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- 1 - Proposed Algorithms for Multimedia Transmission over GPRS (General Packet Radio Service) Nawal A. El_Fishawy 1 , Hala A.K. Mansour 2 , and Rokaia M. Zaki 3 1 Dept. of Communication, Faculty of Electronic Engineering, Menoufia University, Egypt 2, 3 Dept. of Elec. & Communication, Faculty of Engineering, Benha University, Egypt Abstract The General Packet Radio Service (GPRS) is designed for packet switching data transmission and provides mobile access to packet data networks, e.g. the Internet. In this paper, two different protocols are proposed to study the performance of multimedia integrated traffic (as voice, rt-VBR video and data traffics) over GPRS network. Data traffic is presented as Web documents. This work is based on PRMA (Packet Reservation Multiple Access) access techniques. The simulation objectives include maximizing the system capacity "by finding the optimum permission probabilities of sending contending voice and data, the number of video reserved slots, also measuring Qos through two parameters, the packet dropping probability and the average delay suffered by each packet ". The obtained Results show that, the performance of GPRS measured in terms of system throughput, video and voice dropping probability and the average data delay are more enthusiastic compared with the previous studies. So mobile users can access to Internet and obtain data in short time. Keywords General Packet Radio Service, Hyper-Text Transfer Protocol, Multimedia communications, Packet Reservation Multiple Access (PRMA), Web documents, Internet. 1- Introduction GPRS system is developed to work with the existing Global System for Mobile communications (GSM) provides better service for Internet applications than the existing circuit switching services. The bits are modulated using Gaussian minimum shift keying (GMSK), a low-noise method which makes efficient use of the available channel bandwidth. The GPRS standard specifies four different coding schemes, CS1 to CS4. The CS4 scheme does not use error correcting coding. CS1 uses a half-rate convolutional code. The CS2 and CS3 schemes use the same convolutional code, but with different degrees of puncturing. [1] Hyper-Text Transfer Protocol (HTTP) is the key to the World Wide Web (WWW) operation and it uses Transmission Control Protocol (TCP). HTTP has become the dominant method for transferring data over Wide Area Networks (WAN) so there is no doubt that HTTP will continuously be one of the most important protocols in future mobile Internet. HTTP is designed to be a simple request/response protocol to transfer the files making up the parts of Web documents. Both the request and reply contain identification and control information in headers. 1 [email protected] 2 [email protected] 3 [email protected] ICENCO 2007 Third International Computer Engineering Conference Cairo University, December 26-27, 2007 "Smart Applications for the Information Society" IP - 1

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Proposed Algorithms for Multimedia Transmission over GPRS (General Packet Radio Service)

Nawal A. El_Fishawy 1, Hala A.K. Mansour 2, and Rokaia M. Zaki 3

1 Dept. of Communication, Faculty of Electronic Engineering, Menoufia University, Egypt 2, 3 Dept. of Elec. & Communication, Faculty of Engineering, Benha University, Egypt

Abstract The General Packet Radio Service (GPRS) is designed for packet switching data transmission and provides mobile access to packet data networks, e.g. the Internet. In this paper, two different protocols are proposed to study the performance of multimedia integrated traffic (as voice, rt-VBR video and data traffics) over GPRS network. Data traffic is presented as Web documents. This work is based on PRMA (Packet Reservation Multiple Access) access techniques. The simulation objectives include maximizing the system capacity "by finding the optimum permission probabilities of sending contending voice and data, the number of video reserved slots, also measuring Qos through two parameters, the packet dropping probability and the average delay suffered by each packet ". The obtained Results show that, the performance of GPRS measured in terms of system throughput, video and voice dropping probability and the average data delay are more enthusiastic compared with the previous studies. So mobile users can access to Internet and obtain data in short time. Keywords — General Packet Radio Service, Hyper-Text Transfer Protocol, Multimedia communications, Packet Reservation Multiple Access (PRMA), Web documents, Internet.

1- Introduction

GPRS system is developed to work with the existing Global System for Mobile communications (GSM) provides better service for Internet applications than the existing circuit switching services. The bits are modulated using Gaussian minimum shift keying (GMSK), a low-noise method which makes efficient use of the available channel bandwidth. The GPRS standard specifies four different coding schemes, CS1 to CS4. The CS4 scheme does not use error correcting coding. CS1 uses a half-rate convolutional code. The CS2 and CS3 schemes use the same convolutional code, but with different degrees of puncturing. [1]

Hyper-Text Transfer Protocol (HTTP) is the key to the World Wide Web (WWW) operation and it uses Transmission Control Protocol (TCP). HTTP has become the dominant method for transferring data over Wide Area Networks (WAN) so there is no doubt that HTTP will continuously be one of the most important protocols in future mobile Internet. HTTP is designed to be a simple request/response protocol to transfer the files making up the parts of Web documents. Both the request and reply contain identification and control information in headers. 1 [email protected] 2 [email protected] 3 [email protected]

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This paper is organized as follows; Section (2) presents prior studies. Section (3) describes traffic models and simulation scenario. Section (4) presents protocols and the results. Finally, conclusion is presented in Section (5).

2- Prior work In this section, the work of Vikrant A. Chitre [2] is presented. He presented an analytical model to assess throughput of the reverse link as a function of the number of users connected and the distribution of user message lengths for a scenario in which users were continuously backlogged. Next, he investigated the capability of GPRS to support World Wide Web access using a modified version of the analytical model. Specifically, he presented a realistic scenario for user sessions operating under the Hypertext Transfer Protocol (HTTP). The results indicated that, in the case of continuously backlogged users, an increase in number of contention slots did not always translate to an increase in throughput while in the case of users operating HTTP sessions, the downlink services was the main bottleneck in the system. In [3], Simon Hoff, M. Meyer and J. Sachs presented a simulator to identify the performance characteristics of GPRS as access to Internet services. The simulator has to model the whole GPRS nodes chain including the Internet. In [4], Said Elnoubi worked on PRMA protocol. The objective of his work was to find the optimum permission probabilities of sending contending voice, data and video packets allowing the maximum number of users sharing the RF channel. Also the suitable number of reserved slots for video transmission in the beginning of each new frame is determined. The video users contend with the voice and data users for the remaining time slots of the frame. He considered a high capacity wireless channel (5.3 Mpbs) and the frame consisted of 150 time slots. In [5], X. Fang and D. Ghosal studied two major sources of packets delay in the GSM-GPRS wireless network, at Base Station and at GGSN. They presented an analytical model to study the performance of three channel sharing schemes: fixed sharing, partial sharing and complete sharing. In [6], M. Ghaderi and R. Boutaba described an analytical approach for deriving the packet delay distribution in a cell operating based on GPRS standard. Based on that, the average packet delay and packet loss probability were also computed in addition to the effect of voice call handoffs. Finally in [7], M. A. Marsan, P. Laface and M. Meo described an approximate Markovian model for the estimation of the packet delay distribution in a cell of a GSM-GPRS network simultaneously supporting voice and data services. In addition, they validated the analytical model by comparison against discrete-event simulation of the system.

3- Description of the system

The major issue in the wireless multimedia systems design is the selection of a suitable channel sharing media access control (MAC) protocol that provides a sufficient degree of transparency for many different kinds of services. PRMA (packet reservation multiple access) is one of the best alternatives to be used as a MAC protocol, because it is simple and can be efficiently used to transmit voice, data, and video in wireless media [4]. This work depends on the computer simulation (using MATLAB) to present the multimedia traffic over the uplink (mobiles to Base Station) channel. High capacity

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wireless channel with channel rate 3.53 Mbps is considered for this simulation. Using TDMA access techniques, the transmission time is divided into frames of equal length. Each frame has duration of 12 ms [4], [14], and accommodates 100 slots. Each slot accommodates exactly one fixed–length packet of ATM size that contains 53 bytes with 5 bytes header and 48 bytes of information. At the beginning of each frame, a fixed number of slots (M) are reserved to transmit video packets while the remaining video packets are stored in buffer until the beginning of the next frame. In the first protocol, the voice and data packets contend for the remaining time slots of the frame but in the second protocol, the remaining slots are divided between the voice and data users. I. Speech transmission mode The speech source is classified as ON/OFF source or either talking or silent. A speech activity detector (SAD) can be used to detect this pattern. The talk-spurt period is considered as ON-state (source generates packets) and silent gap is considered as OFF-state (no packets are generated). Durations of talk-spurts and silent gaps are modeled as exponential distributions with mean values of 1 and 1.35 sec, respectively [18]. If a voice packet is not sent within its maximum transfer delay (MTD), it should be dropped .In our source model, the MTD is set to be 30 msec [4]. The source rate is taken to be 32 kbps. As we know, the speech users have the highest priority over all kinds of traffic.

II. Data transmission mode The data terminals are accessed to the Internet to transmit or receive Web documents using HTTP. Data source is considered as ON-OFF mode also [4], [19]. Pages are generated through the ON-state while the OFF-state is used for retrieval. Table 1 presents all kinds of distributions for data source. The ON- time is assumed random with Weibull distribution [appendix A] where data users generate HTTP pages with interarrival time described by Weibull distribution. The page size is considered variable and described by Pareto distribution [appendix B], these pages are divided to packets and the interarrival time between packets is assumed random with negative exponential distribution. But the OFF-time is assumed random with Pareto distribution [16]. The generated packets are stored on a buffer and the users contend to send them also through the OFF-time. The source rate is taken to be 2400 bps.

Table 1: Proposed Data source distributions

The component Distribution Model Parameters ON period Weibull 91.0,4.4 == bea OFF period Pareto 9.0sec,60 == βα Page size Pareto 91.0,30000 == βα Page interarrival time Weibull 5.0,5.1 == bea Packet interarrival time Exponential 16.0=μ

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III. Video transmission mode As we know the video is a Real Time- Variable Bit Rate (rt-VBR) which is considered delay sensitive traffic. The video source is modeled by Gaussian distribution with bit rate that changes between 128 and 384kbps with mean rate of 256 kbps and the video signal is sent as image frames (30image frames/sec). The rate of the source varies every 33 msec (the duration of image frame) and the maximum transfer delay of the VBR packet is set to be 33msec so the packet is dropped after waiting this period [14]. Each video frame is sent by different bit rate for 33 msec so each frame has different size. So we must determine the frame size and divide it to packets, these packets are stored in buffer until sent successfully. IV. The simulation scenario We worked by the principles of PRMA protocol which was proposed by Goodman et al, in [4]. PRMA can be viewed as a merger of the slotted Aloha and TDMA [18]. It enables dispersed terminals to transmit packetized information over a shared channel to a Base -Station (BS). The transmission time scale is organized in frames, each containing a fixed number of time slots. The frame rate is identical to the arrival rate of speech packets. The terminals classify each slot as either "reserved" or "available" according to the feedback message received from the BS. Perfect collision is assumed, this means that the BS is unable to detect any packet when there are two or more simultaneous transmissions (that slot still unreserved), and the collided packets have to be retransmitted [4]. If the current slot is available, then active terminals will contend with each other to reserve that slot. Each active terminal (voice or data users) will generate a random number (it is granted according to the state of a pseudo random number generator) and the terminal with a random number less than or equal to the permission probability will try to transmit its packet on that slot. Upon successfully transmitting a packet in a time slot, the voice terminal reserves that slot for uncontend channel access in the next frames until the end of the talk-spurt. If collision occurs the terminal seeks permission to retransmit its packet in subsequent available time slot and this slot didn't carry any packet in this frame [4], [18], [19]. At the end of a talk-spurt, the voice terminal transmits nothing in its reserved slot and the base station receiving no packet so it informs all terminals that the slot is "available" for contention in the next frame [4]. For data terminals, they must contend for each packet transmission and not allowed to make reservation. Data terminals store packets indefinitely while they contend for reservations. But the video user has no permission probability because the BS reserves the first M slots of each frame for video transmission. The video packets are sent in these slots but if there is no packet in the buffer to transmit, the BS will access the free slot to the data user who has the large number of packets in his buffer.

The following conditions must be taken in account for the following results:

1. A voice packet is dropped after 30 msec. delay and the dropping probability of voice packets is less than or equal 0.01.

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2. Average data delay must be less than or equal to 250 msec. 3. A video packet is dropped after 33 msec. delay and the dropping probability of video packets is less than or equal 0.00001 [4], [18], [19].

The following table shows the simulation parameters: Table 2: The simulation parameters

Parameter Nominal value Channel rate 3.53 Mbps Speech coding rate 32000 bps Data rate 2400 bps Packet size 53 BytesPacket header size 5 BytesPacket payload 48 BytesFrame duration 0.012 sSlot duration 0.00012 s No. of slots/ frame 100 slotVoice permission probability variableTalkspurt interarrival time 1.0 sSilent interarrival time 1.35 sMaximum packet delay 0.03 s

Voice

Data permission probability variablePackets interarrival time 0.16 s

Data

Minimum bit rate 128 kbpsMaximum bit rate 384 kbps No. of frames/sec 30 f/sFrame duration 0.033 sMaximum packet delay 0.033 sNo. of reserved video slots variable

Video

4- The system protocols and results

I. Initialization In this part tests are made to choose the suitable number of the reserved video slots, the suitable voice permission probability and the suitable data permission probability.

a. Number of video reserved slots: First, the simulation is run with the number of video reserved slots are considered variable as 12, 13 and 14 slots. Figure 2 shows the relation between the video and voice dropping probability and the number of voice users.

At the beginning of each frame when the BS reserves 12 slots for video user, the dropping probability of video excess 0.001. But that is unacceptable because the dropping probability of video packets is less than or equal 0.00001.

For M=13 slots, the dropping probability of video excess 0.0001. But that is unacceptable also.

Finally, for M=14 slots, the dropping probability of video is zero. So in our protocols the BS will reserve 14 slots for video packets transmission.

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Figure 2: The voice and video dropping probability as function of voice users and the number of

video reserved slots as a parameter.

b. Voice permission probability: In this part, the number of video reserved slots is taken as 14 slots and the voice permission probability is considered as 0.05, 0.07, 0.09 and 0.1. The results are shown in figure 3, the voice permission probability which gives the large number of voice users with voice dropping probability less than 0.01 is voice permission probability =0.09.

Figure 3: The voice dropping probability as function of voice users and voice permission

probability as a parameter.

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c. Data permission probability: The number of video reserved slots is fixed as 14 slots also the voice permission probability is taken as 0.09 but the data permission probability is considered variable as 0.005, 0.007, 0.009 and 0.01. Figure 4 presents that result, the best data permission probability which achieve the large number of voice users with voice dropping probability less than 0.01 is 0.009. So in these protocols; the data permission probability is fixed as 0.009.

Figure 4: The voice dropping probability as function of voice users and data permission

probability as a parameter. The following parameters are fixed as:

Voice users Variable Data users 90 users Video users 1 user Voice perm. prob. 0.09 Data perm. prob. 0.009 No. of reserved video slots : 14 slots

II. Protocol 1

In the first protocol, the video user used the first 14 slots of every frame to send his packets and keep the remaining packets in buffer until the beginning of the next frame. The video user must send every video frame before the beginning of the second one, so any remaining packets will be dropped after 33 msec (a video frame duration).

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As mentioned before, the unused slot from those fourteen slots is accessed to the data user who has maximum number of packets in his buffer.

1 2 ……….. M M+1 ………………………. 99 100

Reserved for video Contention by voice and data users

Figure 5: Protocol (1) frame configuration.

Through the remaining slots of the frame, the voice and data users contending to transmit their packets in one of different three cases

a. Case 1

In this case, the remaining slots of the frame are used by the voice and data users where voice traffic has high priority over data traffic. Data terminal can contend for more than one slot per frame, and not allowed to make reservation. The results are presented through the following curves:

Figure 6: The voice and video dropping probability as function of voice users.

Figure 6 shows that; the video dropping probability is zero and the voice dropping

probability is less than 0.01 until 182 voice users. Figure 7 shows that; the video average delay is constant at 8 msec and the data

average delay increased by increasing the number of voice users but the data average delay is less than 250 msec.

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Figure 7: Average delay of data and video packets versus the number of voice users.

Conclusion: - Through this case the BS can serve 90 data users, 182 voice users and one video user with throughput 91%, the video average delay is 8 msec and data average delay is 20 msec.

b. Case 2 As we know; Mobile Terminals are classified according to the number of time slots they are capable of operating on simultaneously. For example, most current devices are classified as '3+1' meaning that they can simultaneously listen to 3 downlink channels (from BS to mobile), but only transmit on 1 uplink channel to the base station. So in this case the same scenario is considered as before but with one difference, where every data user can use only one slot in every frame which means that any data user can send one data packet only in the same frame.

Figures 8, 9 show that, the video dropping probability is zero and the voice dropping probability is less than 0.01 until 183 voice users. The video average delay is constant at 8 msec and the data average delay is less than 250 msec. Conclusion: - The BS can serve 90 data users, 183 voice users and one video user with throughput 90.3%, the video average delay is 8 msec and data average delay is 23 msec.

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Figure 8: The voice and video dropping probability as function of voice users.

Figure 9: Average delay of data and video packets versus the number of voice users.

c. Case 3

In this case the same scenario of protocol 1 is assumed but if a slot has more than one contender (so no one of them can use it);

• If there is one voice contender only and the others are data contenders, the voice user uses the slot.

• If there are many voice contenders, the BS accessed the slot to the data user who has maximum number of packets in his buffer. Data users can contend for more than one slot per frame, and not allowed to make reservation.

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We obtained the following curves and results: Figure 10 shows that; the video dropping probability is zero and the voice dropping

probability is less than 0.01 until 184 voice users. Figure 11 shows that; the video average delay is constant at 8 msec and the data

average delay is very low. Conclusion: - the data packets average delay is very low also the BS can serve 90 data users, 184 voice users and one video user with throughput 93%, the video average delay is 8 msec and data average delay is 3.2 msec.

Figure 10: The voice and video dropping probability as function of voice users.

Figure 11: Average delay of data and video packets versus the number of voice users.

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III. PROTOCOL 2

In this protocol the frame slots are divided to three groups, the first group is used by video users with the same techniques as before, the second group is used by voice users and the last is used by data users with the same features of contention and collision. Data terminal can contend for more than one slot per frame, and not allowed to make reservation.

1 2 ……... M M+1 M+2 ……. M+N M+N+1 M+N+2 ……. 100

Reserved for video Reserved for voice Reserved for data

Figure 12: Protocol 2 frame configuration. Also with the following concepts:

In the first group, data packets are sending through the slots where no video is available to transmit.

In the second group and third group, data packets are sending through the slots where collision occurs. We choose the data packet from the data user who has the maximum number of packets stored in his buffer. This protocol is simulated twice

First; the frame is divided as, 14 slots for video, 81 slots for voice and 5 slots for data. Second; the frame is divided as, 14 slots for video, 84 slots for voice and 2 slots for

data.

Figure 13: The voice and video dropping probability as function of voice users and number of

reserved slots as a parameter.

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Figure 14: Average delay of data and video packets versus the number of voice users and number

of reserved slots as a parameter. Figure 13 shows that:

For first case (R.S. =14 Video, 81 Voice, 5 Data), the video dropping probability is zero and the voice dropping probability is less than 0.01 until 172 voice users. For second case (R.S. =14 Video, 84 Voice, 2 Data), the video dropping probability is zero and the voice dropping probability is less than 0.01 until 177 voice users.

Figure 14 shows that: For first case, the video average delay is constant at 8 msec and the same for the second case. But the data average delay increased by increasing the number of voice users (but the data average delay is less than 250 msec) in both cases. And the same for the second case but the data average delay is larger than case one. Conclusion:- In Protocol 2; from the previous results we prefer to work with the second case (R.S. =14 Video, 84 Voice, 2 Data), where the system can serve 90 data users, 177 voice users and one video user with throughput 88%, the video average delay is 8 msec. and data average delay is 2.1 msec. 5- CONCLUSION:

In this paper, two protocols are proposed to meet the QoS requirements of different types of traffic. It was found from simulation that the optimum value of the number of time slots reserved for video is M = 14. Using this value, the dropping probability of video terminal becomes zero. The effects of the permission probabilities of different users have been studied and the results presented the optimum values as 0.09 for voice terminals, and 0.009 for data terminals. The obtained results show that: protocol 1 – case 3 achieves enthusiastic results. Because by applying this case on GPRS system, the BS can serve 275 users (90 data users, 184 voice users and one video user) with throughput 93%, the video average delay is 8 msec. and data average delay is 3.2 msec. As we see, we can serve 90 users on internet by a very low delay.

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REFERENCES [1] G. Sanders, L. Thorens, M. Reisky, O. Rulik and S. Deylitz, “GPRS Networks”,

John Wiley & Sons Ltd, England, 2003. [2] V.A. Chitre and J.N. Daigle, "IP Traffic over GPRS-An Internet Service Oriented

Analysis" WCNC'99. IEEE, pp. 1263-1267, vol. 3, September 1999. [3] S.Hoff, M.Meyer and J.Sachs,"Analysis of the General Packet Radio Service

(GPRS) of GSM as Access to the Internet" IEEE ICUPC '98. pp. 415-419, vol. 1, Oct. 1998.

[4] S.Elnoubi and A.M.Alsayh, "A Packet Reservation Multiple Access (PRMA)-Based Algorithm for Wireless System," IEEE Trans. Veh. Technol., vol. 53, No. 1, Jan. 2004.

[5] X. Fang and D. Ghosal, “Analyzing Packet Delay across a GSM/GPRS Network”, IEEE magazine, pp. 1-10, 2003.

[6] M. Ghaderi and R. Boutaba, “Data Service Performance Analysis in GPRS Systems”, Personal, Indoor and Mobile Radio Communications 2004, (PIMRC' 04), 15th IEEE International Symposium, vol. 1, pp. 556-560, September 2004.

[7] M. A. Marsan, P. Laface and M. Meo, “ Packet Delay Analysis in GPRS Systems”, IEEE INFOCOM’03, vol. 2, San Francisco, USA, March 2003. [8] Bruce A.Mah, "An Empirical Model of HTTP Network Traffic" INFOCOM'1997

IEEE Communications Society, pp. 592-600, vol. 2, April 1997. [9] Jeff Sedayao,"World Wide Web Network Traffic Patterns" Compcon'95. Digest of

Papers. pp. 8-12, March 1995. [10] R. Chakravorty and I. Pratt, “WWW Performance over GPRS”, Mobile and

Wireless Communications Network, 4th International workshop, pp. 527-531, Sep. 2002.

[11] Hung-Huan Liu, Jean-Lien C. Wu and Wan-Chih Hsieh,"Delay Analysis of Integrated Voice and Data Service for GPRS" IEEE Communications Letters ,vol. 6, No. 8, August 2002

[12] E.Casilari, A.Reyes-Lecuona, F.J.González , A.Diaz-Estrella and F.Sandoval, "Characterisation of Web Traffic" Global Telecommunications Conference, IEEE, pp. 1862-1866, vol. 3, Nov. 2001.

[13] E.Casilari, F.J.González and F.Sandoval," Modeling of HTTP Traffic" IEEE Communications Letters, vol. 5,No. 6, June 2001

[14] Sami A. EL-Dolil and M. Abd Elnaby, "Dynamic Allocation TDMA MAC Protocol for Wireless ATM Networks", National Radio Science Conference, March 2003.

[15] Z.Liu, Y.Saifullah, M.Greis and S.Sreemanthula,"HTTP Compression Techniques" IEEE Communications Society / WCNC, pp. 2495-2500, vol. 4, March 2005.

[16] W.K.Wong and H.Zhu,"Soft QoS Provisioning Using the Token Bank Fair Queuing Scheduling Algorithm" IEEE Wireless Communications, June 2003

[17] Naylor, T. H., Balintfy, J. L., Burdick, D. S., and Chu, K. "Computer Simulation Techniques", John Wiley & Sons, New York, 1966.

[18] D. J. Goodman, R. A. Valenzuela, K. T. Gayliard, and B. Ramamurthi, “Packet reservation multiple access for local wireless communications,” IEEE Trans. Commun., vol. 37, pp. 885–890, Aug. 1989.

[19] J.Cai and D.J.Goodman,"General Packet Radio Service" IEEE Communication Magazine, 35:10, pp. 122-131, Oct. 1997.

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Appendix A. Weibull Distribution [16], [17] In our simulation we use weibull distribution; here we will give a brief note about it. There are two types of Weibull distribution

Two parameter Weibull distribution. Three parameter Weibull distribution.

We use the two parameter type and its equation is given as following Probability Density Function (PDF) is given by

( ) ( )baxbe

ax

abxf −

⎟⎠⎞

⎜⎝⎛=

1

……. Eq. (1)

Where x = variable b = shape parameter a = scale parameter If PDF is integrated, it will generate CPF Cumulative Density Function (CDF) is given by

( )bax-xF ⎟⎠⎞⎜

⎝⎛

−= e1 ……. Eq. (2) From equations (1) and (2), we can drive an expression for the variable x.

⎟⎟⎟

⎜⎜⎜

⎟⎟

⎜⎜

−=

u11lnax

b1

Where u = random value B. Pareto Distribution [16], [17] In our simulation we use Pareto distribution; here we will give a brief note about it. Probability Density Function (PDF) is given by

( ) 1+= β

βαβx

xf ……. Eq. (3)

Where x = variable β = shape parameter α = location parameter By integrating PDF, we will have CPF Cumulative Density Function (CDF) is given by

…….. Eq. (4) ( )

βα⎟⎠⎞

⎜⎝⎛−=x

xF 1

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From equations (3) and (4), we can drive an expression for the variable x.

βα

1

11

⎟⎟⎠

⎞⎜⎜⎝

−=

ux

Where u = random value In the simulation of data source, we choose the following parameter values: C. Gaussian Distribution [17] If a random variable X has a probability density function given as follows:

( )

2

21

21 ⎟

⎜⎜

⎛ −−

= xxx

exfx

σμ

πσ

Where xσ is positive, then X is said to have a Gaussian distribution with parameters

xμ and xσ . The expected value and variance of the Gaussian distribution are given by:

Expected value = xμ

Variance = 2

xσ The procedure for simulating normal variants on a computer involves taking the sum of K uniformly distributed random variants Krrrr .......,,.........,, 321 where ir is defined over the interval 10 ≤≤ ir . Then we can compute x as follow

x

K

iix

KrK

x μσ +⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛= ∑

= 212

1

21

This equation provides us with a simple formula for generating normally distributed random variants with mean equal to xμ and variance equal to 2

xσ . We choose K = 12 because this value of K truncates the distribution at the σ6± limits. In the simulation of VBR source rate using the truncated Gaussian distribution, we choose the following parameter values:

kbps

kbps

K

x

x

2128384

12128384

12

+=

−=

=

μ

σ

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