1. science
2. mathematics
3. statistics

I²MTC 2008 – IEEE International Instrumentation and
Measurement Technology Conference
Victoria, Vancouver Island, Canada, May 12–15, 2008
A Hierarchical HMM Model for Online Gaming Traffic Patterns
Behnoosh Hariri1,2, Shervin Shirmohammadi1, and Mohammad Reza Pakravan2
1
Distributed Collaborative Virtual Environment Research Laboratory
University of Ottawa, Ottawa, Canada
[BHariri | Shervin]@discover.uottawa.ca
2
Department of Electrical Engineering
Sharif University of Technology, Tehran, Iran
[hariri | pakravan]@ee.sharif.edu
Abstract
Online games seem to become major contributors to Internet traffic.
Therefore a great deal of effort is being devoted to the analysis and
modeling of network game traffic. However the results from the
previous measurements have not been unified into a single frame
work while gaming traffic model is of high importance to network
designers. Considering the fact that Gaming traffic is generated by
the player’s interaction during game sessions, we propose to model
the player’s activities and later use this model to extract the traffic
pattern. We will propose a model for the gaming player behavior
regarding traffic generation based on hierarchical hidden markov
model. Player activities are inherently highly complicated. In order
to deal with the complicated Player activities, it is necessary to
incorporate a hierarchical structure in representation of activities,
in which a Player activity is represented by a combination of
multiple activity units, or actions. Any action or any combination of
actions may occur during a game session. The HHMM hierarchy
ends in production states that result in the transmission of update
messages to the game server. HHMM Observations are considered
to be client packet size and packet interarrival time.
Keywords – Massively Multiuser Online Gaming, Traffic Modeling
and Measurement, Hierarchical HMM.
I.
INTRODUCTION
Online games are expected to be major contributors to
World Wide Web traffic. DFC Intelligence forecasted the
worldwide online game market to grow from $4.5 billion in
2006 to over $13 billion in 2011 and the total overall number
of online gamers in the twenty leading online game countries
is expected to increase 51% from 2006 to 2012. It has been
estimated that roughly 9 percent of the traffic sent back and
forth over the US backbone was due to online gaming in
2002 [1]. As the performance of gaming hardware platforms
get better and number of online gamers increase
exponentially, game environment will have much faster
connectivity requirements. Therefore, measurement and
modeling of online gaming traffic has been the subject of
many recent works.
The leading online game category is expected to remain
high-end massively multiplayer online games (MMOGs).
There are several types of massively multiplayer online
games. Massively multiplayer online role-playing games
(MMORPG) such as World of Warcraft are online games in
which a large number of players interact with one another in
a virtual world. First-person shooters (FPS) games such as
quake are those MMOs that provide large-scale, sometimes
team-based combat in real time virtual environment. Real
time strategy (RTS) games as age of empire typically
combine real-time strategy with a large number of
simultaneous army commanders in resource competition.
Turn based strategy games (SG) such as Panzer General 3D
are games that focus on socialization instead of objectivebased game play. In such games two or more participants
make their moves sequentially in turns. Massively
multiplayer online racing are online versions of racing games.
Simulators such as Grand Prix simulate certain aspects of the
real world where the main emphasis is on fast moving
environment. There are several other MMO games Such as
massively multiplayer online manager games, Online Rhythm
Games multiplayer and online tycoon game that are
considered to be less popular than the previous ones[2]. The
fastest growing MMOG game segments are expected to be
First Person-Shooters (FPS/Action) and Sports/Racing In
terms of market share growth between 2006 and 2012
according to IDC forecast. Therefore
As online games seem to become major contributors to
Internet traffic, a great deal of effort is being devoted to the
analysis and modeling of network game traffic. Gaming
traffic varies over time during the days and over days during
a week; it is also considered self-similar with heavy-tailed
distribution for several games according to the measurements.
This Long-term correlation such as hourly and daily game
play trends is good for knowing the busy times at which there
is more demand for bandwidth and QoS related parameters.
Therefore; In order for the model to be a realistic fit of
gaming traffic, it should describe both short range and longrange traffic characteristics.
Most of the previous works have been concentrated
around the representation of real world traffic measurement
and fitting some standard distribution over the measured
traffic where the distribution parameters follow several game
and player related parameters. However few works addressed
the issue of general traffic modeling. Therefore the result of
their work only applies to a specific game in a specific state
and cannot be extended to the cases other than the one for
which the measurement has been performed.
The motivation behind this work is to propose a
generalized framework to cover all the previous
measurements that has been performed for FPS games. The
model would have a general description and a number of
parameters that can be selected in a way to customize the
model for a specific FPS game in a specific case regarding
the game and player state. This model can later be used as a
traffic synthesizer for FPS games that is necessary as a
reference for all gaming related protocol and network design
works that require using a realistic traffic model in their
designs. Such works are not customized to a specific game
and therefore need a prototype model that fits to the wide
variety of games under a specified category like FPS.
This paper aims at the proposal of a generic model for
gaming traffic. Considering the fact that gaming traffic is
generated by the players interactions during game session, we
propose to model players activities and later use this model to
extract the traffic pattern. We will use the term activity for
representing a sequence of player actions, and an action for
representing a component motion, such as “walking”,
“sitting”, “going into a room”, “reading a book” and so on. It
should be noted that this model would contain a lot more
information regarding game states beyond the traffic related
statistics. Therefore, the basic idea of our work is to prepare a
model for players activities, such that the model represents
the total sequence of players actions during a game session.
Players activities are inherently highly complicated. In order
to deal with such complicated behavior it is necessary to
incorporate a hierarchical structure in representation of
activities, in which a Player activity is represented by a
combination of multiple activity units, or actions. Any action
or any combination of actions may occur during a game
session.
Our proposed approach for the modeling of a player
activity is based on Hierarchical Hidden Markov model. The
model has been defined in a way to describe the temporal
behavior of an online game client and the results of recent
gaming traffic have been used to determine the model
parameters for a specific game. This general model can then
be used to predict various statistical parameters such as
player wining chance.
The traffic generated by a player is normally a function of
player current action and the game state. Therefore the best
way to predict the traffic generated by a player is to predict
the player action during the game. The player current action
at each state depends on the sequence of his previous states.
Therefore the player current state can be described as a
probabilistic function of his previous states. A number of
mathematical models can be used to describe such chained
statistical behavior. Markov Model is among these analytical
models. In probability theory, a Markov process is a
stochastic process in which the probability distribution of the
current state is conditionally independent of the path of past
states, a characteristic called the Markov property. A hidden
Markov model (HMM) is a statistical model in which the
system being modeled is assumed to be a Markov process
with unknown parameters, and the challenge is to determine
the hidden parameters from the observable parameters. In the
hierarchical hidden Markov model (HHMM) each state is
considered to be a self contained probabilistic model where
each state of the HHMM is a markov model by itself. HHMM
is Useful in representing “vertical” structure in a time-series
model.
As for our case, the selection of Markov Model is due to
the similarity of a player behavior to a markov process.
Therefore our goal is to model a player behavior in the form
of a markov chain while the parameters of the markov model
for a specific game can be found using the traffic
measurement results for that game. In other words, we would
like discover the parameters of the markov model given a
dataset of observation sequences. However it should be noted
that the observation in each state of the markov model is
supposed to be traffic characteristics such as packet size and
packet interarrival time that are statistically de pendant on the
player state in the model. Therefore the model is actually
hidden and we want to estimate the hidden model parameters
from the traffic measurements that are supposed to be
observations. This explains the reason behind the HMM
model selection. Moreover we will use the Hierarchical
Hidden markov model in order to have to more object
oriented representation of a player behavior where the top
HMM models the main action while each action can be
modeled as a sequence of sub-actions using a separate HMM.
In our proposed approach the sequence of player actions in
game states is modeled by a hidden markov mixture of first
order markov chains. A second hidden markov chain
describes the action variations between consecutive states,
while state change occurs upon the receiving of a new game
state from the server. The HHMM hierarchy ends in
production states where production states are defined to be
the states that results in the update message generation for the
server. The HHMM observations are considered to be client
packet size and packet interarrival time that are supposed to
be statistically related to the players actions.
II. RELATED WORK
In the case of first person shouter MMO games,
measurements have been reported for Counter-strike [3]-[6],
quake [7]-[10], half-life [11], halo[12][13] and strategies tribe
[14] for parameters such as interarrival time and packet size
in both client and server sides. StarCraft traffic pattern has
been analyzed as a representative of Real time Strategy
MMO games [15][16] and Lineage has been considered as a
representative for massive multiplayer Online Role playing
game in [17]. Traffic measurement results have also been
reported for Shen Zhu online in [18]. Most of these works
have been concentrated around the measurement results for a
specific game and tried to fit some standard distribution over
the results and the results cannot therefore be used in a
generalized case. Only [19] demonstrates the possible use of
predictive model for FPS traffic patterns where the
distribution for multiple client games proposed to be found
by convolving the distribution of lower player games.
In this paper, we would propose to model a single player
traffic generation pattern using a Hierarchical HMM model.
This model may later be used to predict several parameters
such as the expected number of players actions, winning
probability, game duration and several other useful
information.
III.
BACKGROUND: HIERARCHICAL HIDDEN
MARKOV MODELS
Hierarchical hidden Markov models (HHMM) are
structured multi-level stochastic processes. HHMMs
generalize the standard HMMs by making each of the hidden
states an “autonomous” probabilistic model on its own.
Therefore each state in HHMM model is an HHMM as well.
The states of an HHMM emit sequences rather than a single
symbol. An HHMM generates sequences by a recursive
activation of one of the substates of a state. This substate
might also be composed of substates and would thus activate
one of its substates. This process of recursive activations ends
when we reach a special state that is known as a production
state. The production states are the only states that actually
emit output symbols through the usual HMM state output
mechanism: an output symbol emitted in a production state is
chosen according to a probability distribution over the set of
output symbols.
HHMM can be generally characterized in terms of the
following parameters:
1. D that is the number of hierarchy levels where
(d ∈ {1,.., D}) . The hierarchy index of the root is 1 and the
hierarchy index of the production states is D. An HHMM
state of is therefore denoted by q di where i is the state index
and d is the hierarchy index.
2. q di that is considered to be the number of substates of
an internal state q id .
3. The HHMM is also characterized by the state transition
probability between the internal states. For each internal
state q id , there is a state transition probability of making a
horizontal transition from the ith state to the jth in level d.
This can be represented as a matrix as denoted in (1)
d
d
(
)
A q = {a ijq = P q dj q id }
(1)
4. Similarly the initial probability of making a vertical
transition to substate q id +1 from its parent state q d can be
denoted as described in (2).
∏
qd
qd
(
)
= {π (q id +1 ) = P q id +1 q d }
(2)
5. K is the number of distinct observation symbols per
production state. The observation symbols correspond to
the physical outputs of the system being modeled. We
denote the set of symbols as V ={v1, v2, . . . vK} where Vk{
k = 1, 2, . . .,K} is an individual symbol.
6. Each production state is also parameterized by its output
probability vector as described in (3)
D
D
(
)
B qi = {b qi (k ) = P v k q iD }
(3)
7. The observation sequence O =O1,O2,O3, . . .OR, where
each observation Ot is one of the symbols from V, and R is
the number of observations in the sequence.
It is evident that a complete specification of an HHMM
requires the estimation model parameters, D and q id , and
three probability distributions A, B, and Π.
There are three canonical problems associated with
HHMM. The first problem is called forward-backward
algorithm and deals with the computation of the probability
of a particular output sequence and the probabilities of the
hidden state values given that output sequence. The second
problem is Viterbi algorithm and provides the solution to the
problem of finding the most likely sequence of hidden states
that could have generated a given output sequence. Finally,
Baum-Welch algorithm considers the case of finding the most
likely set of state transition and output probabilities when an
output sequence or a set of such sequences is given. As we
aim at discovering the parameters of the HHMM given a set
of measurements as observations, the problem that we would
address in this paper would be Baum-Welch case.
IV.
HHMM MODEL FOR GAMING PLAYER
ACTIONS
Most games utilize a client-server model. Every client’s
actions are sent in short messages to the server, and every
client is regularly updated with the actions taken by other
players. Generally, the game traffic can be modeled by
independent traffic streams from each client to the server and
a traffic stream from the server to the clients assuming that
clients behave independently and client traffic is independent
of the server traffic. Players run around shooting and
interacting with each other at this time. The game may also
be paused as the server changes maps or restarts a previous
map. A client transmit cycle consists of reading a server
packet, processing it, rendering the client’s current view on
the screen, sampling input devices, then transmitting an
update packet to the server. The client packet size usually
depends on the player action such as walking, running,
attacking and state in the game but independent of the
number of players, computer hardware or map type.
Consider a player that is in the playing process during an
online game session. Each local status update is reported in
the form of update messages to the game server for global
updates. The Game server receives the update and performs
the subsequent actions. This in addition to the updates from
the other players would result in updates that are transmitted
from the game server to the players.
From the network side traffic measurements, the types of
action that are performed in that session is not included in the
traffic log. That is, the states are not observable but some
functions, possibly random, of the states are observed. Our
goal is to try to find the players actions from the traffic
profile. Later In this section we describe our approach to
modeling player’s actions using a hierarchical hidden Markov
mixture of Markov chains. As explained in the previous
section such specification would require the estimation of
number of hierarchy levels and states in each hierarchy as
well as the probability distributions for both vertical,
horizontal and also the output in each state.
The first parameter in the HHMM definition is the
hierarchy level. The level of hierarchy is defined to be 3. The
highest level is related to the game states where the
transitions are modeled using a markov model. A markov
model is also used to model the player’s actions in each game
state. Player activities are arranged into a two-level hierarchy
of events ranked by complexity, where the lower level
contains shorter motions that chain together to form higherlevel events which are longer and more abstract. Therefore
each action is in turn modeled using a Hidden markov model.
The states in the lowest hierarchy level are production states.
In other words these are the states that result in update
message generation. The observation for the production
states is assumed to be the packet size and packet interarrival
time. Each of these outputs results in one observation
sequence and model parameter estimation can be done based
on one or both of the observations.
The choice of parameter values for the HHMM is an
estimation problem and it is desired to find the best parameter
values for the model. The usual criterion is maximum
likelihood. That is finding the values of parameters which
maximize the probability of the observed data. This is the
problem that the Baum-Welch computation addresses. BaumWelch training is an expectation-maximization algorithm for
training the emission and transition probabilities in an HMM
structure. What's important about the Baum-Welch Training
Method is that we can feed in observation sequences, and as
long as we present enough data, we will get an HMM that is
pretty close to optimal for the given training sequences. Thus,
if the training sequences are characteristic of the actual
distribution of observation sequences in the system we are
modeling, our HMM will be able to tell us what state the
system is in with a high degree of certainty.
Therefore we would use Baum-Welch algorithm to
estimate the HHMM parameters for each player. The
algorithm starts with an initial estimate of HHMM parameters
A, B, and Π and converges to the nearest local maximum of
the likelihood function. Initial state probability distribution in
each hierarchy level is considered to be uniform, that is, if
there are N states, then the initial probability of each state is
1/N. The Baum-Welch algorithm is based on the computation
of two functions, known as Forward and Backward
probabilities for each state and each frame of an observation
sequence where one frame of observation sequence is defined
to be a game session for a player. Once Forward and
Backward probabilities are computed, they are used to weight
the contributions of each observation to the HMM
parameters.
In the previous steps, we have defined an HHMM model
that describes a single player behavior and explained the
training method to find the model parameters using the
training data. The only remaining issue here is to provide a
set of observation data to the training process. Later in the
next section we would explain the way that we have extracted
a general set of training data from the results of the previous
measurements. In order to do that we would refer to a number
of recent measurements on the gaming traffic pattern and try
to draw a consistent pattern from these measurements.
V. HHMM TRAING DATA AQUIZATION
Several measurement results have been reported for a
number of popular online games during the last few years.
The results obtained from the measurements vary from game
to game especially when the games are in different
categories. This is due to the fact that the gaming traffic
pattern is strongly impacted by the game logic. Therefore it is
seems reasonable for the traffic pattern of highly dynamic
FPS games to be totally different from less dynamic strategy
based games. Therefore we would focus on a single class of
games known as First person shooter games that are known to
be the most challenging games regarding the networking
point of view. However it should be noted that the proposed
HHMM modeling can be applied to any other class of online
games through the model redefinition.
Therefore we would concentrate on a general traffic
extraction for FPS games that can later be used for HHMM
model training. It should be noted that even for the class of
FPS games measurements are considered to be dependant on
the game map and some other player related parameter such
as rendering engine. Therefore using a single model for all
FPS games will result in model inaccuracy due to the
considerable difference in players actions in different game
classes.
A more exact HHMM model can still be obtained using
only measurement results from single FPS game and even the
model can be further customized to the client types to make a
better match, however the availability of a general
approximate model is still valuable for network design.
Therefore we would concentrate on the definition of such a
model instead of extracting an exact but specific one. In order
to extract such training data for a general model, we would
try to draw a consistent approximate result from all FPS
traffic measurements.
The training data can be both considered to be packet
length or packet interarrival time of the traffic. Here we
would refer to a number of measurements for these two
parameters and choose distributions that best fits the client
packet interarrival time and client packet length. Later we
also refer to the session time distribution for the clients. The
training sequence for each of the observations can then be
extracted from the distribution of the related parameter and
the session time duration distribution.
For counter-strike game, Client interarrival time peak has
been measured to be 60 ms with surrounding peaks every
10ms or 20ms [3]. This value has been reported to be 33 ms
and 50 for OpenGL clients in quake [11] and 40 ms for Halo
players [13]. It has also been measured around 40-50 ms for
half-life client while it is independent from the map in half
life case and fixed at 50ms for half life clients using
Direct3D.
Although most of the client packets arrive in regular
intervals, the client interarrival distribution still shows a
heavy–tailed
behavior.
Therefore,
Exponential
or
deterministic distribution can be a proper model for client
interarrival time. Returning to the case of HHMM modeling,
the previous measurements reveal the fact that the transition
in client actions is expected performed with a probability p
that is near 1 most of the times due to the regular packet
transmission. However the heavy tailed behavior implies that
the probability is slightly less than one in some of the states.
The probability for use in the model can either be selected as
a deterministic value or can be selected as a normalized value
of the (0-90%) part of the exponential interarrival time
distribution.
Client packets have been estimated to have an extremely
narrow distribution with the mean size of around 40
bytes(without UDP/Ethernet header) for counter strike[3][5],
it has also been measured to be distributed between 50 and 70
bytes for quake [10] and between 60 and 90 bytes for half life
[11]. As for counter-strike, extreme (41,6) was proposed as a
good fit for client packet size in the range [20:100] [3]. The
client packet size has also been modeled by lognormal (75,3)
for quake[7].
The measurement results demonstrate the fact that the
client packet size can be best approximated by a number of
impulse functions distributed between 50 and 70 bytes for
most FPS games [19]. Therefore we would use this model as
our training data.
The outer markov chain is triggered by receiving the
update messages from the server. Therefore we may have a
good estimate on the probability transition on the outer chain
by knowing the server packet interarrival time.
The main server task is to receive the individual client
actions, calculate the new game state, and send it to all the
clients. Therefore the server data rate increases with the
increase in the number of clients; However Traffic rates from
server to one client do not vary that much and was mainly
designed to saturate the narrowest last-mile link. Packet
interarrival time of server is independent on the number of
players and in-game behaviors. The mean of server
interarrival time for individual client has been measured
around 50ms[7][8][4] for counter-strike and quake, 60 ms or
50% at 50 ms and 50% at 70ms depending on the map for
half life and around 40 ms for Halo[13].
There are also some high frequency components in server
traffic for counter-strike, The frequency component around
30 minutes is due the 30 minute map time of the server
during which a dip in traffic occurs when server is doing
local tasks to perform the map change over. Other low
frequency components also happen due to round changes.
According to the measurement results, the server packet
interarrival time has been modeled with a burst of 60 ms
interarrival time [4] for counter-strike ,deterministic at 50ms
[7][11] for quake, 60 ms [10] for half life and a combination
of extreme and normal distributions for almost all FPS games
[9]-[14]. Therefore it can be concluded that the server packet
interarrival time is mostly regular except for a few cases. The
outer markov chain will therefore have a transition
probability that is near one. This probability can be used as
initial values for state transition on that chain.
The only remaining issue for HHMM definition is the
observation sequence. In other words we should be able to
define the duration of a typical observation frame for the
training data. In order to have a good estimate on this, we
again refer to the recent measurement results on the player
session duration.
It has been observed that a significant number of players
play only for a short time before disconnecting and that the
number of players that play for longer periods of time drops
sharply as time increases [4]; however the game duration
process has a Heavy-tailed distribution due to a number of
long-time players [5]. According to these results, the twoparameter form of the Weibull with beta = 0.5, eta = 20, and
gamma = 0 was proposed to be a good choice for session time
distribution [4][20].
Each observation frame represents a game session for a
player. The previously mentioned distribution for session
time can therefore be used to determine the observation frame
duration.
In this section we have explained the way to extract proper
training data from the available measurement results for FPS
games. The HHMM model can now be trained with this data
and the HHMM parameters are therefore estimated. The
resulting model can now be used as a traffic synthesizer for
the gaming traffic and also as a way to estimate several game
related statistics.
VI.
EXPERIMENTAL EVALUATION
The previously described HHMM model has been used to
describe a player activity in a generic FPS game whose traffic
pattern has been considered to be a typical pattern for the FPS
games as described in the previous session.
The resulting model have been used to find the
dependency of player winning probability to the player
session time. The results are illustrated in figure 1. The
modeling results show that the chance of winning becomes
higher as the session time increases for the players; However
it shows a saturation behavior above a specified point to the
fact that most players are able to win the game up to that
time.
Figure 2 shows the probability of players leaving the game
after a specific time interval. The simulation results show that
there is a high probability that a player leaves the game in the
first few minutes that he started. Later the probability of
staying in the game increases and finally the probability of
staying in sessions longer than a specified value decreases.
These results seem to be compatible with the measurement
results for session duration.
0.8
0.7
Winning chance
0.6
0.5
level hierarchy of events. A series of measurement data for
some popular online FPS games have also been used as the
model training data. And the model was trained using the
classic Baum-Welch algorithm.
The resulting model was then used to estimate a number
statistical parameters regarding player behavior such as
winning probability and the chance of leaving the game.
VIII.
REFERENCES
0.4
0.3
0.2
0.1
0
0
20
40
60
Minutes
80
100
120
Figure 1 Player Winning Chance over time
0.6
0.55
0.5
Leaving chance
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0
20
40
60
80
Minutes
100
120
140
Figure 2 Player leaving Chance over time
VII.
SUMMARY AND CONCLUSION
The motivation behind this work was to propose a
generalized framework to cover all the previous
measurements that were performed on FPS game traffic.
Therefore we aimed at proposing an analytical model for
gaming traffic synthesis. Considering the fact that Gaming
traffic is generated by the players interactions during game
sessions, it would be possible to model the players activities
and later use this model to extract the traffic pattern. In order
to deal with the complicated Player activities, we proposed to
incorporate a hierarchical structure in representation of
activities, in which a Player activity is represented by a
combination of multiple activity units, or actions.
Therefore we have chosen hierarchical hidden markov
model that is best suited to the representation of vertical
structure in a time-series model. The level of hierarchy was
defined to be 3 where a game states are modeled using a
markov model and Player activities are arranged into a two-
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