Prediction of State of Wireless Network Using Markov and ... - CiteSeerX

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JOURNAL OF NETWORKS, VOL. 4, NO. 10, DECEMBER 2009

Prediction of State of Wireless Network Using Markov and Hidden Markov Model MD.Osman Gani Military Institute of Science and Technology, Department of Computer Science and Engineering, Dhaka, Bangladesh Email: [email protected]

Hasan Sarwar and Chowdhury Mofizur Rahman United International University, Department of Computer Science and Engineering, Dhaka, Bangladesh Email: {mdhasan70, cmrbuet}@yahoo.com

Abstract—Optimal resource allocation and higher quality of service is a much needed requirement in case of wireless networks. In order to improve the above factors, intelligent prediction of network behavior plays a very important role. Markov Model (MM) and Hidden Markov Model (HMM) are proven prediction techniques used in many fields. In this paper, we have used Markov and Hidden Markov prediction tools to predict the number of wireless devices that are connected to a specific Access Point (AP) at a specific instant of time. Prediction has been performed in two stages. In the first stage, we have found state sequence of wireless access points (AP) in a wireless network by observing the traffic load sequence in time. It is found that a particular choice of data may lead to 91% accuracy in predicting the real scenario. In the second stage, we have used Markov Model to find out the future state sequence of the previously found sequence from first stage. The prediction of next state of an AP performed by Markov Tool shows 88.71% accuracy. It is found that Markov Model can predict with an accuracy of 95.55% if initial transition matrix is calculated directly. We have also shown that O(1) Markov Model gives slightly better accuracy in prediction compared to O(2) MM for predicting far future. Index Terms—state prediction, Markov model, Hidden Markov model, access point.

I. INTRODUCTION WLAN is now the choice for a LAN at present. They are easily deployable and ensure quick connectivity among laptop, PDA and other mobile devices. An access point (AP) is a device that creates wireless connectivity with a station (STA) within their WLAN. An access point supports a particular number of devices at a time. These numbers are changing since new mobile devices come within the LAN and existing mobile devices leave by. As a result, there are changes in the number of users who are supported by an AP at a time unlike a hub or router of a fixed network whose number of clients is fixed. As the number of users is changing within a WLAN, so is the amount of traffic. The boundaries of WLANs are not well-defined from one moment the next, mostly due to the mobility of the nodes (the addressable units of the WLAN). At one

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moment - a congestion free network may turn into a congested network within a short while due to the change in number of client stations or their change in behavior of using multimedia services. By analyzing the history of an access point, future workload of the access point may be determined in terms of its traffic load. The variation of the number of client nodes in a WLAN and the change in traffic load on the access point may affect the router in taking its decision to find the best route to destination. In order to take early action before such a situation arises, it requires the incorporation of intelligence in congestion control algorithm or in routing. A good prediction of network traffic at each access point helps in early allocation of network resources as well as guaranteed quality of service. Resource allocation to individual users now depends on many parameters. Inclusion of prediction scheme is performed in many algorithms now-a-days. A lot of works have been performed in this regard for mobility prediction [1-4], where attempts are being made to predict the future time and space of a mobile node. However, from the perspective of access point, rarely attempts have been made to predict the future states of an access point in terms of its traffic load variation in time. Traffic load on an access point varies with time. This variation depends on the number of nodes that are attached with that access point. Again, the type of services that are in use may cause performance variation in throughput. For example today’s video, audio and data rich multimedia applications may require more bandwidth than a simple application might require, A model might be used to forecast the future status of an access point in terms of its traffic load. For example, the amount of traffic loads that are going to be carried by the access point may be predicted earlier. The Congestion control algorithms may use this prediction data to take actions, or the routing mechanism may use this prediction data to dynamically select less costly route. We propose a scheme which predicts network situation in an indirect way. The scheme works in two phases. In the first phase, we have analyzed traffic load at an access point with respect to time. Later we used this information to find out the load assignment on an access point. Thus

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by using the traffic traces, we have generated a sequence of states of an access point. In the second phase, we made a prediction to find out the future load of an access point. We used Hidden Markov Model for the first phase calculation and in the second phase, we have used Markov Model as a prediction tool. Literature review suggests that a lot of research works have been reported on congestion control, routing mechanism, mobility management, bandwidth reservation, and call admission control in wireless networks. Effective prediction mechanisms have been considered in these publications. The major contribution of our work is that our scheme is able to predict the load scenario of an access point in an indirect way. We focused on the usage of an access point. This can surely help in taking decisions in all of the above cases. Moreover, a better network topology may be suggested based on the usage of an access point at a particular location. Our scheme can be helpful in determining efficient bandwidth management system as well. This paper is organized as follows: Section II gives an account of related works. Section III and IV mention about the Markov Model and the Hidden Markov Model. Section V describes the data sets of traffic traces. Section VI and VII presents the implementation of the models on data sets and comes with the results achieved. Finally the conclusion is outlined in Section VIII.

II. RELATED WORKS Traffic prediction is important to assess network capacity requirements for future and to plan future network developments. It can also help in early detection of network congestion. Congestion deteriorates system throughput and results in energy loss of nodes in wireless networks. The importance of prediction is shown in a congestion detection algorithm, presented in [5] which decreases packet drops and provides high packet delivery ratio. In [6], a suite of predictive congestion control scheme is shown that increases network throughput, efficiency, and satisfies energy conservation for wireless sensor network. Traffic prediction can also be an important basis for planning the fastest route to a given destination in a network [7] [8], a traffic aware routing metric for realtime communications (RTC) has been proposed. It is known that under the condition of busy network and time varying topology, a dynamic Ad-Hoc Routing Algorithm that dynamically changes the routing paths according to the channel condition proves to be more efficient. Time varying nature of the wireless channel may cause serious degradation in case of route quality and data throughput. Several other developments are found in [9] [10]. Generally, for the purpose of prediction of future network traffic, a time series model Auto-Regressive Integrated Moving Average (ARIMA) model is used. A © 2009 ACADEMY PUBLISHER

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variation of ARIMA model that captures seasonal pattern is shown in SARIMA. a comparative analysis among parametric predictors (i.e. Auto-Regressive Integrated Moving Average (ARIMA) and fractional ARIMA (FARIMA) predictors) and nonparametric predictors (i.e. artificial neural network (ANN) and wavelet-based predictors) have been given [11][12]. A novel network traffic one-step-ahead prediction technique is proposed on a state-of-the-art learning model called minimax probability machine (MPM) in [13].

III. MARKOV MODEL A Markov chain is a stochastic process with Markov property [14-16]. Markov property means that, given the present state, future states are independent of the past states. A probabilistic approach is used to determine the future state. Information of the present states influences the evolution of the process. The change of state, i.e., from current state to another state, or the same state, is called a transition, and the probabilities associated with various state changes are called transition probabilities. A Markov chain is a sequence of random variables X1, X2, X3 ... Formally,

Pr( X n 1

x | Xn

= Pr( X n 1

x n ,..., X 1 x | Xn

x1 )

xn )

(1)

The possible values of Xi form a countable set S called the state space of the chain which is denoted by

S

{1,2,3,..., N  1, N } .

(2)

And St denotes the state at time t. Thus, St ranges over the set S. We have interest in the probability, Ȇt,i, that the Markov model will be in state i at time t. We denote this as

3 t ,i

Pr( S t

i ), i 1, 2, 3, · · ·, N

(3)

The transition probabilities, Aij, denote the probability of going from state i at time t (St = i) to state j at time t + 1 (St+1 = j). So,

Aij

Pr( S t 1

j | St

i), i, j 1, 2, 3, · · ·N (4)

IV. HIDDEN MARKOV MODEL The Hidden Markov Model (HMM) [17] is a powerful statistical tool for modeling generative sequences that can be characterized by an underlying process generating an observable sequence. HMM is used for modeling & analyzing time series or sequential data in various fields today, such as automatic speech recognition, cryptanalysis, natural language processing, computational biology, bioinformatics etc. With its prior knowledge, HMM is concerned about the unobserved sequence of hidden states and the corresponding sequence of related

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Connection ID

Time Stamp IN

C6d41f77041b6b72 89f9fd9af1fb5476

2007-08-28 17:52:46

1ba6e1a57801fbd68 754f5a786f1daf4

2007-08-28 16:42:48

89c26264c5501119 676650110722f6f5

2007-08-28 16:33:48

A2b809b87878ba2d 54371ad0a696d1e6

2007-08-28 16:11:19

13c33027b1142bd2 d966e581824aadc7

2007-08-28 15:48:24

C620a55893b24504 4f06403b7db0ec1d

2007-08-28 14:55:23

TABLE I DETAILS OF USER SESSION Time Node ID User ID Stamp Out d919294205e44a1 24a3f7cc2b5aa569 cf18fac49c2db65f NULL 5a4d080d3885ed1 7 9 d919294205e44a1 0115d2bb055e85c 2007-08-28 cf18fac49c2db65f c0be89eeae7ddfd3 17:13:00 7 f d919294205e44a1 2007-08-28 e6bbc2939f1abcec cf18fac49c2db65f 16:42:52 f9fe85f45785d561 7 d919294205e44a1 2007-08-28 e6bbc2939f1abcec cf18fac49c2db65f 16:20:51 f9fe85f45785d561 7 d919294205e44a1 ea1e3b4b418bdda 2007-08-28 cf18fac49c2db65f 4ccfae995e3d7dea 16:24:52 7 8 29b8ac284559a4e d919294205e44a1 2007-08-28 6a447a4f2b5fef10 cf18fac49c2db65f 15:17:56 6 7

observation. An HMM is defined with respect to states, observations & their probabilities. These are: N = Number of states in the model M = Number of observation T = length of observation sequence V = {v1, v2, … , vM} the discrete set of possible observations S = {Si}, Si = P(St = i), the initial probability of the system will be in state i A = {aij} where aij = P(St+1 = j | St = i), the probability of being in state j at time t+1 given that the system was in state i at time t. B = {bj(k)}, bj(k) = P(vk at t | St = j), the probability of observation will be vk given that the system is in state j. Ot will denote the observation symbol observed at time instant t. O = (A, B, S) is the compact notation to denote an HMM. Applications of HMMs are reduced to solving three main problems. These are: 1. Given the model O = (A,B,S) compute P(O|O), the probability of occurrence of the observation sequence O = O1,O2,…,OT 2. Given the model O = (A,B,S) what will be the state sequence I = i1,i2,…, iT so that P(O,I|O), the joint probability of the observation sequence O = O1,O2,…,OT and the state sequence is maximized. 3. Adjustment of the HMM model parameters O = (A,B,S) so that P(O|O) or P(O,I|O) will be maximized. The nature of our problem falls in the category 2. Here Observation sequence O is the observed traffic, State sequence I corresponds to the state sequence of APs. The state of an AP can assume 3 values, namely low, mid, high, based on the number of active connections In this case We want to find the most likely state sequence for a given sequence of observations, O = O1, O2, … , OT and a model, O = (A,B,S). The solution to this problem depends upon the way ``most likely state sequence'' is defined. One approach is to find the most likely state St at t=t and to concatenate all such ' St's. But

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User MAC f2129958494bf6 da5895e58f7ea6a 5bc 8dad09844457b0 d73d487e17fc8d 9493 7663756184a005 6baf9267c501b4 9d86 7663756184a005 6baf9267c501b4 9d86 3f15d887a41883 0f65642027fc6c7 cc6 ecfb5cbac5e3191 c970e19af35af9f 82

Incoming Data

Outgoing Data

285489

177490

1205807

224965

1117223

59685

765625

56922

122218210

40821009

12614543

375922

some time this method does not give a physically meaningful state sequence. Therefore we would go for an effective method known as Viterbi algorithm, the whole state sequence with the maximum likelihood is found. In order to facilitate the computation we define an auxiliary variable,

w t (i )

max P{S1 , S 2 ,..., S t

S1 , S 2 ,... S t 1

i, O1 , O2 ,..., Ot | O}

(5) which gives the highest probability that partial observation sequence and state sequence up to t=t can have, when the current state is i. It is easy to observe that the following recursive relationship holds.

>

@

w t 1 ( j ) b j (Ot 1 ) max w t (i )aij ,1 d i d N ,1 d t d T  1 1di d N

(6) where,

w 1 ( j ) S j b j (O1 ),1 d j d N

(7) So the procedure to find the most likely state sequence starts from calculation of w T ( j ),1 d j d N using recursion in above equation, while always keeping a pointer to the ``winning state'' in the maximum finding operation. Finally the state

j*

j * , is found where

arg max w T ( j )

1d j d N (8) and starting from this state, the sequence of states is back-tracked as the pointer in each state indicates. This gives the required set of states. This whole algorithm can be interpreted as a search in a graph whose nodes are formed by the states of the HMM in each of the time

instant t, 1 d t d T . V. DATA SETS We have used trace files of wireless data. The files are available at CRAWDAD (Community Resource for Archiving Wireless Data) [18]. We have chosen two different datasets to implement our scheme. The first dataset [19] that we have used to model our scheme contains summary of a connection that is created between

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TABLE II AP AcadBldg10AP10 AcadBldg10AP11 AcadBldg10AP12 AcadBldg10AP13 AcadBldg10AP14 AcadBldg10AP15 AcadBldg10AP16

t0 0 0 0 0 0 9 0

TRAFFIC LOAD ON ACCESS POINT t1 t2 t3 t4 0 4 24 0 2 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 8 0 2 0 0

a node and an AP. The specific information that refines from each row of this file is a particular connection id, node id, MAC address of the user, and the time stamp in, the time stamp out, the total incoming and outgoing data in bytes during the session interval. These user sessions are created in various Wi-Fi hotspots in Montréal, Québec, Canada for three years. The dataset have the tabular format shown in TABLE I. The second dataset [20] have been created in a network scenario which employed 6202 wireless devices and 624 wireless access points in the Dartmouth campus. This dataset contains network behavior of 300 consecutive days. AP traces of each day are kept in individual file.

t5 0 0 0 0 0 0 0

t6 0 0 0 23 0 0 0

… … … … … … … …

t48 0 0 0 0 0 17 0

S = {low, mid, high} An AP makes transitions among the low, mid and high states. State status is updated at the start of each time interval. Each time interval is of 15 minutes. Probability of changing state from one status to another status is known as transition probability, Aij. While i=low and j=high, that is, Alow,high indicates the transition probability of changing the state status of an access point from low to high. For our three-state model, there will be nine probabilities of interest for each access point. Let St and St+1 denote the state of the AP at time t and at time t+1, respectively. We define the nine transition probabilities as

The number of wireless devices associated with each AP throughout the day is stored in each row of 49 columns shown in TABLE II. In TABLE II, the 1st column shows the location of an AP. The location format for an AP is as follows: [Building Name][Building Number][AP][AP Number] The 2nd column specifies the number of associated wireless devices with the AP, mentioned in 1st column, between time intervals of 1200AM to 1230AM. Similarly the other columns show the number of wireless devices connected with the AP in 30-minutes intervals throughout the day. VI. HMM IMPLEMENTATION AND RESULTS To set the stage for Hidden Markov models for the first dataset, we consider a three state model. An AP may attain ‘low’, ‘mid’ or ‘high’ state status. Being in a ‘low’ state indicates that at present the access point is connected to 0 (minimum) to 2 (maximum) number of devices. Being in a state ‘mid’ corresponds to a situation where the access point is connected to 3 (minimum) to 6 (maximum) number of devices. Similarly a ‘high’ state status corresponds to a situation where access point is connected with more than 6 devices. For convenience of graph plotting low, mid and high state status have been indexed as 1, 2, and 3 respectively, shown in TABLE III. TABLE III STATE DEFINITION No of No of connections (MM) connections(HMM) 0-5 0–2 6-10 3–6 >10 >6

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State Low (1) Mid (2) High (3)

Fig.1. The transition between the three states A low, low (t) = Pr {St+1 = low | St = low} A low, mid (t) = Pr {St+1 = mid | St = low} A low, high (t) = Pr {St+1 = high | St = low} A mid, low (t) = Pr {St+1 = low | St = mid} A mid, mid (t) = Pr {St+1 = mid | St = mid} A mid, high (t) = Pr {St+1 = high | St = mid} A high, low (t) = Pr {St+1 = low | St = high} A high, mid (t) = Pr {St+1 = mid | St = high} A high, high (t) = Pr {St+1 = high | St = high} This can be represented by the state transition matrix

A(t) =

Alow,low Amid,low Ahigh,low

Alow,mid Alow, high Amid,mid Amid, high Ahigh,mid Ahigh, high

We have classified traffic flow, i.e. our observation, in several types. A data transfer which involves total number of bytes less than 1000,000 is classified as observation type 1. The other observation types are shown in TABLE IV.

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Initialize time slot length. In our algorithm we have assumed it to be 15 minutes Create state definitions according to table III. Create observation types according to table IV. // Determine (time slot index, state status, observation type) For each row Find number of connections and accumulate it to respective time slots Assign a state status for each time slot following rules given in table I Find the number of data transferred and accumulate it to respective time slots Assign an observation type for each time slot following rules in table II // Determination of HMM parameters Compute initial probability matrix Compute Transition Matrix A Compute Observation Matrix B Fig.2. Algorithm to convert data set values into HMM parameters The first dataset is processed to transform it as a set of rows containing time slot index, state status and observation type. In order to create HMM parameters, we process this according to the following algorithm given in Fig-2. We have run our algorithm, mentioned in Fig-2, on user sessions of the node id “d919294205e44a1cf18fac49c2db65f7” and found out the parameters of HMM. For a training set of size 60 days the parameters of HMM are tabulated in the TABLE V, VI and VII. Using the parameter values from the TABLE V, VI, VII we have executed the Viterbi algorithm. Generally, TABLE IV DEFINITION OF OBSERVATION TYPE No of Data Transferred in Byte Observation Type 0 0