simulation system has been decomposed into number
parameters that need to be adjusted before the simulation (Fig. 6):
1. The Straits characteristics:
a. Direction and length of all navigation routes.
b. The location of ports, if any, inside the Straits.
Arrival
End
simulation
Enter
Straits
Weatherr
conditions
Fig. 5. Event graph for the Bosporus Straits model.
Exit
Straits
Sun
Set/Rise
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319
1.1.Traffic routes
1.2.Internal ports
1.3.Weather conditions
1.3.1.Complete shutdown
1.3.2.Partial shutdown
1.Waterway
1.4.1.Complete shutdown
1.4.Accident probability
1.4.2.Partial shutdown
1.5.Special physical characteristics
2.Queue
1.5.1.Narrowings
2.1.Number of queues
2.2.Sorting scheme
Parameters of system
3.1.1.Universal rules
3.1.Availability of waterway
3.1.2.Specific rules
3.1.3.Scheduling rules
3.Regulations
3.2.Entrance, same lane traffic
3.2.1.Safety distance
3.3.Entrance, opposite lane traffic
3.3.1.Avoidance of meeting
3.4.1.Transit speed
3.4.Transit rules
3.4.2.Berthing capability
4.Traffic
4.1.1.LOA
4.1.Vessels attributes
4.1.2.Type of cargo
4.1.3.Laden/In ballast
4.2. Traffic distribution
Fig. 6. Straits system parameterization.
c. The probability, extent (resulting on complete or partial service shutdown) and average duration of service shutdown due to severe weather conditions.
d. The probability, extent (resulting on complete or partial service shutdown) and average duration of service shutdown due to an accident occurring inside the Straits.
e. Any special structural characteristics such as narrowings.
2. Entrance queues:
a. The number of queues in each of the entrances as well as any classification scheme that queues arriving
vessels according to their attributes.
b. The sorting function of the waiting queues.
3. The set of rules that regulate traffic:
a. Availability of Bosporus, where entrance may be prohibited due to universally applied rules (e.g. severe
weather conditions or accident occurrence), partially applied rules (e.g. no dangerous cargo vessels passing during nighttime) or maritime traffic scheduling rules (e.g. waiting until a batch is completed, as in
Suez Canal).
b. Entrance constraints with regard to the same lane traffic, where all considerations are effectively modeled as an appropriate safety distance between two consecutive vessels.
c. Entrance constraints with regard to the opposite lane traffic, in case that an inbound vessel must not
meet with a vessel of certain attributes within the whole or part of the waterway.
d. Regulations regarding the mode of transit, where the transit speed of the vessel and whether it can use a
port inside the waterway are determined.
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4. The traffic characteristics and attributes of the vessels that use the waterway:
a. A small number of attributes for each vessel, namely its overall length (LOA), the type of its cargo and
whether it is laden or in ballast.
b. Arriving traffic can be represented by a function or historic distribution that defines the interarrival time
of vessels. In its more complex form, this function will depend on all three attributes of the arriving vessel and on the time and date of the arrival.
2.2. Adjustment of the model parameters
Following the proposed parameterization, the simulation model is adjusted according to the actual physical
characteristics of the Bosporus, the transit rules and regulations, as applied by the Turkish authorities and the
historical traffic statistics [2,5,9,11,12,15–17]:
1. Waterway
a. Traffic routes: Two directions of traffic, northbound (Marmara Sea to Black Sea) and southbound
(Black Sea to Marmara Sea), each 31 km long.
b. Internal ports: In this paper, internal ports of Bosporus are not modeled.
c. Weather conditions: An independent event for weather conditions is triggered every 4 h of simulation
time. Using a Poisson distribution, a decision is made of whether the Straits are suitable for navigation due to severe weather or not for the next 4 h. The distribution is set so that the Straits are closed,
on average, for 480 h every year [5,9]. Shutdowns due to weather conditions apply to the whole
waterway.
d. Accident probability: On average, 30 h every year are added to the severe weather period to count in for
the closing of the Straits due to accidents or mechanical problems of the transiting vessels [5,9]. Shutdowns due to accidents apply to the whole waterway.
e. Special physical characteristics: A special set of rules apply for the Straits narrowing between Vanikoy
and Kanlica.
2. Queues
a. Number of queues: One queue per direction for all vessels.
b. Sorting scheme: According to the applied regulations, passenger vessels are scheduled to enter the Straits
with top priority over all other vessels. Dangerous cargo vessels are scheduled to enter the Straits with
minimum priority over the remaining types of cargo [12].
3. Regulations: Detailed regulations, as applied by the Turkish authorities, can be found in [12]. In brief:
a. Availability of waterway: During severe weather conditions or accident occurrences, no vessel can enter
the Straits. Moreover, vessels longer than 200 m, carrying dangerous cargo can navigate through the
Straits only during daytime.
b. Entrance, same lane traffic: The safety distance between two consecutive vessels that enter the Straits in
the same direction is defined to 8 cables (1482 m). The safety distance is considerably longer between
two large dangerous cargo vessels; nearly 29 km for northbound vessels and 23 km for southbound
vessels.
c. Entrance, opposite lane traffic: Virtually no dangerous cargo vessels are accepted on the opposite direction of an already transiting dangerous cargo vessel. Moreover, two-way traffic is suspended, when a
long dangerous cargo vessel transits the Straits. Special attention is paid to schedule transits so as to
avoid meetings of almost all types of vessels between Vanikoy and Kanlica.
d. Transit rules: A constant transit speed of 10 Nm/h relative to land is used for all vessels and overtaking
is not allowed. All vessels transit the whole length of the Straits; a vessel does not depart from or arrive
in a port within Bosporus.
4. Traffic: The simulation system uses as its input historical data that have been processed to match the conventions of the model [2,5,9,15–17]. A uniform distribution is used to generate all possible events for the
discrete-event model. Arrival rate is defined to be the same at both entrances and its year-round fluctuations
follow the graph of Fig. 3. According to the data, arriving vessels can be distributed to a matrix consisted of
all possible length and cargo categories. In Table 1, the coefficients of the matrix are presented normalized
D. Mavrakis, N. Kontinakis / Simulation Modelling Practice and Theory 16 (2008) 315–328
321
Table 1
Arriving vessels’ attributes distributions (normalized)
Passenger cargo
General cargo
Dangerous cargo
50–100
100–150
150–200
200–250
250–300
0.15
42.56
0.84
0.47
32.02
1.14
0.24
12.09
4.31
0.04
1.83
2.40
0.10
0.39
1.42
Table 2
Vessels laden/in ballast (%)
Passenger cargo (%)
General cargo (%)
Dangerous cargo (%)
Southbound
Laden
In ballast
100
0
75
25
90
10
Northbound
Laden
In ballast
100
0
75
25
20
80
to have a total sum of 100. Since, for safety reasons, the applied transit regulations discriminate laden from
in ballast vessels, a distribution for the cargo state of arriving vessels is needed. Following a series of interviews with maritime agents, passenger vessels (passenger, RO–RO, etc.) are assumed to be always laden
during transit for both directions, while general cargo vessels (bulk carriers, container carriers, general
cargo ships, etc.) are assumed to be 75% laden during transit for both directions. On the other hand, dangerous cargo vessels (which according to the IMO and, subsequently, the Turkish authorities include oil
tankers, chemical tankers, LPG/LNG carriers, etc.) are assumed to heavily depend on the direction of transit: for southbound transits 90% of the vessels are considered laden a ratio that for northbound transits falls
to only 20%. This bias can be justified by the general pattern of the Black Sea oil industry which mainly
exports large amounts of Caspian Sea and Russian oil using the ports of Novorossiysk, Supsa and Tuapse
through the Straits and imports smaller quantities of oil for refining in Bulgaria and Romania. Actually, for
the period 1997–1998, the quantity of oil and oil products that was transited southbound through the
Straits was 6-fold the quantity that was transited the opposite way [2,11].
Vessels under 50 m are not included in the input data since they transit the Straits essentially unconditionally, while transits for vessels over 300 m are rare incidents [17].
3. Simulating the maritime traffic
To simulate the maritime traffic in the Bosporus Straits, two set of input variables are defined: the vessels
arrival rate in the Straits entrances and the distribution of the vessels with regard to their overall length and
cargo. In order to deduce useful conclusions, two series of simulation runs are performed:
During the first, the distribution of the vessels with regard to their overall length and cargo is fixed and
follows the historical distribution and only the vessels arrival rate is a free variable.
During the second, the vessels arrival rate is set so as to generate approximately 56 350 transits per year
(historical data rate +15%) while various distributions of the vessels, with regard to their overall length
and cargo, are simulated.
3.1. Simulation series 1
For the first series of simulation runs, data from Table 1 are used for the distribution of the vessels with
regard to their overall length and cargo. Table 3 summarizes the five scenarios that run with regard to the vessels arrival rate.
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The first scenario is considered as the base scenario, since it corresponds to the historical data that has been
processed for the simulation. All other scenarios imply several degrees of increase in the total number of vessels that transit the Straits.
The percentage of bad weather days (including these of mechanical breakdowns) is pre-defined to 510 h/
year, while the speed of transit is pre-defined to 10 Nm/h.
The model is run for 1 (one) year simulation time for each of the scenarios.
3.2. Simulation results
The results of the simulation are given in Table 4 (NB stands for northbound transit, SB for southbound
transit). Waiting times are given in minutes and are rounded to the closest integer, while total time of bad
weather is given in days.
Table 3
Vessels arrivals distributions
Number of vessels (both directions)
Arrival intervals (min/direction)
Scenario ID
49 000
55 000
60 000
65 000
70 000
21.45
19.11
17.52
16.17
15.02
1
2
3
4
5
Table 4
Results of simulation series 1
Scenario ID
Number of vessels
Number of vessels that passed
Number of vessels that passed (Passenger)
Number of vessels that passed (General cargo)
Number of vessels that passed (Dangerous cargo)
Waiting time
Average waiting time
Standard deviation
Average waiting time (Passenger)
Average waiting time (General cargo)
Average waiting time (Dangerous cargo)
Waiting queue
Average queue length
Standard deviation
Maximum queue length
Bad Weather
Total time closed
1
2
3
4
5
NB
SB
NB
SB
NB
SB
NB
SB
24 639
24 451
251
236
21 933
21 708
2455
2507
27 628
27 542
259
269
24 491
24 538
2878
2735
29 704
30 019
282
307
26 317
26 889
3105
2823
32 589
32 318
311
327
29 002
29 005
3276
2986
34 879
34 633
342
355
31 102
31 410
3435
2868
NB
SB
NB
SB
NB
SB
NB
SB
NB
SB
53
131
132
519
27
25
34
33
225
989
67
399
172
1697
22
30
39
40
311
3652
98
575
318
2430
27
31
42
43
576
5708
105
1709
305
5846
30
26
47
44
622
18 009
114
3035
380
10 586
27
32
47
48
737
36 128
NB
SB
NB
SB
NB
SB
3.3
7.0
3.7
7.2
38
41
4.4
22.1
4.5
22.7
35
88
6.3
37.1
6.8
34.0
52
152
7.3
114.8
7.2
57.7
53
262
8.4
245.1
8.9
102.4
73
586
19.83
22.17
21.17
20.17
22.83
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323
Increase in the total number of vessels that transit the Straits tends to be reflected in the primary benchmark variables, namely the average waiting time and the average queue length (Fig. 7). The main factor for
this behavior is the dangerous cargo vessels (increasing from nearly 2500 in scenario 1 to nearly 3500, for
each direction, in scenario 5) that are subject to a number of strict transit constraints. Passenger and general
cargo vessels statistics are affected to a minimum (Fig. 8). Moreover, the aforementioned asymmetry
between the two traffic directions (Table 2) results to a clearly observed difference in the simulation’s results
since many of the empty vessels that transit northbound can enter the Straits during nighttime or generally
under more relaxed constraints. This asymmetry can, also, explain the diverging number of total vessels that
transit each direction, especially after scenario 3. In the last two scenarios, an ever increasing number of
vessels traveling southbound are piled up in the waiting list and the total number of vessels that are serviced
declines (Fig. 9).
The queue length (all vessels queue and dangerous cargo vessels only queue) for both directions, in
relation to roughly 3000 min of simulation time, for scenario 3 can be seen in Fig. 10 (January 2 and
3). ‘‘Daytime & weather permit” can have three values (‘‘0”, ‘‘1” & ‘‘2”) and is the arithmetic sum of
two variables:
Period of the day (‘‘1” for day, ‘‘0” for night). It is a periodic variable with each period representing a 24-h
period. Since Fig. 10 depicts a winter period of time, daytime is appreciably smaller than nighttime.
Average waiting time
Average queue length
300
4000
3000
200
NB
2000
SB
100
1000
0
0
1
2
3
4
5
1
2
3
4
5
Fig. 7. Average waiting time (minutes) and queue length (number of vessels).
Average waiting time per cargo type
100000
10000
1000
100
10
1
1
2
3
4
5
Passenger - NB
Passenger- SB
General - NB
General - SB
Dangerous - NB
Dangerous - SB
Fig. 8. Average waiting time per cargo type (minutes).
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Total
Passenger
36000
400
350
32000
300
28000
250
200
24000
1
2
3
4
5
1
2
General cargo
4
5
4
5
Dangerous cargo
4000
32000
3
3500
28000
3000
24000
2500
2000
20000
1
2
3
4
5
1
2
3
NB
SB
Fig. 9. Number of vessels that transited.
24 hours
50
2
Night
Day
40
30
1
20
Sum
Num. of vessels
Closed due to
bad weather
10
0
1000
1250
1500
1750
2000
2250
2500
2750
3000
3250
3500
3750
0
4000
Time in minutes.
NB Total
NB Dangerous
SB Total
SB Dangerous
Daytime + Weather Permit
Fig. 10. NB & SB queue time evolution.
Weather conditions (‘‘0” Straits closed due to weather, ‘‘1” no weather problem in the Straits). It is a random variable and in Fig. 10, the traffic is suspended two times (during the nights of the 2nd and 3rd of
January).
As evident, the queue length is primarily defined by the dangerous cargo vessels, since passenger and general cargo vessels are forwarded on first occasion. Moreover, northbound direction, having the advantage of
receiving most dangerous cargo vessels in ballast, has the option of relieving its queue all day round, while
southbound direction can forward laden dangerous cargo vessels only during daytime. Build-ups in the mod-
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325
el’s queues happen mainly whenever the Straits are shut down due to bad weather conditions when all vessels
are not allowed to transit. Small temporary build-ups (of 5 up to 10 vessels) are possible during daytime when
large safety distance and suspension of the two-way traffic that accompanies transit of dangerous cargo vessels
reduces the rate of passenger and general cargo vessels.
Table 5
Arriving vessels’ attributes distributions (normalized)
50–100
100–150
150–200
200–250
250–300
Tankers’ distribution
Scenario ID
Passenger cargo
General cargo
Dangerous cargo
0.15
43.52
0.67
0.48
32.74
0.91
0.25
12.36
3.45
0.04
1.87
1.92
0.10
0.40
1.14
Dangerous cargo
1
Passenger cargo
General cargo
Dangerous cargo
0.15
42.56
0.84
0.47
32.02
1.14
0.24
12.09
4.31
0.04
1.83
2.40
0.10
0.39
1.42
Historical data distribution
2
Passenger cargo
General cargo
Dangerous cargo
0.15
42.08
0.92
0.46
31.66
1.25
0.24
11.96
4.74
0.04
1.81
2.64
0.10
0.39
1.56
Dangerous cargo +10%
3
Passenger cargo
General cargo
Dangerous cargo
0.15
41.60
1.01
0.46
31.30
1.37
0.23
11.82
5.17
0.04
1.79
2.88
0.10
0.38
1.70
Dangerous cargo +20%
4
20%
Table 6
Results of simulation series 2
Scenario ID
Number of vessels
Number of vessels that passed
Number of vessels that passed (Passenger)
Number of vessels that passed (General cargo)
Number of vessels that passed (Dangerous cargo)
Waiting time
Average waiting time
Standard deviation
Average waiting time (Passenger)
Average waiting time (General cargo)
Average waiting time (Dangerous cargo)
Waiting queue
Average queue length
Standard deviation
Maximum queue length
Bad weather
Total time closed
1
2
3
4
NB
SB
NB
SB
NB
SB
NB
SB
28 234
28 310
252
296
25 732
25 778
2250
2236
28 227
28 232
286
300
25 129
25 140
2812
2792
28 654
27 908
260
291
24 954
24 522
3440
3095
28 102
26 743
272
288
23 666
23 428
4164
3027
NB
SB
NB
SB
NB
SB
NB
SB
NB
SB
53
85
161
316
17
20
32
33
300
691
73
674
204
2843
27
27
41
40
371
6454
131
2602
509
7845
37
26
45
44
767
23 115
188
7740
576
23 934
26
33
46
49
1009
67 998
NB
SB
3.7
5.5
4.8
38.2
8.0
152.3
10.9
569.3
NB
SB
NB
SB
4.0
5.5
38
46
5.1
38.6
39
135
9.9
59.2
93
303
10.6
282.0
90
1232
19.33
21.17
21.67
19.83
326
D. Mavrakis, N. Kontinakis / Simulation Modelling Practice and Theory 16 (2008) 315–328
3.3. Simulation series 2
For the second series of simulation runs, the vessels arrival rate is set constant in order to have approximately 56 350 transits generated per year (an arrival interval of 18.65 min; historical data rate +15%) for both
directions while various distributions of the vessels with regard to their overall length and cargo are simulated.
Except for the distribution that represents the historical data (Table 1), a second scenario assumes that there is
a 20% decrease in the ratio of dangerous cargo vessels that transit the Straits. This scenario could emerge, for
example, after the construction of a Bosporus bypass pipeline. In the contrary, two more scenarios assume an
increase in the ratio of dangerous cargo vessels that transit the Straits by 10% and 20%, respectively. These
scenarios can represent a situation where further quantities of Caspian Sea and Russian oil are exported
via the Black Sea terminals [2,11,16]. Table 5 summarizes the four scenarios that are run with regard to the
vessels’ attributes distributions.
The second scenario is considered the base scenario, since it corresponds to the historical data distribution.
The percentage of bad weather days (including these of mechanical breakdowns) is pre-defined to 510 h/year,
while the speed of transit is pre-defined to 10 Nm/h.
The set of the transit rules that are applied during these simulation runs is identical to the one of the previous runs. The model is run for 1 (one) year simulation time for each of the scenarios.
3.4. Simulation results
The results of the simulation are given in Table 6 (NB stands for northbound transit, SB for southbound
transit). Waiting times are given in minutes and are rounded to the closest integer, while total time of bad
weather is given in days.
Average waiting time
Average queue length
8000
600
6000
450
4000
300
2000
150
NB
SB
0
0
1
2
3
1
4
2
3
4
Fig. 11. Average waiting time (minutes) and queue length (number of vessels).
Average waiting time per cargo type
100000
10000
1000
100
10
1
1
2
3
4
Passenger - NB
Passenger - SB
General - NB
General - SB
Dangerous - NB
Dangerous - SB
Fig. 12. Average waiting time per cargo type (minutes).
D. Mavrakis, N. Kontinakis / Simulation Modelling Practice and Theory 16 (2008) 315–328
Total
327
Passenger
32000
400
30000
350
28000
300
26000
250
24000
200
1
2
3
4
1
General cargo
2
3
4
Dangerous cargo
28000
4500
4000
3500
3000
2500
2000
26000
24000
22000
20000
1
2
3
4
1
2
3
4
NB
SB
Fig. 13. Number of vessels that transited.
In contrary to simulation series 1 there is no increase in the total number of vessels that transit the Straits.
However, the relative increase of the dangerous cargo vessels (from nearly 2200 in scenario 1 to nearly 4300,
for each direction, in scenario 4) tends to be reflected in the primary benchmark variables, namely the average
waiting time and the average queue length (Fig. 11). Since the total number of transiting vessels remains constant, the share of time for the dangerous cargo vessels is increased. Nevertheless, this does not seem to be a
decisive factor, since for a similar increase in the total number of the dangerous cargo vessels, the average
waiting time is increased by two orders of magnitude, as can be seen by comparing Fig. 12 to Fig. 8.
Fig. 13 confirms the conclusions that were derived from Fig. 9: though in the northbound direction, extra
dangerous cargo traffic can be compensated, the southbound direction fails to serve the same number of
vessels.
4. Conclusions
The presented model supports the results of previous articles, e.g. [5], but, nevertheless, offers the opportunity for more accurate conclusions due to the accurate representation of the Straits characteristics, the applied
regulations and the traffic statistical properties. Thus, though both models agree that a linear increase of the
arriving vessels result in an exponential increase in both the average waiting time in queue and average number
of vessels in queue, the presented model offers a better resolution with regard to the attributes of the transiting
vessels. The results indicate, in both simulation series that the Straits, in regard to passenger and general cargo
vessels, cannot be considered as congested. The Straits can service increasing numbers of these vessels without
considerable increase in the average waiting time (Figs. 8 and 12). Applied transit regulations are biased
against the transit of dangerous cargo vessels, thus leading to large build-ups of waiting queues that cannot
easily be serviced, especially after traffic suspension due to bad weather conditions (e.g. Figs. 7, 8 and 10).
The distinction between vessels that are laden or in ballast underpins the aforementioned trend (Figs. 7 and
11). Thus, in both simulation series, Bosporus becomes saturated, for northbound dangerous cargo vessels at
around 3000 vessels per year, while, at the same time, at least up to 4200 northbound dangerous cargo vessels
can be efficiently serviced (Figs. 9 and 13).
Acknowledgement
Mr. Nikolaos Kontinakis is under EDA ATTIKIS S.A. scholarship. The authors would like to thank AB
Maritime Inc. (Piraeus) and Mariner SA (Istanbul) companies for explaining practical aspects of commodities
shipping via the Straits.
328
D. Mavrakis, N. Kontinakis / Simulation Modelling Practice and Theory 16 (2008) 315–328
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