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UBICC Journal CPN 242

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UBICC Journal CPN 242 Powered By Docstoc
					COLORED PETRI NET MODELING AND THROUGHPUT ANALYSIS FOR WIRELESS INFRASTRUCTURE NETWORKS
H. Abdul Rauf, Dean (CSE/IT), V.L.B. Janakiammal College of Engineering & Technology, Coimbatore A. Ebenezer Jeyakumar Principal, Government College of Engineering, Salem harauf@yahoo.com

ABSTRACT CPN model consists of a set of modules, each of which contains a network of places, transitions and arcs. The modules interact with each other through a set of well-defined interfaces, in a similar way as known from many modern programming languages. The graphical representation makes it easy to see the basic structure of a complex CPN model, i.e., understand how the individual processes interact with each other. Throughput is a measure of the actual data that can be sent per unit of time across a network, channel or interface. Throughput is more often used in a practical sense, for example, to measure the amount of data actually sent across a network. Keywords: Throughput, Colored Petri Net, Access Point, Network Response Time, Model Time Unit

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INTRODUCTION Miorandi, Kherani A. A. and Altman E. (2004) proposed TCP flow control over 802.11. The flow control aspect of Transmission Control Protocol (TCP) strongly influenced the Medium Access Control (MAC) layer behaviour, including the probabilities of packet collisions between wireless stations. The method does not handle a wide variety of network scenarios including the co-existence of both upstream and downstream TCP flows. Taka Sukari and Stephan Hanly (2004) proposed that in the wider Internet, the large bulk of traffic on a typical WLAN consists of applications such as web browsing that are carried over the TCP and collision between TCP packets are the main causes for the performance degradation of the network. The TCP throughput has been analyzed as a function of number of TCP flows when transmitted over an IEEE 802.11 WLAN and dependent on the number of stations. The method validates the analytical results with simulation.

Colored Petri Net (CPN) is a graphical oriented language for design, specification, simulation and verification of systems. It is in particular well-suited for systems that consist of a number of processes which communicate and synchronize. Typical examples of application areas are communication protocols, distributed systems, automated production systems, and work flow analysis. Throughput can be a theoretical term like bandwidth, but in this paper it is used to measure the amount of data actually sent across a network in the real world. The remainder of the paper is organized as follows: Section (2) details the theory and background of the paper. Section (3) focuses on modelling of network components. Section (4) emphasizes on throughput analysis and graphical output. Section (5) the conclusion and future scope of the paper.

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BACKGROUND 3 HETEROGENEOUS ENTERPRISE NETWORK MODEL

Dmitry A. Zaitsev (2005) proposed Colored Petri Net model for the representation of wired LAN and a special measuring model to determine the network response time. The drawback of this scheme is that the results are obtained by simulation and does not provide accurate results. Also, the model excludes WLAN.

The Enterprise Network Model consists of various components of the network which involves wired network and wireless network.

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3.1 Model of Switch A model for a static switching table is constructed. A separate input and output buffers of frames for each port and common buffer of the switched frames are considered. The model of switch is presented in Figure 1. The swi represents records of switching table. It maps each known MAC address to the number of port. The swf describes the switched frames, waiting for output buffer allocation. The field portnum stores the number of the target port. The places Port*In and Port*Out represent the input and output buffers of the ports correspondingly.
[dst=target] f(src,dst,nf) Port* In In* [target,port] SwTa *

token avail. The places Port*In and Port*Out are contacted ones. 3.2 Model of Access Point The model of Access Point (AP) is same as that of switch except that the delay involved in it varies. It is represented in Figure 2.
[dst=target] Port* In f(src,dst,nf) In* [target,port] APta*

seg avail

@+272

Api (src,dst,nf,port)

Port* Out swi seg avail @+1 (src,dst,nf,port) seg

f(src,dst,nf) Out* (src,dst,nf,1) @+272

Bu*

avail

Apf

Figure 2. Model of Access Point
Port* Out f(src,dst,nf) Out* (src,dst,nf,1) Bu*

3.3 Model of Workstation To investigate the frames, flow transmitting through LAN and to estimate the Network Response Time (NRT) it is necessary to construct the models of terminal devices attached to the network. For an accepted degree of elaboration it is consider that periodically repeated requests of workstations to servers with random uniformly distributed delays.
[dst=target] f(src,dst,nf) LAN in Receive target Own

seg avail

@+1

swf

Figure 1. Model of Switch Each token represents the record of the switching table, for example’(1,1)++1’(2,1)++1’(3,2)++1’(4,2). For instance, token 1’(4,2) means that the host with MAC address 4 is attached to port 2. The fusion place Buffer is represented with Bu* (Bu1, Bu2, Bu3) and it corresponds to the switched frames buffer. The fusion place SwitchTable is represented with SwTa* (SwTa1, SwTa2, SwTa3). It allows the convenient modeling of switches with an arbitrary number of ports avoiding numerous cross lines. The transitions In* model the processing of input frames. The frame is extracted from the input buffer only in cases where the switching table contains a record with an address that equals to the destination address of the frame (dst =target). During the frame displacement the target port number (port) is stored in the buffer. The transitions Out* model the displacement of switched frames to the output ports’ buffers. The fixed time delays (@+1) are assigned to the operations of the switching and the writing of the frame to the output buffer. When a frame is extracted from the input buffer by transition In*, it is replaced with the label avail. The label avail indicates that the channel is free and available for transmission. Before the transition Out* sends a frame into a port, it analyses if the channel is available by checking the

seg avail

@+22 src

mac

dst@+delay() f(src,dst,1) LAN out Send Remote

seg

avail

@+22

dst

mac

Figure 3. Model of Workstation On reply to an accepted request a server sends a few packets to the address of the requested workstation. The number of packets sent and the time delays are uniformly distributed random values. A model of workstation is represented in Figure 3. The places LANin and LANout model the input and output channels of the LAN correspondingly.

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The workstation listens to the network by means of transition Receive that receives frames with the destination address, which is equal to the own address of the workstation (dst=target) saved in the place Own. The processing of received frames is represented by the simple absorption of them. The workstation sends periodic requests to servers by means of transition Send. The servers addresses are held in the place Remote. The sending of the frame is implemented only if the LAN segment is free. It operates by checking place LANout for a token avail. The workstation interacts with a few servers holding their addresses in the place Remote. The workstation only assigns the value of a unit to it. 3.4 Device Delay Calculation The experimental setup with wired (two desktops with a switch) and wireless network (two laptops with an access point) is considered. A file is transferred from one node to another via twisted pair cable to determine the overall transfer time, T1. The same file is transferred between the same pair of nodes via switch. Then, the transfer time is noted as T2. Again the same file is transferred between the same pair of nodes via switch and AP. The transfer time is taken as T3. The Switch delay is calculated by the difference between T2 and T1. The AP delay is determined by the difference between T3 and T2. 3.5 Parameters of Model and Delay Values Obtained The unit of Model Time Unit (MTU) equals 1 millisecond. The parameters, real value obtained after experimentation and model value obtained as shown in Table 1. Using these values CPN model obtained as shown in Figure 4. The port in and port out are mentioned as P1 In and P1 Out as shown in Figure 4. Similarly, the workstations connected through AP will be connected using ports for input and output of packets. Table 1 Parameters of Model

Model of Workstation

Model of Workstation

P1 In P1 In P1 Out
Model of Switch

P1 Out

Model of Access Point

Model of Workstation

Model of Workstation

Figure 4. Colored Petri Net for the Experimental Set-up 4 THROUGHPUT ANALYSIS

The TCP throughput over IEEE 802.11 WLANs for the experimental set-up shown in Figure 5 is estimated. Various network configurations, starting with the case of one STAtion (STA) and Active Window (AWND) > 1 are considered and then finally generalized to the case of multiple STAs.

Parameters

Real value (ms)

Model value

LAN switch read frame delay LAN switch write frame delay Access point read frame delay Access point write frame delay Workstation delay

0.035 0.035 9.548 9.548 0.771

1 1 272 272 22 Figure 5. Experimental Set-up and IP Connected 4.1 Single Station The assumption AWND > 1 means that collisions between TCP data packets and TCP Acknowledge (ACK) packets are possible. It also

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means that the TCP sender, after transmitting a data packet, does not always need to wait for a TCP ACK before sending another packet, since it may already have another packet in queue. To simplify the analysis, the key assumption that the transmit buffer at the TCP sender is never empty. In this approach the analysis of throughput is by focusing on the average time tcycle between successfully transmitted packets by the TCP sending node. The second key assumption is that the system achieves an equilibrium state where the average rate of successfully transmitted packets from the TCP sending node equals the average rate of successfully transmitted TCP ACKs from the TCP receiving node. In other words, the average time between successfully transmitted packets by the TCP receiving node is also given by tcycle. The throughput is given by, S = l data/t cycle Mbps Where, t cycle = t data + t ack + t bc The tdata is given by tdata=tphy +((lmac+ltcpip+ldata)/rdata)+ tsifs+tphy+(lack/rctrl)+tdifs The tack is given by tack=tphy+((lmac+ltcpip)/rdata)+ tsifs+tphy+(lack/rctrl)+tdifs (4) (3) (1) (2)

MAC acknowledgement timeout parameter defines the time that must elapse before the sending MAC layer deems that a collision has occurred. 4.2 Multiple Stations A model for the case of n > 2 active STAs is developed. In this case, either all TCP data packets (in the downstream case) or all TCP acknowledgement packets (in the upstream case) flow through the AP transmit buffer. Therefore, it is reasonable to assume that the AP transmit buffer never empties. It is denoted by tcycle the average time between packets successfully transmitted by the AP, and assumed that an equilibrium state is reached such that the combined effect of the n active STAs is to yield a sequence of successfully transmitted TCP packets (either data packets or ACK packets) with average spacing that is also equal to tcycle. The throughput is given by, S = l data / t cycle Mbps Where tcycle=tdata+tack+tbc + β (8)

(9)

In a t cycle period, the TCP sending node successfully transmits one packet, freezes its back-off counter when the TCP receiving node successfully transmits one packet, and increases its back-off stage whenever there is a collision. In this case it is assumed that, each transmitted packet has a constant and independent collision probability p. With this assumption, the quantity tbc can be written as tbc = (1-p)A0+p(1-p)A1+……..p m-1 (1-p)A m-1 Case 1: For 0<=k<=m’ Ak = k tcoll+ tslot ∑ ((2jWmin-1)/2) …lim j=0 to k Case 2: For k>m’ Ak = k tcoll+ tslot ∑ ((2jWmin-1)/2) + (k-m’) (2m’Wmin-1)/2) …lim j=0 to m’ (7) Where, tcoll is the time duration of the collided packet plus the MAC acknowledgement timeout. The (5)

The assumption that at each transmission attempt of a given AP packet, there is a probability p of colliding with STA packets, resulting in an average back-off window, τ. This assumption on the average packet spacing for the STA population as a whole implies that each individual STA produces a sequence of successfully transmitted packets with an average spacing ntcycle. Given this assumption, it is natural to assume that each STA has an average effective back-off time of nτ. The probability q that in any given slot is determined and a packet from the tagged STA has a collision with a packet from at least one other STA but not with a packet from the AP. The probability of a collision with a packet from at least one other STA is 1-(1-1/(nτ))n-1, and the probability of a collision with an AP packet is 1/τ. Therefore, the Eq. 10 is obtained, q = ( 1- ( 1- ( 1/nτ ) ) n-1)(1-(1/τ)) (10)

(6)

The total number of retransmissions per packet from the tagged STA is then given by q=(1-q), and the total occupancy of the channel β due to collisions between STA packets is given by, β = tsta q /(1-q) (11)

In case of upstream flows, the packet is a TCP ACK packet, tsta =tack

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In case of downstream flows, the packet is a TCP data packet, tsta=tdata 4.3 Throughput Calculation
Throughput

Collision probability Vs Throughput for n=2
60 55 50 45 40 35 30 25 20 15 10 5

Using the delay values calculated in the Section 3.5 and the parameters in the Table 2, throughput is calculated. Table 2 802.11g MAC and Physical Parameters S.No 1 2 3 4 5 6 7 8 9 10 11 12 13 4.4 Graphical Output The Collision Probability versus the Throughput for single station and multiple stations are shown in Figure 6 and Figure 7 respectively.
collision probability Vs Throughput for n=1
60 55 50 45 40

Throughput

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

collision probability

Parameters rdata rctrl lack lmac l tcpip tphy tslot tsifs tdifs Wmin Wmax M m’

Value 54Mbps 1Mbps 112 bits 224 bits 320 bits 192 s 20 s 10 s 50 s 16 1024 7 5

Figure 7. Collision Probability versus Throughput for Two Station 5 CONCLUSION The CPN model has been developed for various components of the experimental set-up and experimentation is conducted to measure the delay caused by the switch, the AP and the workstations. Throughput for WLAN decreases as the probability of collision increases. When the number of stations connected within the network increases, throughput decreases for a certain level. Once it reached a saturation level, throughput remains constant even when the number of stations goes on increasing in the network. 6 REFERENCES

T h ro u g h p u t

35 30

Throughput
25 20 15 10 5 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

collision Probability

Figure 6. Collision Probability versus Throughput for Single Station

[1] M. Beaudouin-Lafon, W.E. Mackay, M. Jensen: CPN Tools: A Tool for Editing and Simulating Colored Petri Nets. LNCS 2031: Tools and Algorithms for the Construction and Analysis of Systems, pp. 574-580 (2001). [2] Daniele Miorandi, Arzad A. Kherani, and Eitan Altman: A queueing model for HTTP traffic over IEEE 802.11 WLANs, In Proceedings of ITC Specialist Seminar on Performance Evaluation of Wireless and Mobile Systems, Antwerp, (2004). [3] Daniele Miorandi and Eitan Altman: On the effect of feedback traffic in IEEE 802.11b WLANs, Technical Report, RR4908, INRIA, (2003). [4] D.P. Heyman, T.V. Lakshman, and A.L. Neidhardt: A new method for analyzing feedback based protocols with applications to engineering web traffic over the internet. In Proceedings of ACM SIGMETRICS, pp. 24 – 38 (1997). [5] M. Elsaadany, T. Singhal, Lui Ming: Performance study of buffering within switches in local area networks. In Proceedings of fourth International Conference on Computer Communications and Networks, pp. 451 – 452 (1995). [6] Giuseppe Bianchi: Performance analysis of the IEEE 802.11 distributed coordination function.

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IEEE Journal on Select Areas in Communication, Vol. 18, pp. 535 – 547 (2000). [7] W. Cohen: The multiple phase service network with generalized processor sharing. Acta Informatica, Vol. 12, pp. 245 – 284 (1979). [8] L.L.H. Andrew, S.V. Hanly, and R.G. Mukhtar: CLAMP: Maximizing the performance of TCP over low bandwidth variable rate access links. Technical Report, 2004-02-01, CUBIN, University of Melbourne (2004). [9] W. Berger, and Y. Kogan: Dimensioning bandwidth for elastic traffic in high-speed data networks. IEEE/ACM Transactions on Networking, Vol. 8, pp. 643 – 654 (2000).

H. Abdul Rauf received the Bachelors Degree in Electrical and Electronics Engineering in 1987. He completed his Masters degree in Business Administration (M.B.A) Degree in the year 1996 and his masters degree in Computer Science and Engineering in the year 1999.He is currently a PhD candidate in the faculty of Information and Communication Engineering, Anna University of Chennai. His research interests includes mobile computing, Computer Networks, Network Security, Advanced Networks and Performance Evaluation of Computer Networks. He is currently the Dean (CSE/IT), V.L.B. Janakiammal College of Engineering & Technology, Coimbatore, India Dr. Ebenezer Jeyakumar is currently the Principal of Government College of Engineering, Salem, India. Being an eminent professor of Anna University, there are many students doing their research under his guidance in various fields. Some of main areas of research are Networking, mobile computing, high voltage engineering and other related areas.

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