計測自動制御学会産業論文集
Vol. 6, No. 11, 85/92 (2007)

Effects of Passengers’ Arrival Distribution to Double-deckElevator Group Supervisory Control Systems Using
Genetic Network Programming
Lu YU＊, Jin ZHOU＊, Shingo MABU＊, Kotaro HIRASAWA＊, Jinglu HU＊and Sandor MARKON＊＊
The Elevator Group Supervisory Control Systems (EGSCS) are the control systems that systematically manage three or moreelevators in order to effciently transport the passengers in buildings. Double-deck elevators, where two cages are connected witheach other, are expected to be the next generation elevator systems. Meanwhile, Destination Floor Guidance Systems (DFGS) arealso expected in Double-Deck Elevator Systems (DDES). With these, the passengers could be served at two consecutive floors
and could input their destinations at elevator halls instead of conventional systems without DFGS. Such systems become more
complex than the traditional systems. Recently, Genetic Network Programming (GNP), a graph-based evolutionary method, hasbeen applied to EGSCS of DDES with DFGS and its advantages are shown in some previous papers. GNP can obtain the strategy
of a new hall call assignment to the optimal elevator because it performs crossover and mutation operations to judgment nodes
and processing nodes. In the past studies the passengers’ arrival distribution has been assumed to take Exponential distribution formany years. In this paper, we have applied Erlang distribution and Binomial distribution in order to study how the passengers’
arrival distribution affects EGSCS. We have found that the passengers’ arrival distribution has great influences on EGSCS of
DDES with DFGS.
Keywords: elevator group supervisory control system, passengers' arrival, erlang distribution, genetic network programmingor to increase the travel comfort for the passengers. Generally, insuch elevator systems, the distribution of the arrival time interval
would influence on the performances of elevator groupsupervisory control systems(5). Therefore, it is natural to use
Erlang and Binominal distribution, especially when the passengers
who get off at the railway stations adjacent to the buildings arriveat the floors of elevators. In this paper, it is studied how the
distribution of passengers’ arrival time interval influences on
EGSCS of DDES with DFGS and Genetic Network Programming(GNP) (6) (7) (8) (9) (10), which is a newly developed graph-based
evolutionary computation method.
The paper is organized as follows. Section 2, 3 and 4 gives an
overview of DDES, GNP and describes the details of Erlang and
Binominal distribution used for EGSCS, respectively. Section 5
explains EGSCS using GNP. Section 6 shows the simulation
conditions and results. Finally, some conclusions are described in
section 7.

1. INTRODUCTION
There have been installed more and more high-rise buildings in
the cities for the spatial and economical considerations. To provide
transportation services among floors in the building, elevatorsystems are installed as primary service facilities. Elevator groupsupervisory control systems (EGSCS)(1) are responsible forcontrolling elevators to provide convenient and comfortable
services for passengers. The new generation elevators,
Double-deck elevators (DDES)(2) are designed to connect two
cages in an elevator shaft. This allows passengers on two
consecutive floors to use the elevator simultaneously, significantly
increasing the transportation capacity of elevator systems.
Recently, Destination Floor Guidance System (DFGS) (3) (4) isgetting more and more popular. Differently from traditional
systems, the passengers input not only their presence and intended
direction, but also their destination at floors in DFGS. This allows
more efficient control of grouping elevators by their destinations,thus reducing the number of stops of the elevators.
Furthermore, since the elevator system is driven by passengers’
arrival, its probability distribution characterizes the traffic in theelevator systems. In order to get tractable analytical results,
researchers have used Exponential distribution to model theelevator systems for many years. However, Erlang distribution ismore general distribution of nonnegative random variables. In
many cases, elevator installation has been carried out in order toincrease the efficiency of the passengers’ movement in buildings

2. ELEVATOR GROUP SUPERVISORY CONTROLSYSTEMS (EGSCS)
Elevator Group Supervisory Control Systems (EGSCS) arecontrol systems that manage multiple elevators in a building inorder to efficiently transport the passengers. The systems assign aservice car for a new passenger waiting in a hall. The assignmentis a kind of real-time scheduling problem for transportation
systems. The performance of EGSCS is measured by several
criteria such as the average waiting time of passengers, thepercentage of passengers’ waiting more than 60 seconds, andpower consumption(11) (12), then, EGSCS manages elevators tominimize the above evaluation criteria; it is, however, difficult tosatisfy all criteria at the same time. In this paper, the following
two criteria are used.

* Graduate School of Information, Production and Systems, Waseda
University.
Hibikino 2-7, Wakamatsu-ku, Kitakyushu, Fukuoka, 808-0135,
Japan** Fujitec Co. Ltd.
Big Wing, Hikone, Shinga, 522-8588, Japan(Received January 15, 2007)85

1) Average waiting time (AWT) is the average time until theservice elevator arrives at the floor after a passenger presses a hallcall button.
2) Average traveling time (ATT) is AWT plus the average timeafter the passengers get into the cage until drop off at thedestination floor.
The passenger traffic pattern in modern buildings with EGSCS
varies considerably throughout a typical business day. Early in themorning, most of the passengers travel from the lobby to the upper
floors (Up-peak), while at the end of the day, most of thepassengers leave the floors and travel primarily to the lobby inorder to exit the building (Down-peak). And other part of the day
has its own characteristic patterns (Regular). Different traffic
patterns have very different effects, and each pattern requires its
own analysis. Up-peak and down-peak elevator traffic are notsimply equivalent in the sense of opposite directions, as one might
initially guess. Down-peak traffic has many arrival floors and asingle destination, while up-peak traffic has a single arrival floor
and many destinations. So, we study the systems with three typesof traffic patterns, i.e., "Up-peak Time", "Down-peak Time" and"Regular Time".

Fig.1. Outline of Double-Deck Elevator System

Double-Deck Elevator Systems (DDES) become more complex intheir behavior than conventional Single-Deck Elevator Systems(SDES).
DDES has specific features as shown below, and their carefulconsideration is expected to improve the performances of groupsupervisory control.
One Cage Service: Self cage stops without any service while theother cage serves passengers at the floor. This situation causes not
only the deterioration of transportation capability but also
psychological stress to passengers.
Coincident Service: Both cages serve passengers at a stop.
Coincident service can contribute to improve both transportation
capability and comfortable riding.
Separate Riding for Identical Destination: Passengers for theidentical destination ride on both cages. Therefore, thetransportation capability deteriorates by two stops at the same
floor.

2.1 Destination Floor Guidance System (DFGS)In traditional elevator systems, EGSCS consists of hall callbuttons and car call buttons. If a passenger wants to go to anotherfloor, he presses a direction (hall call) button and waits for anelevator to arrive, then enters the elevator and presses a
destination floor (car call) button in the elevator. The EGSCS
selects a suitable elevator when a passenger presses the hall callbutton. In order to obtain more accurate information onpassenger's destination, Destination Floor Guidance System(DFGS) (12) has been developed, so that passengers can input theirdestinations at elevator halls. At each floor there is a keypad where
the passenger selects which floor they wish to go to. The systemthen guides the passenger to an elevator that will be stopping attheir destination floor. There are no floor buttons inside the cage.
Such systems claim that the average waiting time can be reduced
by up to 30%, by grouping passengers with common destinations
into the same cage, and thus reducing the number of stops thatneed to be made.

3. PASSENGER’S ARRIVAL DISTRIBUTION
Queueing systems use a particular form of state equations
known as Markov chains(13). To drive a queueing model that
represents real systems, we prefer a form that is simple or tractable,
but it should be sufficiently realistic. It has been found convenient
to work with probability distribution which exhibits thememoryless property, as it commonly simplifies the mathematics
involved. As a result, queuing models are frequently modeled as
Poisson Processes through the use of the exponential distribution.
EGSCS of DDES with DFGS has been modeled by using theExponential distribution as the passengers’ arrival distribution.
However, is this case passengers’ arrival completely at random intime, which is not enough in traffic analysis. Sometimes we needto control the distribution of the passengers’ arrival time intervalin order to make the model close to the real one. Especially, if thepassengers who get off at the stations adjacent to the buildings
arrive at the floors of elevators by the batch, we should consider
the above. So here, we use the Erlang distribution to realize thetime interval of passengers’ arrival and use the Binomial
distribution to assign the number of the batch in order to study
how the distribution of the passengers’ arrival influences on theperformances of EGSCS of DDES with DFGS, because it has

2.2 Double-Deck Elevator System (DDES)
Recently, for improving the capability of EGSCS, theDouble-Deck elevator, where two cages are connected with eachother, is expected as the next generation elevator. It allows thepassengers at two consecutive floors could be serviced
simultaneously. Such a scheme could be efficient in buildings
where the traffic would have a stopping at every floor.
Architecturally, double-deck elevators occupy less building core
space than traditional single-deck elevators do for the same levelof traffic. This allows much more efficient use of space, as thefloor area required by elevators tends to be quite significant.
Fig.1 shows the outline of Double-Deck Elevator Systems(DDES). In DDES, a passenger can in principle board either the
lower or upper cage. Here, instead of "upper cage" and "lower
cage", we also use the terms "self cage" and "other cage" in amore general sense. As the upper cage could not get to the bottom
floor, we divide the base floor into "up-base floor" and"down-base floor". The two bottom floors are named "Base Floor".
With the DFGS, when passengers come to the lobby of thebuilding, the panel would tell them that they should go to the
up-base floor or down-base floor to be serviced. Obviously,86been never studied yet in the past. It fits the passengers’ arrival
characteristics and facilitates our further analysis.

3.1 Erlang Distribution
A random variable X has an Erlang-k (k = 1, 2, …) distribution
with mean k/µ if is the sum of k independent random variables
X1, … , Xk having a common exponential distribution with mean
1/µ. The common notation is Ek(µ) or briefly Ek. The density of an
Ek(µ) distribution is given byf (t ) = µ(µt )k −1 − µte ,(k − 1)!

t > 0.

(1)

The distribution function equals( µt ) j − µt
e ,
j!
j =0

k −1

F (t ) = 1 − ∑t ≥ 0.

(2)

The parameter µ is called the scale parameter, k is the shapeparameter. In Fig.2 we display the density of the Erlang-k
distribution with mean 1 (so k/µ=1) for various values of k.
When k=1, the distribution is reduced to the exponential
distribution which realizes the random process. As the shapeparameter k increases, the distribution becomes like symmetry.
When k≥30, it closes to normal distribution. When k→∞, it
becomes a delta function at the value of k/µ. So, the Erlang-k
distribution could make the time interval of passengers’ arrival tobe the form from completely random to a certain value. It provides
wider applicability to real systems. The Fig.3 illustrates that thetime interval of the Erlang arrivals is much more equal than
exponential arrivals and describes the number of the batch which
is produced by Binomial distribution.

Fig.2. The density of Erlang-k distribution

Fig.3. Exponential arrivals, Erlang-10 and Binominal-Erlang-10 arrivals

initial boot node

processing node

The binomial distribution Pk is a discrete probability
distribution taking from 0 to n with mean of np. It denotes thenumber of successes in a sequence of n independent yes/noexperiments, each of which yields success with probability p

Pk = C kn p k (1 − p ) n − k , k = 0,1,2,..., nP1

judgment noden!
k!(n − k )!

0
2

1

d3

(3)

3

J1

d71

d41

J2

J3

4

6

5
d6

d42
d72

8
P1

(4)

J2

We can realize passengers’ arrivals in the batch mode having
the mean arrival rate of µnp/k by combining Ek(µ) and Pk.

97

node gene
NIDi

4. GENETIC NETWORK PROGRAMMING (GNP)

NTi NFi

node 0

0

0

0

2

0

node 1

2

1

5

3

0

node 2

1

1

1

3

0

node 3

2

2

5

6

0

J1

P2

time delay

Where,

C kn =

Genotype

Phenotype

3.2 Binomial Distribution

P2

1

0

0

node 4

1

1

1

2

0

8

node 5

1

3

1

8

0

6

0

node 6

1

2

1

9

0

2

0

node 7

1

2

1

1

0

4

0

node 8

2

1

5

5

0

node 9

2

2

5

7

0

connection genedi

Ci1 di1

Ci2

di2

CiN(i)

diN(i)

Library

Fig.4 shows the basic structure of GNP. As an extension of GA
and GP, GNP has been proposed to have a network structure
where functional nodes are connected by directed branches. GNP
program is composed of one start node and plural judgment nodes
and processing nodes. The start node has no functions and noconditional branches. Judgment nodes have decision functions
with conditional branches. Each judgment node returns a
judgment result and determines the next node to be executed.
Processing nodes work as action functions. After the start node,
the current node is transferred according to the node connections
and judgment results. In processing nodes, actions are conductedto environments. All kinds of judgment and processing function
labels (Judgment node: {1, 2, …, J}, Processing node:{1, 2, …,P}) are set up in the libraries, which are prepared by the designers.
The node transition begins from a start node, and there is no
terminal node.

Judgement Node

Processing Node

1 :
2 :

1 :
2 :

J:

P:

Fig.4. Basic structure of GNP

GNP has two kinds of time delays: one spends on judgment
nodes or processing nodes, and the other one spends on nodetransitions. Since time delays are listed in each node gene and are
unique attributes of each node, GNP can evolve flexible programs
considering time delays.
As shown in Fig.4, GNP can be illustrated by its "Phenotype"and "Genotype". Phenotype GNP shows the directed graphstructure where nodes are connected by directed branches, andGenotype GNP provides the chromosomes encoded into bit-strings.
The structure of the gene of node i is set as shown in Fig.4. There
are node genes and connection genes in the genes of nodes. NTi is87the allele of node type (0: start node, 1: judgment node, 2:
processing node). NFi indicates the function label which is definedin the library. di is the time delay of node i. Cik denotes the kth
connecting node number from the current node i and dik shows thetime delay of the transition.
In evolutionary computation, each individual is evaluated in the
problem environment. Then the offspring who can survive to thenext generation is decided by fitness. Crossover, Mutation,
Tournament Selection and Elite Preservation are used as thegenetic operators of GNP. The outline of evolution is described asfollows:
1.
Generate initial population and calculate the fitness of initial
population;
2.
Execute tournament selection, genetic operations to
individuals and generate new individuals for the next
generation;3.
Calculate the fitness of the new individuals;
4.
Repeat 2-3 until the terminal condition meets.

Fig.5. Structure of the proposed system

CHCsd: Check whether the emerged hall call coincides with the
car calls of the self cage

5. APPLICATION OF GNP TO EGSCS

ATd : Sum of the incremental predicted arrival time of the alreadyassigned hall calls to the other cage

Double-Deck Elevator Systems with Destination Floor
Guidance Systems are so complex in that the assignment of the
optimal cage to each new hall call is fairly difficult due to theenormous amount of information obtained. GNP is expected to beappropriate for the assignment problem in elevator systems. The
reason is that: GNP can realize a rule based Elevator Group
Supervisory Control System (EGSCS) due to its directed graphstructure with judgment nodes and processing nodes, which makes
EGSCS more flexible in different traffics. And also, EGSCS canbe generated by an evolutionary method with mutation, crossoverand selection, which could develop new efficient and effective
rules that elevator experts can not imagine as well as saving thetime for designing EGSCS.
The structure of Double-Deck Elevator System (DDES) with
Destination Floor Guidance System (DFGS) using GNP is shownin Fig.5. The Elevator Group Supervisory Control System(EGSCS) includes Elevator System and GNP controller. When ahall call occurs, System Information and Cage Information arecollected. Then the GNP Controller uses these data, and doessome calculation and evaluation. The GNP Controller consists of
the System Information Judgment Part, Cage Selection Part, Cage
Judgment Part and Hall Call Assignment Part. The information istransferred through those parts.

AETd: Maximum of the arrival time plus elapsed time since theassignment of the hall calls to the other cage
DNPd: Difference of the number of passengers between the self
and other cage
DNCd: Difference of the number of assigned hall calls between
the self and other cage
CCSd : Check the coincident service
CSRd : Check the separate riding for identical destination

5.2 Assigning Algorithm(7)(8)
In the GNP controller part, firstly, the information on theelevator system is transferred to the system information judgmentpart. There, the degree of variance of the elevator position, thefloor and direction of the new hall call and the destination floor of
the new hall call are judged by the system information judgment
nodes. An activated node in the system information judgment partis transferred to an appropriate node in the cage selection part. In
other words, the best initial node in the cage selection part isdetermined by studying the elevator positions and the informationon the emerged and destination floors of a new hall call.
Secondly, a candidate cage with the minimum value of theevaluation function is selected in the cage selection part. The
evaluation function might include some of the 12 items, which are
mentioned before (ATsd, AETsd, NPsd, NCsd, RRsd, CHCsd, ATd, AETd,
DNPd, DNCd, CCSd, CSRd). The candidate cage should be the self
cage, not the other cage, because we suppose that a new hall call is
assigned to the best cage in the self cages. The self cage could be
the upper cage or the lower cage. In the cage selection part, wehave only processing nodes and each of these continues tocalculate one of the 12 items of all self cages by node transition
until an activated node in the cage selection part moves to thenode in the cage judgment part. Different from the conventional
methods, the number and combination of the items for theevaluation function are decided by evolution. In other words, theconnection from the current processing node to the next node,
which might be another node in the cage selection part or the nodeof the cage judgment part, is determined by evolution of GNP.
Meanwhile, each item in the evaluation function has a weight

5.1 Evaluation Items
In our proposed method, the following 12 evaluation items aredefined and employed to construct GNP considering the featuresof DDES with DFGS.
ATsd : Predicted arrival time of the assigned hall call to the self
cage including the incremental arriving time of the alreadyregistered hall calls to the self cage
AETsd: Maximum of the arrival time plus elapsed time since theassignment of the hall calls to the self cage
NPsd : Number of passengers in the self cage
NCsd: Number of assigned hall calls to the self cage
RRsd : Predicted riding rate ( passenger number/ cage capacity) of
the self cage when the self cage arrives at the assigned hallcall including the incremented riding rate of alreadyregistered hall calls to the self cage88Part.
It should be noted that all the connections in the nodes in fourparts of GNP mentioned above could be changed by evolution.

adjusted by GA. The cage evaluation function e(i) of cage i is
calculated by Eq.(5). Now we suppose that item X for cages isevaluated at the cage selection node p∈Pe(i ) = ∑ w p ⋅ x p (i )5.3 Node Functions(5)

There are 4 kinds of nodes in the parts of the algorithm
described in the previous sub-section. They are as follows.
< System Information Judgment Node >p∈P

The normalized value xp(i) of the evaluation item X of cage i atthe cage selection node p is calculated by Eq. (6)x p (i ) =X p (i ) ,JVPsd : Judge the degree of variance of the elevator position(6)

JEFsd : Judge the floor and direction of the new hall call

X AveMax

JDFsd : Judge the destination floor of the new hall callwhere,
P : Set of suffixes of nodes transited in the cage selection part

< Cage Selection Node >wp: Weighting parameter of cage selection node p

S(X) : select evaluation item X from 12 items by the nodetransition in the cage selection part and calculate Eq. (7)

Xp(i): Value of evaluation item X of cage i at the cage selection
node p

X∈{ATsd, AETsd, NPsd, NCsd, RRsd, ATd, AETd, DNPd, DNCd,

xp(i): Normalized value of evaluation item X of cage i at the cage
selection node p

CCSd, CSRd}< Cage Judgment Node >XAveMax: Maximum value of averaged evaluation item X over past
5 minutes among cages

JZ : Judge whether yj(d)≤rjY is satisfied or not

As for the evaluation item {CHCsd, CCSd }, xp(i)=0 if thecondition is satisfied, and xp(i)=1 if not satisfied. As for theevaluation item {CSRd }, it is vice versa. Finally, we calculate thecage evaluation function of each cage and choose the optimal caged as a candidate cage by Eq(7)d = arg min e(i ) ,Y∈{ ATsd, AETsd, NPsd, NCsd, RRsd, CHCsd, ATd, AETd, DNPd,
DNCd }JZ (d): Judge whether Z of cage d is satisfied or not
Z∈{ CHCsd, CCSd, CSRd}

(7)

i∈I

where,
I: set of cage IDs
Then, the selected candidate cage d is evaluated again byindividual evaluation items each by each in the cage judgment partin order to study if the candidate cage would be a reallysatisfactory one in point of each evaluation item. In concrete, thebinary judgment like Eq. (8) is carried out except {CHCsd, CCSd,
CSRd } in cage judgment nodes j.
Ify j (d ) ≤ r jY , ( j ∈ J )<Hall Assignment Node>
A(d) : Assign the new hall call to cage d
5.4 Fitness Function
The fitness function of GNP individual is calculated by aweighed sum of waiting time, maximum waiting time, one cage
service and loops of GNP as follows.

Fitness =(8)

where,y j (d ) =1 N 2∑ tn + wt ⋅ (tmax )2 + wc ⋅ (nc )2 + wl ⋅ l 2
N n =1(10)

N : Total number of passengers

Y j (d )tn : Waiting time of n-th passenger(9)

Y AveMax

tmax: Maximum waiting time among N passengers

J : Set of suffixes of nodes in the cage judgment partnc: Total number of passengers experiencing one cage service

rjY : Parameter of evaluation item Y at cage judgment nodel : Number of loops of GNP per an hour evaluation

Yj(d):Value of evaluation item Y of cage d at cage judgment node j

6. SIMULATIONSYAveMax : Maximum value of averaged evaluation item Y over past 5
minutes among cages

6.1 Simulation Conditions
In this paper, we study how the passengers’ arrival distribution
affects EGSCS using GNP in a typical office building, having 16
floors and 6 double-deck elevators running at 2.5m/s. Table 1
shows the specifications of the system simulator. Simulations are
executed under 5 kinds of random sequences considering theprobabilistic feature of DDES.
As shown in Table 2, simulations are implemented for the threekinds of traffic flow, "Regular Time", "Up-peak Time" and"Down-peak Time". The row of the Table represents the floor

As for {CHCsd, CCSd, CSRd }, the binary judgment (satisfy/not)is done. If the candidate cage d satisfies Eq(8), then the new hallcall is assigned to the best cage d in the hall call assignment part.
Otherwise, the node transition is resumed from the cage selection
part in order to select another candidate cage.
After the hall call assignment to the best cage completes, GNP
stops transitions until another new hall call occurs and thetransition begins at the node in the System Information Part,
which is connected from the node in the Hall Call Assignment

89

Table 4. Performance of the proposed method.
(unit: second)(a) Performance of different k of Erlang arrival without Batch

Table 1. Specifications of Elevator Simulator.
Items
Value
Number of Floors
Number of Shafts (Cage)

16
6(12)

Floor Distance [m]Max. Velocity [m/s]Max. Acceleration [m/s2]

4.5
2.5

Jerk [m/s3]

0.7
0.7

Cage Capacity [person]
Time for Opening Door [s]Time for Closing Door [s]Time for Riding [person/h]

20
2.0
2.3
1.0

Passenger Density [person/h]
Regular Time
Up-peak Time
Down-peak Time

2400
2700
3300

k=1
k=10
k=50

General

Items

Base
---5

Gen.
5
2

Base
---1

Gen.
19
2

Base
---19

k=1
k=10
k=50

Crossover
Mutation
Elite
Node Size
Crossover Rate Pc
Mutation Rate Pm
Evaluation Time [h]wt , wc, wl

Down-peakAWT ATT
27.80 60.31
25.29 59.27
24.30 57.08

RegularAWT ATT
31.47 60.39
29.51 58.90
27.92 58.42

Up-peakAWT ATT
34.20 89.86
33.44 90.89
32.33 88.18

Down-peakAWT ATT
34.07 61.44
31.11 60.78
30.03 59.71

Table 5. AWT of different k of Erlang arrival in Training andTesting.
(unit: second)(a) Regular Time
Testing
k=1
k=10
k=50
Training
k=1
27.76
27.89
28.01
k=10
27.94
26.86
27.53
k=50
27.85
27.02
26.32
(b) Up-peak Time
Testing
k=1
k=10
k=50
Training
k=1
30.06
30.10
28.69
k=10
28.02
27.98
27.85
k=50
30.11
28.02
26.88
(c) Down-peak Time
Testing
k=1
k=10
k=50
Training
k=1
27.80
27.79
26.97
k=10
27.89
25.29
25.30
k=50
27.93
25.29
24.30

Gen.
2
1

Table 3. Evolutional Conditions of GNP
Value

Generation
Population Size

Up-peakAWT ATT
30.06 60.24
27.98 58.52
26.88 59.28(b) Performance of different k of Erlang arrival with Batch.

Table 2. Traffic Flow Ratios.
RegularUp-peakDown-peak
BaseRegularAWT ATT
27.67 59.30
26.86 58.16
26.32 57.02

300
300
120
170
10
91+Initial Boot Node
0.1
0.01
2
0.007, 0.001, 0.6

emerge at floors by batch. Here, we set the parameters ofBinomial distribution as n=50, p=0.06. It means the mean of the
distribution is n x p=3. It indicates 3 passengers on average might
emerge at the same time. Fig.7 shows the fitness curves of eachtraffic using Erlang distribution in the batch mode. The batch
passengers make the system more complex, so we could see thefitness is higher than the cases without batch, but it is still under
the influence of the parameter of Erlang distribution.
The fitness values of down-peak traffic are lower than those in
up-peak and regular traffic because down-peak traffic has morediversified flows of traffic than up-peak time, and also it is simpler,i.e., mainly one direction, than regular traffic.
The performance of AWT(average waiting time) and ATT(average traveling time) are shown in Table 4 ((a) Performances
without batch. (b) Performances with batch.). It is shown from
Table 4 that most of the values are decreased except for Up-peak if
parameter k increases.
Note that the results in "Up-peak Time" are a bit different. The
reason causing those results are due to the inherent properties in
up-peak time, where most of passengers emerge at the base floor
and go to higher floors (14). So the performance in this pattern is
not influenced by the parameter of Erlang distribution so much.

where passengers emerge, and the column represents the floor
where passengers plan to go. Here, passengers emerge at a floor
whose type is listed as "Base Floor (Base)" or "General Floor(Gen.)".
The parameters for evolving GNP are set as shown in Table 3.

6.2 Results and Discussions
The fitness curves of the best GNP individual in each traffic
using Erlang distribution are shown in Fig.6 ((a) Regular Time, (b)Up-peak Time, (c) Down-peak Time). The fitness curve of the bestindividual is the average over 5 kinds of random sequences. The
shape of the fitness curves differs traffic flows by traffic flows. We
made simulations under the different parameters of k= 1, 10 and
50 of Erlang distribution. When k is large enough, the timeinterval of the passengers’ arrival is regular. From the figures offitness curves, we could find two important things when parameterk increases. Firstly, the speed of the evolution in each traffic
becomes faster. In other words, the case of using small k needs
more generations for convergence. Secondly, the lager value of kwould make the lower fitness value.
Also, we made the simulations with the batch arrival using
Erlang and Binomial distribution. In this case, the passengers

90

4500

4500
Regular Time k=1
Regular Time k=10
Regular Time k=50

4000

3500

3500

3000

3000

Fitness

Fitness

Regular Time k=1
Regular Time k=10
Regular Time k=50

4000

2500

2000

2500

2000

1500

1500

1000

1000

500
0

50

100

150

200

250

500

300

0

50

100

Generation(a) Regular Time

250

300

4500
Up Peak Time k=1
Up Peak Time k=10
Up Peak Time k=50

4000

Up Peak Time k=1
Up Peak Time k=10
Up Peak Time k=50

4000

3500

3500

3000

3000
Fitness

Fitness

200(a) Regular Time

4500

2500

2000

2500

2000

1500

1500

1000

1000

500
0

50

100

150

200

250

500

300

0

50

100

Generation(b) Up-peak Time

150
Generation

200

250

300

(b) Up-peak Time

4500

4500

4000

Down Peak Time k=1
Down Peak Time k=10
Down Peak Time k=50

Down Peak Time k=1
Down Peak Time k=10
Down Peak Time k=50

4000

3500

3500

3000

3000

Fitness

Fitness

150
Generation

2500

2000

2500

2000

1500

1500

1000

1000

500
0

50

100

150
Generation

200

250

500

300

0

50

100

150

200

250

Generation(c) Down-peak Time
Fig. 6. Fitness Curves using Erlang distribution without Batch(c) Down-peak Time
Fig. 7. Fitness Curves using Erlang distribution with Batch.

91

300

Fig.6, Fig.7 and Table 4 were obtained using the same value ofparameter k when training and testing, while Table 5 shows theaverage waiting time when different k is used in training andtesting. It is found from Table 5 that testing results with k being 1,
10, 50 do not have so much differences when trained using k=1,
on the other hand, testing results have much differences when
k=50 is used in training, i.e., the larger k is, the smaller AWT is.

Jing Zhou
From 1996 to 2004, he was with BBH Corp.
He received ME degree from Waseda
University, Japan in 2006. Since April, 2006,
he has been a PhD student in Graduate Schoolof Information, Production and System,
Waseda University, Japan

7. CONCLUSIONS
Shingo Mabu

In this paper, studying the effects of passengers’ arrival
distribution to elevator group supervisory control systems using
GNP has been shown. It has been clarified from the simulations ofusing Erlang and Binominal distribution for passengers’ arrivalthat Erlang arrival and Batch arrival have great influences on
average waiting time and average traveling time in terms ofincreasing these values.

He received the BE and ME degrees inElectricalEngineering
from
KyushuUniversity, Japan in 2001 and 2003,
respectively, and Ph. D degree from Waseda
University, Japan in 2006. From April 2006 to
March 2007, he was a Visiting Lecturer in
Graduate School of Information, Productionand Systems of Waseda University. Since April 2007, he has beena Assistant Professor in Graduate School of Information,
Production and Systems of Waseda University. Dr. .Mabu is amember of the Society of Instrument and Control Engineers, theInstitute of Electrical Engineers of Japan and IEEE.

[ References ]
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(14)

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Kotaro Hirasawa
He received the BE and ME degrees from
Kyushu University, Japan in 1964 and 1966,
respectively. From 1966 to 1992, he was with
Hitachi Ltd, where he served as a vicepresident of Hitachi Research Laboratory.
From December 1992 to August 2002, he wasa Professor in Graduate School of Information Science andElectrical Engineering of Kyushu University. Since September
2002, he has been a Professor in Graduate School of Information,
Production and Systems of Waseda University. Dr Hirasawa is amember of the Society of Instrument and Control Engineers, theInstitute of Electrical Engineers of Japan and IEEE.
Jinglu Hu
He received the MS degree in Electronic
Engineering from Zhongshan University,
China in 1986, and the Ph.D degree in
Computer Science and Engineering from
Kyushu Institute of Technology, Japan in 1997.
From 1986 to 1993, he worked in Zhongshan
University, where he was a Research
Associate and the Lecturer. From 1997 to March 2003, he was a
Research Associate in Graduate School of Information Scienceand Electrical Engineering, Kyushu University, Japan. Since April
2003, he has been an Associate Professor in Graduate School ofInformation, Production and Systems of Waseda University. Dr
Hu is a member of the Society of Instrument and Control
Engineers, the Institute of Electrical Engineers of Japan.
Sandor Markon

Lu Yu

He received Dipl.Ing. from Budapest
Technical University in 1973. From 1975 to
1977, he was a research student at Kyoto
University. Since 1979, he joined Fujitec
Co.Ltd. He received PhD degree from Kyoto
University in 1996. Dr. Markon is a memberof IEEE, INNS, JNNS and SSJ.

She received the BE degree from Beijing
Institute of Technology, China in 2005.
Since September, 2005, she has been a
Master course student at Graduate School ofInformation, Production and System,
Waseda University, Japan.

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