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PAPER

Special Section on Human Communication I

Structures of Human Relations and User-Dynamics Revealed byTraﬃc Data
Masaki AIDA†a) , Keisuke ISHIBASHI† , Hiroyoshi MIWA†† , Chisa TAKANO††† ,and Shin-ichi KURIBAYASHI†††† , Members

SUMMARY The number of customers of a service for Internet accessfrom cellular phones in Japan has been explosively increasing for sometime. We analyze the relation between the number of customers and thevolume of traﬃc, with a view to finding clues to the structure of humanrelations among the very large set of potential customers of the service.
The traﬃc data reveals that this structure is a scale-free network, and we
calculate the exponent that governs the distribution of node degree in thisnetwork. The data also indicates that people who have many friends tend
to subscribe to the service at an earlier stage. These results are useful forinvestigating various fields, including marketing strategies, the propagationof rumors, the spread of computer viruses, and so on.
key words: i-mode, traﬃc, scale-free network, human relations, Zipf’s law

1. Introduction
The number of customers of NTT DoCoMo’s ‘i-mode service’ in Japan (for Internet access from cellular phones)
has been explosively increasing and recently reached about
40,000,000, although the service was only introduced five
years ago [1]. Statistics on i-mode’s growth thus provide
an interesting body of information on the behavior of large
numbers of users. Complex networks such as structuresof social relations do not have an engineered architecture;
rather, they are self-organized by the actions of large numbers of individuals. The local interactions can lead to thenontrivial global phenomenon of a scale-free distribution ofnode degree [2], which in turn leads to a small-world property [3], [4]. In this paper, we analyze the relation between
the number of i-mode customers and the volume of traﬃc,with a view to finding clues to the structure of human relations among the very large set of potential i-mode customers. The traﬃc data reveals that this structure is a scalefree network, and we calculate the exponent that governs the
distribution of node degree in this network. The data also indicates that people who have more friends tend to subscribe
to the i-mode service at an earlier stage.
Manuscript received October 22, 2003.
Manuscript revised January 9, 2004.
†
The authors are with NTT Information Sharing Platform Laboratories, NTT Corporation, Musashino-shi, 180–8585 Japan.
††
The author is with Department of Informatics, School of
Science and Technology, Kwansei Gakuin University, Sanda-shi,
669–1337 Japan.
†††
The author is with Traﬃc Engineering Division, NTT Advanced Technology Corporation (NTT-AT), Musashino-shi, 180–
0006 Japan.
††††
The author is with Department of Applied Physics, Seikei
University, Musashino-shi, 180–8633 Japan.
a) E-mail: aida@m.ieice.org

If we consider each person as a node and each relation
between two people as a link, we have a graphical model ofhuman relations. If we can systematically characterize thestructure of graphs thus derived, the characterization should
be applicable to marketing strategies, the propagation of rumors and epidemic, and demand forecasting for telecommunications services, among others.
Networks of hyperlinks among web pages on the Internet and certain social networks have been reported to show
small-world properties and act as scale-free networks. A
scale-free network has a small number of ‘hub’ nodes, eachof which has quite a lot of links. This feature acts to suppress increases in network diameter when the number ofnodes increases. As a result, the average numbers of hops
in the routes between all pairs of nodes are extremely small
and information spreads with remarkable speed. The defining feature of a scale-free network is that the distributionof node degree obeys a power law, i.e. n(k) ∝ k−γ , wherek and n(k) denote the node degree (number of links) andthe number of nodes of degree k, respectively, and γ is apositive constant. A wide variety of scale-free networks has
been found, in both technological and social realms. In mostcases, the relation 2.0 ≤ γ ≤ 3.4 applies [5]. Ebel et al. [6]analyzed the logs of the e-mail server at Kiel University andproduced a graph that represents the relationships among thee-mail accounts of the students. A link in the graph indicatesthe passage of at least one e-mail message between the corresponding pair of accounts. The graph in this case was ascale-free network with the slightly atypical γ value of 1.81.
This result reflects human relations within a small community, in this case the set of people who use the university’s
e-mail server. The result is thus not applicable to people
in general. Furthermore, since an e-mail log will almost
certainly include records of multicast messages, i.e. messages sent to accounts on a mailing list, the passage of ane-mail message does not necessarily indicate a relationshipbetween the owners of the corresponding pair of accounts,
so the result does not solely reflect human relations. Abello
et al. [7] and Aiello et al. [8] analyzed telephone calls on acertain day and produced a graph that represents the relationships among phone numbers. In this case, a link represents the setting up of a connection between the corresponding pair of numbers. This graph is a scale-free network with
γ = 2.1. The data in this case is on a large number of nonspecified people so the result should be generally applicable;
however, a phone number often corresponds to a company

AIDA et al.: STRUCTURES OF HUMAN RELATIONS AND USER-DYNAMICS REVEALED BY TRAFFIC DATA

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or family rather than an individual, so the result does notreliably reflect human relations.
This paper is on our investigation of the relation between the number of i-mode customers and the volume ofi-mode traﬃc. Simple analysis of this relation reveals somefundamental features of human relations for a large numberof non-specified persons (the population within reach of theservice). In addition, we clarify this population’s dynamic
behavior as a set of potential service subscribers.
The rest of this paper is organized as follows. In Sect. 2,
we introduce our traﬃc data and point out the characteristics
which make them desirable as a basis for analyzing humanrelations. In Sect. 3, we explain our assumptions and theframework of our investigation, and present the analyticaland general form of the relation that characterizes i-modee-mail usage. In Sects. 4–6, we assume various rules for theselection of new i-mode subscribers, and investigate the patterns of human relations they reflect and the user dynamics
we would expect if the rule were correct. The rules are random distribution, identical and independent distributions,and a deterministic rule. Section 7 reveals that the structure of human relations forms a scale-free network. Finally,
we conclude our discussion with Sect. 8.

Fig. 1 A log-log plot of the number of i-mode customers versus the volume of web traﬃc (as the number of site-access operations). Traﬃc data is
for August 1, 1999 to January 31, 2000. For both axes, the quantities arenormalized on the result for August 1, 1999 as one. The line with slope one
is for comparison.

2. Traﬃc Data
Data on i-mode service traﬃc is of particular interest for thefollowing reasons.
(a) The explosive growth of the service minimizes the effect on traﬃc of external factors such as changes in
economic circumstances, family structure, and so on.
(b) Since almost all cellular phone terminals are for personal use, the transfer of an e-mail message between
two terminals unambiguously represents communication between the corresponding pair of customers.
(c) Almost all e-mail traﬃc in the service is one to one,so we can assume proportionality between the volumeof e-mail traﬃc and the number of customer pairs exchanging messages.
(d) Sending an e-mail message is much cheaper than avoice communication, so external factors, e.g. the income of users, only have negligible eﬀects on the traﬃcpatterns.
(e) In the early stages of popularization of the i-mode service, the combination of few e-mail advertisements andlittle sensationalism to attract nuisance users meant thatvery little of the traﬃc was independent of relationships among people.
(f) The service was heavily advertised in the mass media.
Information about the i-mode service was thus widely
propagated within a short period and the intensity ofthe public campaign meant that propagation was independent of the topology of human relations.
The number of customers grew about three-fold, from
1,290,000 to 3,740,000, over the six months from Aug. 1999
to Jan. 2000 [1]. The relationship between the number ofFig. 2 A log-log plot of the number of i-mode customers versus the volume of e-mail traﬃc (as the number of messages sent). Traﬃc data is forAugust 1, 1999 to January 31, 2000. For both axes, the quantities are normalized on the August result as one. The lines are given for comparison.

customers and the volume of i-mode web-service traﬃc inthis period is shown in Fig. 1. Let the number of i-mode
customers be m; the relationship is then written as(i-mode web traﬃc) ∝ m.

(1)

The most reasonable explanation for this is a stable frequency of web access per user. The reason for this is asfollows: if users who have subscribed to the i-mode service
at an earlier stage are heavier users than more recent subscribers, the volume of web traﬃc will not be proportional
to m. The result thus implies that the usage characteristicsof the i-mode service for the average customer were stable
over this period. The number of i-mode customers and thenumber of i-mode messages in the same period is given in
Fig. 2. The data follows this power law:(i-mode e-mail traﬃc) ∝ m1.55 .

(2)

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Fig. 3 The graph representing human relations, G(V, E), and the subgraph Gm (Vm , Em ) induced byi-mode customers.

Therefore, the number of e-mail messages increases more
quickly than the volume of web traﬃc. If the number of
e-mail messages for an average customer is independent of
the number of i-mode customers and is stable, it should be
proportional to m. A value greater than m reflects growthover time in the number of partners with whom the averagecustomer might want to communicate. On the other hand, if
the average customer knows a certain constant proportion ofcustomers (even if this proportion is small, e.g. 0.0001%),
the volume of e-mail traﬃc should be proportional to m2 .
The fact that the volume of e-mail traﬃc is proportional tom1+α , where 0 < α < 1, means that while the number ofpossible communication partners increases, the ratio of thisnumber to the number of all customers falls. The parameterα = 0.55 characterizes the rate of growth for e-mail traﬃc.
It also tells us something about the strength of human relations. Hereafter, we investigate the characteristics of humanrelations that satisfy Eq. (2).
3. Notation and Assumptions
Let the set of people in Japan (i.e. the set of all potential
customers of the i-mode service) be V, and the set of pairsof people who exchange information with each other be E.
The number of elements in V is |V| = n. We define humanrelations as a graph G(V, E). We assume that G(V, E) is stationary. Next, we use a rule to select m elements from V and
let the subset of these selected elements be Vm (m ≤ n). Let
the subgraph induced by Vm from G(V, E) be Gm (Vm , Em ).
That is, a node pair is connected by a link in Gm (Vm , Em ) if
and only if the corresponding node pair in G(V, E) is connected by a link. Each element of Vm is an i-mode customer
and human relations among all i-mode customers are represented by Gm (Vm , Em ) (see Fig. 3). We assume that the
number of links, |Em |, in the induced subgraph Gm (Vm , Em )is proportional to the volume of e-mail traﬃc (as the number of messages) flowing in the i-mode service. Thus, toclarify the origin of the behavior that leads to Eq. (2), i.e. to
0 < α < 1, we need to find the condition of human relations
G(V, E), and not just of the subset of relations Gm (Vm , Em ),that satisfies|Em | ∝ m1+α .

(3)In the following sections, we assume various possible

rules for selection of subscribers to the i-mode service, identify the rule which corresponds with our data, that is, the rule
which characterizes user-participation dynamics, and show
the structure of human relations G(V, E) thus implied.
4. Random Selection of New i-mode Customers
We sort all elements of V into descending order of degree(number of links connected to the element) with respect tothe graph G(V, E), and let the degree of the i-th element be
Di (i = 1, 2, . . . , n). In cases where multiple nodes have thesame degree, i is arbitrarily assigned. Similarly, all elementsof Vm are sorted into descending order of degree with respect
to the subgraph Gm (Vm , Em ). We let the degree of the j-thelement be d j ( j = 1, 2, . . . , m).
Next, let us consider continuous versions of the degree
distributions Di and d j , denoted by D(x) and d(y), respectively, where 0 ≤ x ≤ n and 0 ≤ y ≤ m. The distribution
D(x) of degree is a monotonically decreasing function of x,
and we choose D(x) that satisfies
b


Di =

 b
D(x) dx,

(4)

a−1

i=a

where arbitrary parameters a and b are integers which satisfy
1 ≤ a ≤ b ≤ n. We choose the distribution d(y) in a similarway.
Since the elements of Vm are chosen from V, anode, which has the j-th largest degree, d j ( j ∈ Vm ), in
Gm (Vm , Em ), will on average correspond to a node in the set
with the i-th (i = (n/m) j) largest degree in G(V, E). In addition, since the probability that the nodes connected to thenode i ∈ V in G(V, E) are in Vm is (m − 1)/(n − 1),
dj 

m−1
Di ,
n−1

(5)

on average. So, the expectation of the number of links in
Gm (Vm , Em ), that is, F(m) := E [|Em |] are expressed as
1 
dj
2 j=1
 m
1
=
d(y) dy
2 0m

F(m) =

AIDA et al.: STRUCTURES OF HUMAN RELATIONS AND USER-DYNAMICS REVEALED BY TRAFFIC DATA

1457

 m
1 m−1
D((n/m)y) dy
2 n−1 0
 n
1 m−1
dy
=
dx
D(x)
2 n−1 0dx
 n
1 m (m − 1)=
D(x) dx
2 n (n − 1) 0n
1 m (m − 1) =Di
2 n (n − 1) i=1(7){x1 , x2 , . . . , xm }, which is a sequence of the points selectedby probability density function p(x) from [0, 1] and sorted
into ascending order. If we apply the distribution function P to transform the points {x1 , x2 , . . . , xm }, the points in{P(x1 ), P(x2 ), . . . , P(xm )} are uniformly distributed on [0, 1].
So, the node corresponding to a node j ∈ Vm is, on average,
x = P−1 ( j/m). Therefore, we can express the relationshipbetween D(x) and d(y) as m
 md(y) dy  c(m)D(P−1 (y/m)) dy,(11)

From the law of large numbers, we have F(m) = |Em |for m  1. We therefore obtain

where c(m) is a function of m. Incidentally, in the case in
the previous section,= O(m2 ).

|Em | = O(m2 ).

(6)

(8)

Consequently, if we assume that new customers of i-mode
are selected at random, the volume of e-mail traﬃc is independent of the structure of human relations and increases byO(m2 ). This does not agree with Eq. (3).

00c(m) =

m−1
,
n−1

(12)

and p(x) is a constant.
Then, the expectation of the number of links in
Gm (Vm , Em ), F(m) := E [|Em |] is expressed by
1 
dj
2 j=1
 m
1
=
d(y) dy2 0
 m1
D(P−1 (y/m)) dy c(m)
20 n1dy= c(m)
dx.
D(x)
2
dx
0
m

5. Selection of New i-mode Customers according to
Identical and Independent Distributions
In a similar way to the previous section, we sort all elementsof V into descending order of degree, and let the degree of
the i-th element be Di (i = 1, 2, . . . , n). We assign the probability pi (i = 1, 2, . . . , n) to all nodes i ∈ V and select m
nodes from V according to the probability pi . We assume
that node selection is according to an identical and independent distribution (i.i.d.), that is, it negligibly aﬀects theprobability distribution pi . This assumption indicates that
1 for all i ∈ V.
m n and requires pi
Let the set of m nodes selected from V be Vm , and thesubgraph of G(V, E) induced by Vm be Gm (Vm , Em ). All elements of Vm are again sorted into descending order of degreein the subgraph Gm (Vm , Em ); and let the degree of the j-thelement be d j ( j = 1, 2, . . . , m).
As we did with the random-selection case, let us consider the continuous versions of the distributions of degree
Di and d j as D(x) and d(y), and of probability pi as p(x),where 0 ≤ x ≤ n and 0 ≤ y ≤ m. If pi > 0 for all i(i = 1, 2, . . . , n), we can choose the density p(x), which satisfies p(x) > 0 for arbitrary x (0 ≤ x ≤ n) and
b

i=a

pi =

 b
p(x) dx,(9)a−1where a and b are arbitrary integers that satisfy 1 ≤ a ≤ b ≤n.
Let us consider the distribution function that corresponds to the density function p(x), x
P(x) :=
p(s) ds.
(10)0Since p(x) > 0, there exists an inverse of the distribution function, P−1 (u), for all u ∈ [0, 1]. Consider

F(m) =(13)

Since x = P−1 (y/m), we can obtain dy/dx = m p(x). Thus, nm
F(m) = c(m)D(x) p(x) dx.
(14)
2
0
If the probability density p(x) is independent of the topologyof the original graph G(V, E), we can determine c(m) = (m −1)/(n − 1), and get
F(m) =n
1 m (m − 1) Di p i .
2 (n − 1) i=1(15)

Comparison with Eq. (6) shows us that Eq. (15) is equivalent
to selecting nodes at random for the graph with degree distribution Di = n Di pi . In particular, if nodes are selected at
random, that is, p(x) = 1/n, Eq. (15) becomes identical with
Eq. (6).
In popularization of the i-mode service, advertising in
the mass media had far more power than did word of mouth.
So, we can assume that the popularization process was independent of the topology of human relations. The number of subscribers among the average user’s friends and acquaintances is thus proportional to the number of i-mode
subscribers, so we can state thatc(m) ∝ m.
Thus, we have

(16)

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1458

F(m)  O(m2 ) ×

 n
D(x) p(x) dx.

(17)

0

Since, in order to realize |Vm | = O(m1+α ), F(m) has tosatisfy F(m) = O(m1+α ). So, we have nD(x) p(x) dx = O(mα−1 ),(18)0or in discrete form,n
Di pi = O(mα−1 ).

(19)

i=1

Since D(x) and Di are independent of m, Eqs. (18) and (19)mean that p(x) and pi depend on m. This result contradicts
the assumption of i.i.d.
6. The Structure of Human Relations and the Rule for
Subscription to the i-mode Service
The previous section demonstrated that the probability of
selecting a given node changes after each node selection.
Since setting a new probability for every node selection iscomplex, we adopt a deterministic approach.
We sort all elements of V into descending order of degree (number of links connected to the element), and let thedegree of the i-th element be Di (i = 1, 2, . . . , n). In cases
where multiple nodes have the same degree, i is arbitrarily
assigned. Similarly, all elements of Vm are sorted into descending order of degree in the subgraph Gm (Vm , Em ). We
let the degree of the j-th element be d j ( j = 1, 2, . . . , m).
On the other hand, we sort those elements of V thathave been selected for Vm into their order of selection,and let the degree within V of the k-th element be D(s)k(k = 1, 2, . . . , n). All elements of Vm are sorted into thesame order. Let the degree within Vm of the h-th element
be dh(s) (h = 1, 2, . . . , m). While the g-th element, g ∈ Vm ,corresponds to g ∈ V, dg(s) is very rarely the same as D(s)g .
If we select m elements from V, the degree within
Gm (Vm , Em ) of the selected elements can be written asmmdk(s)  c(m)
D(s)
(20)
k ,
k=1

k=1

where c(m) is a function of m. The number of links in
Gm (Vm , Em ) is then written asm
1  (s)d|Em | =
2 k=1 k


m

1
c(m)
D(s)
k .
2
k=1

(21)

As was earlier stated, advertising in the mass media had far
more power as a popularizer of the i-mode service than did
word of mouth, from which we obtained Eq. (16). Then,from Eq. (3), we have
m

k=1

α
D(s)
k ∝m .

(22)

Since Eq. (22) is valid for all m, we have
α−1
.
D(s)
k ∝k

(23)

The above results are rephrased below.
• (Result A) The elements of Vm tend to be selected fromV in descending order of degree in G(V, E). In otherwords, a person who has many friends tends to subscribe to the i-mode service at an earlier stage.
• (Result B) The distribution of degree among the elements of V obeys Zipf’s law [9]. That is, for the degree
Di of the i-th element of V (the indices are determined
in descending order of degree)
Di ∝ i−β(24)holds, where β > 0 is a constant and β = 1 − α.
Conversely, Results A and B along with c(m) ∝ m lead us toEq. (3).
7. The Structure of Human Relations as a Scale-Free
Network
We consider the distribution of degree, n(k), for a G(V, E)
the elements of which satisfy Result B. Let the slope of
Zipf’s law in the log-log plane be −β. We consider the degree of the x-th element, Z(x). For constants a > 0 and
c1 > 0, the degrees of the x-th and ax-th elements are written asc1(25)Z(x) = β , andxc1
Z(ax) =.
(26)(ax) βSince the slopes at both (x, Z(x)) and (ax, Z(ax)) are −β ona log-log scale, let us consider two triangles which are congruent in the log-log plane (see Fig. 4). The lengths of thebases of the two triangles are related to n(Z(x)) and n(Z(ax)).
More specifically, the ratio of the two lengths in the linear plane is equal to n(Z(x)) : n(Z(ax)). Thus, we haven(Z(x)) : n(Z(ax)) = 1 : a. Consequently, for a constantc2 > 0,n(Z(x)) = c2 , andn(Z(ax)) = c2 a.

(27)
(28)

We can plot the points (Z(x), n(Z(x))) and (Z(ax), n(Z(ax)))
and then derive the slope of the line connecting the twopoints on the log-log plane asγ=

log n(Z(ax)) − log n(Z(x)) 1.
log Z(x) − log Z(ax) β(29)

The above equation, Eq. (29), is independent of a. Thus, thedistribution of degree is obtained asn(k) ∝ k−γ ,(30)where γ = 1/β. This relation is called Lotka’s law [9]; sinceAIDA et al.: STRUCTURES OF HUMAN RELATIONS AND USER-DYNAMICS REVEALED BY TRAFFIC DATA

1459

and C are valid as descriptions of human relations and bothwill be useful for investigating other fields including marketing strategies, the propagation of rumors, and the spreadof epidemics.
In addition to information on the structure of humanrelations, we also obtained Result A, which concerns the
dynamic behavior of customers. This result is applicable asa description of how a money spinner emerges. We expectthat combining knowledge of the three results will lead toeﬃcient marketing strategies.
References

Fig. 4 Two points extracted from data that satisfies Zipf’s law (upper
panel) and plotted on a Lotka-type graph (lower panel).

it is a consequence of Zipf’s law, the two laws accompany
each other (e.g. in Internet access [10]). From the above discussion and Result B, we get the following result:• (Result C) The graph that represents human relations
is a scale-free network, with distribution of degree described by Eq. (30) and[1] DoCoMo Net, Usage of i-mode (in Japanese),
http://www.nttdocomo.co.jp/p_s/imode/[2] A.-L. Barabási and R. Albert, “Emergence of scaling in random networks, ” Science, vol.286, pp.509–512, 1999.
[3] D.J. Watts and S.H. Strogatz, “Collective dynamics of ‘small-world’
networks,” Nature (London), vol.393, pp.440–442, 1998.
[4] D.J. Watts, Small-Worlds, Princeton University Press, Princeton, NJ,
1999.
[5] R. Albert and A.-L. Barabási, “Statistical mechanics of complex networks,” Rev. Mod. Phys., vol.74, pp.47–97, 2002.
[6] H. Ebel, L.-I. Mielsch, and S. Bornholdt, “Scale-free topology ofe-mail networks,” Phys. Rev. E, vol.E66, 035103(R), 2002.
[7] J. Abello, P.M. Pardalos, and M.G.C. Resende, “On maximum
clique problems in very large graphs,” DIMACS Series in Discrete
Mathematics and Theoretical Computer Science, vol.50, pp.119–
130, 1999.
[8] W. Aiello, F. Chung, and L. Lu, “A random graph model for massive graphs,” 32nd ACM Symposium on the Theory of Computing,pp.171–180, 2000.
[9] R. Rousseau and S. Rousseau, “Informetric distributions: A tutorial
review,” Can. J. Inf. Libr. Sci., vol.18, no.2, pp.51–63, 1993.
[10] M. Aida, N. Takahashi, and T. Abe, “A proposal of dual Zipfianmodel describing http access trends and its application to address
cache design,” IEICE Trans. Commun., vol.E81-B, no.7, pp.1475–
1485, July 1998.

1
.
(31)
1−α
By using the experimental value α = 0.55, we getγ=n(k) ∝ k−2.22 .

(32)

8. Concluding Remarks
Results A–C were derived on the assumption that c(m) ∝ m,where m is the number of subscribers and c(m) is, for the
average user, the ratio of the number of friends who aresubscribers to the i-mode service to his/her total number offriends. This is based on the assumption that the processof popularization is independent of the topology of humanrelations, which is in turn based on the fact that advertisements for i-mode in the mass media have been very much
more powerful as popularizers of the service than the diﬀusion of information by word of mouth. However, in cases
where the diﬀusion of information by word of mouth plays
a non-negligible role, c(m)  O(m). Our purpose in thispaper has been to describe the characteristics of human relations revealed by data on the i-mode service. Results B

Masaki Aida
received his B.S. and M.S.
in Theoretical Physics from St. Paul’s University, Tokyo, Japan, in 1987 and 1989, and received the Ph.D. in Telecommunication Engineering from the University of Tokyo, Japan,
in 1999. Since joining NTT Laboratories in
1989, he has been mainly engaged in researchon traﬃc issues in ATM networks and computercommunication networks. From March 1998 to
March 2001, he was a manager at Traﬃc Research Center, NTT Advanced Technology Corporation (NTT-AT). He is currently a Senior Research Engineer at NTT
Information Sharing Platform Laboratories. His current interests include
traﬃc issues in communication systems. He received IEICE’s Young Investigators Award in 1996, and Information Network Research Awards in
2001, 2002, 2003, and 2004. Dr. Aida is a member of the IEEE and the
Operations Research Society of Japan.

IEICE TRANS. INF. & SYST., VOL.E87–D, NO.6 JUNE 2004

1460
Keisuke Ishibashi
received his B.S. and
M.S. in Mathematics from Tohoku University,
Sendai, Japan in 1993 and 1995, respectively.
Since joining NTT in 1995, he has been engaged
in research on traﬃc issues in computer communication networks. He received IEICE’s Young
Investigators Award and Information Network
Research Award in 2002. Mr. Ishibashi is amember of the IEEE and the Operations Research Society of Japan.

Hiroyoshi Miwa
received the B.S. degree
in mathematics from the University of Tokyoin 1992 and the Dr. of Informatics degree fromthe Department of Applied Mathematics andPhysics of the Graduate School of Informatics,
Kyoto University in 2000. He has been engaged
in research on the network design and control issues, and the theory of combinatorial optimization for graphs and networks. From 2002, he is
an assistant professor in the Department of Informatics of the School of Science and Technology at Kwansei Gakuin University. He received the Young Excellent Author Award at the ninth Workshop on Circuits and Systems in Karuizawa in
1997.

Chisa Takano
received the B.E. in Telecommunication Engineering from Osaka University,
Japan, in 2000. In 2000 she joined Traﬃc
Research Center, NTT Advanced Technology
Corporation (NTT-AT). She has been engaged
in research and development of computer networks. She received IEICE’s Young Investigators Award in 2003, and Information Network
Research Award in 2004.

Shin-ichi Kuribayashi
received his B.E.,
M.E., and Ph.D. in engineering from Tohoku
University, Sendai, in 1978, 1980, and 1988 respectively. He joined the NTT Electrical Communications Labs in 1980. He has been engaged in the design and development of DDX
and ISDN packet switching, ATM, PHS, and the
IMT2000 and IP-VPN systems. He researched
distributed communication systems at Stanford
University from December 1988 through December 1989. He participated in international
standardization on the ATM signaling and IMT2000 signaling protocols at
the ITU-T SG11 from 1990 through 2000. Since April 2004, he has been a
Professor in Department of Applied Physics, Faculty of Engineering, Seikei
University.