Specialized software for the assessment
of service quality and berths occupancy
Introduction
In 1985 a fundamental study was published [1] which for long decades defined the
views over the port development. One of the most prominent results of the study was the
employment of the queuering theory. Under some restrictions (not important at that time) this
tool enabled to achieve the results before considered impossible: the introduction of the berth
utilization coefficient Кocc as a control parameter tied together infrastructural and commercial
characteristics of the port. Really, port always used to be a collision point of ship owners and
terminal operators interests: both would like to see their expensive assets earning money. The
ship owner likes to see all the berths in the port idle and waiting for his ship to serve; the port
operator dreams of all berths occupied, preferably with the queue of ships waiting for a first
berth to free. The queuing theory offered a simple and understandable way to set a desired
balance of port and ship losses.
Sea port as a queuing system
A port could be treated as a queuering system with ships as the jobs arriving to the
servers (berths in this case) [4]. The mean arrival rate could be determined by the number of
ships calling at the port within a year N or the mean interval between arrivals Тint :

N
365

1
Т int
The ship berthing time in this case could be interpreted as an average serving time Тserv.
The jobs served and leaving the system are described by the serving rate

1
Tserv
.
The value    is referred to as relative density of arrival. This value shows how many

vessels would arrive during the berthing time of one vessels. The number of ships which should
be served simultaneously defines the number of berths in the port. Too lowk; number would
cause the queues and losses for the ship owners, too big number would lead to losses for the port
owners due to inefficient utilization of expensive capital assets (berths). The queuering theory
offers a way to find the balance of these losses thus finding the optimal value of nopt.
Specifically, the theory provides a formula for the average length of the queue ms
This formula includes as variables the number of servers n and the relative density  .
Since Кocc=  /n, for practical purposes it is more illustrative to express ms as a function of Кocc.
This dependence was presented in [1] as a table, without sufficient explanations and with
references to special literature sources. The missing link in reasoning put certain obstacles in
development of advance perception and heuristic enhancement of the proposed approach. As an
additional unpleasant consequence the fact should be mentioned that Кocc started to be generally
treated as a design parameter, while the nature of this value makes it just an intermediate one.
It is more logical to set the dependence of two main values vitally important for ship
owners and port operators – average waiting ratio and utilization of berths – as functions of the
annual cargo turnover Q and number of berth n in the port.
The dependence of Кocc from Q at given berth number n in this case is trivial:
Кocc=(N*Тserv)/(n*365)=(Q*Тserv)/(n*365*V), where V is the ship capacity. In more complicated
cases to be studied below, this dependence will be not as simple. If we denote the berth
productivity as P=V/Тserv, then in order to handle the annual cargo turnover Q the time Twork=Q/P
would needed.
Since the time budget of
n berths is n*365, eventually we have
Кзан=Q/(P*n*365)/
Thus we formed a gueuering system model with a new structure (Figure 1).
Figure 1 – New structure of the gueuering model
The restrictions of the queuering models
Today, with new vessel size range, route rationalization and port infrastructure design,
nearly all main assumptions to the ship arrival discipline are not observed. The arrival flow is
never stationary due to commercial circumstances, some ships arrive randomly, some obey the
schedules etc. Still, the most important is totally different interpretation needed for the berths as
servers.
Historically, a berth as construction entity was equal to administrative (management)
unit. Since the ship’s sizes were close to the berth length, this fact did not cause any problem.
The constant growth of the ship and berth sizes caused problems in interpretation of berth
occupancy, since in some cases several ships could be served at one berth and in other cases one
ship could occupy more than one berth.
The definition of Кocc in this case could corrected Кocc =( Σ l shipi.tshipi ) / L.Тб , but anyway
it would ruin the basic assumption enabling to use the queuering theory.
The description of general model
Let us assume that we would like to estimate the maximal cargo turnover Q during an
interval Т realized with the ships with different capacity, whose inputs in Q are defined by the
probability distribution P(V). An example of this distribution is given by Figure 2.
Figure 2 – Histogram of ship capacity distribution
This distribution gives probabilities pi of appearance among all N ships during the
interval T the ships of capacity vi , i.e.
Thus we have
That enables us to calculate the average number of calls of the ships of different capacity:
For every ship type we can assess the average arrival interval τi = T/ni . Let us also
assume that the stochastic value of every ship type arrival fluctuates around this mean interval. If
we assume a low of the fluctuation, possibly different for every type, we could generate a partial
arrival flows for every ship type (Figure 3).
Figure 3 – Partial arrival flows of different ship types
Let us further assume that we have several different berths, Bk, k=1,…,K , whose
characteristics (permitted ship length and draft, cargo handling equipment, commercial terms of
the contracts with shipping lines etc.) permit to accepts not all ships at every berth, while
different productivity establish different turnaround time at different berths. In a general case the
equipment could build a common pool to be distributed by some specific lows among singl
berths in the group.
Let us introduce a matrix [tik]
IxK
, whose element tik shows, at what time a ship of
capacity vi is handled at the bert Bk. If tik=0, the ship cannot be accommodated at this particular
berth (see Figure 4).
Figure 4– Matrix of serving time at different berths
The genera structure of the model dealing with the above mentioned assumptions is
illustrated by Figure 5.
Figure 5 - The structure of the proposed model
The proposed model enables us to undertake the study of main parameters – occupation
of different berths and waiting ratio for different ship types – as function of cargo turnover Q.
Every single model’s run at fixed external parameters involves the changing of possible cargo
turnover from zero to a given value (or a value showing unlimited waiting ratio growth at least
for one berth).
Implementation of the model
The full-scaled imitation model implementing the described approach is realized on a
very sophisticated and licensed object-oriented platform. For many applications, for example for
technological design of ports and terminals, when the number of berths and number of STS is
under optimization, there would be enough to use a simplified versions, since the use of the
advanced software would be connected with the barrier of learning. For this purposes a MS
EXCEL version of the model was developed, where the common spreadsheets are used as a
common or easily studying interface. The sophisticated software “engine” is hidden “under the
hood” of this product, looking very simple and innocent.
The data are keyed in the tables shown on figures 6-8.
Description
Total length of the quaywall
Cargo turnover for interval of simulation
STS productivity
unit
Denotation
Value
[m]
L
Q
P0
3 840
12 000 000
25
1,75
0,90
0,10
0,80
8 760
[teu/interval]
[moves/hour]
TEU-factor
Ship capacity utilization
Mooring interval as share of LOA
Decrease of Р from the number of STS
Simulation interval
[teu/box]
K teu
K ship
K moor
K STS
[hours]
T
Annual cargo turnover for an experiment
Seria of experiments
Annual cargo turnover
[teu/year]
Q year
12 000 000
End
Step
No of steps
6 000 000 12 000 000
1 000 000
6
Begin
Figure 6 - General data on the project
Vessel types
Vessel capacity
v1
1000
v2
2000
v3
3000
v4
4000
v5
5000
v6
6000
v7
7000
v8
8000
v9
9000
v10
10000
Im vi
900
1800
2700
3600
4500
5400
6300
7200
8100
9000
Ex vi
900
1800
2700
3600
4500
5400
6300
7200
8100
9000
Share in the cargo turnover
αi
0,05
0,05
0,075
0,15
0,2
0,15
0,15
0,075
0,05
0,05
Number of ship calls
Ni
306
153
153
229
244
153
131
57
34
31
Optimal allocation of STS per ship
ni
2
2
3
3
4
4
5
5
6
6
[m]
li
200
210
250
280
300
350
400
400
400
400
Delays
[hour]
τi
Ship operation time
[hour]
ti
discharge time
[hour]
Im ti
11,4
22,9
23,7
31,6
30,3
36,3
34,3
39,2
37,0
charge time
[hour]
Ex ti
11,4
22,9
23,7
31,6
30,3
36,3
34,3
39,2
37,0
[hour]
Ti
[teu]
vi
Import party
[teu]
Export party
[teu]
Length of the ship (LOA)
Ship berth time
Interval distribution low
Parameter 1
Parameter 2
Average interval
1
22,9
23,9
Erlang
code
[hour]
1
45,7
2
47,5
46,7
Erlang
2
63,3
49,5
Erlang
2
2
60,5
65,3
Erlang
3
72,6
62,5
Erlang
68,6
74,6
Erlang
3
3
78,4
71,6
Erlang
74,1
81,4
Erlang
3
82,3
77,1
Erlang
41,1
41,1
85,3
Erlang
2
2
3
3
4
4
5
5
5
5
29
57
57
38
36
57
67
153
258
287
Figure 7- Ships description
Ships
STS per ship
Berths
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
v1
2
1
1
1
1
v2
2
1
1
1
1
v3
3
1
1
1
1
v4
3
1
1
1
1
1
1
v5
4
1
1
1
1
1
1
v6
4
1
1
1
1
1
1
v7
5
1
1
1
1
v8
5
1
1
1
1
v9
6
1
1
1
1
v10
6
1
1
1
1
Berth length
No of STS
[м]
280
280
380
380
380
380
440
440
440
440
[шт]
2
2
3
3
4
4
5
5
6
6
L/T utilization
STS utilization
Occupancy
Figure 8- Berths description and ship/berth compatibility
Figures 9-10 display the screenshots of the model’s serial run over some interval where
the cargo turnover reaches maximally accepted values for a given ship capacity distribution and
specified berth’s characteristics.
Figure 9 – Screenshot for the waiting ratio as a function of the cargo turnover
Figure 10 – Screenshot for berth occupancy as a function of the cargo turnover
Brief operational manual
The first spreadsheet named Terms of Reference (ToR) is designated for input of general
information about the port study project. This window offers to key in main parameters of the
project under study: STS hour productivity, TEU-factor, ship capacity utilization, increase of the
space occupied by the ship at berth caused by mooring, decrease of the STS productivity due to
interference of operations and the simulation interval (Fig.11).
Figure 11 – ToR spreadsheet
The string “Annual cargo turnover” sets the variation range of the main project variable,
i.e. the terminal throughput (the beginning value, the end value, the step of increase).
The general rule here and later on this description is that all values which should and
could be set are highlighted by red font, while the calculated interim and resulting values are
colored black .
Next spreadsheet is named SHIPS and enables to input information about the vessels
calling at the port under study (Fig.12).
Figure 12 – SHIPS spreadsheet
Here one can define vessel type names (ten different types in the trial version denoted v1v10), their capacities, shares of import and export parties (implicitly set by capacity utilization
set by ToR, Fig.11), vessel shares (vessel inputs) in the total cargo turnover, required (desired)
number of STS to handle, LOA, average operational delays at berth. The distribution of the
intervals between the ship arrivals in this trial version is supposed to be governed by Erlang
laws, and the order of the Erlang low could be set different for different vessels. (Erlang 0 is pure
random Poisson distribution, with the growth of the order it starts to be more and more close to
regular intervals).
Graphics on the right side of Fig.12 illustrate the given distribution by vessel percentage
in the cargo turnover and calculated mean values of the arrival intervals.
The spreadsheet named BERTHS is provided to describe the berths characteristics,
specifically their length and available number of cranes (which could differ from required for a
ship), as well as compatibility of ships and berths (Fig.13).
Figure 13– BERTHS spreadsheet
The symbol “1” in the crossing of a column i and string j means that the vessel Vi could
be accepted by the berth Bj. At different berths the same ship could be handled in different time
defined by the number of STS available at this berth. That’s why some berth are preferable for a
particular ship, while the others available should be selected only when all optimal berths are
already occupied.
After all these data are keyed in, one could run the simulation. In order to do so, one
should select the most right button at the upper bar in any spreadsheet (“superstructure”, Fig14).
Figure 14 – The control of the simulation run
Here one can set the number of model run iterations to be performed at every step of the
cargo throughput increase from the beginning to the end, select the berth optimization algorithm
(first available of optimal ones or the most idle of optimal), switch on or off the initial warm-up
period to bring the process on the stable level. The button “calculate” run the experiment series.
The spreadsheet WAIT RATIOO displays the dynamics of the queue’s length during the
simulation run, as is shown by Fig.15.
Figure 15 –WAIT RATIO spreadsheet
Figure 16 – OCCUPANCE SERIES spreadsheet
The course of the simulation is displayed by a special indicator as shown on the Fig.17.
Figure 17 – Progress indicator
Conclusions
1. The approach is described which could be treated as a logical extension of the queuering
theory for modern berths and cargo handling equipment in port design procedures.
2. The adequacy of the approach is proven by the comparison with the queuering theory
results when applicable.
3. The approach is implemented both in a highly specific product (built in the full-scale
simulation model used for the task of global resource optimization software under
development) and a stand-alone version using MS EXCEL as a friendly interface.
4. The MS EXCEL version proved to be useful and efficient at the stage of port and
terminal design for the optimization of berth number and STS fleet justification.
5. The product could be recommended for any persons engaged in the optimization of the
number of berths, berth productivity, number of cranes on the berths, the influence on the
port capacity of the different ship calls distribution.
6. Especially usefully this instrument could be when design and planning of port operations
for non-interchangeable berths.
7. Any interested specialists could apply for an advanced simulation tools with much wide
scope and enhanced research features.
Literature
1. Port development. A handbook for planners in developing countries. United Nations,
UNCTAD, New York, 1985