Performance Analysis of Two Case Studies for a Power Line Communication Network

Transcription

1 178 International Journal of Communication Networks and Information Security (IJCNIS) Vol. 3, No. 2, August 211 Performance Analysis of Two Case Studies for a Power Line Communication Network Shensheng Tang Missouri Western State University 4525 Downs Dr., St. Joseph, MO 6457, USA stang@missouriwestern.edu Abstract: Power line communication (PLC) is a promising technique for information transmission using existing power lines. We analytically model a finite-source PLC network subect to channel failure and evaluate its call-level performance through a queueing theoretic framework. The proposed PLC network model consists of a base station (BS), which is located at a transformer station and connected to the backbone communication networks, and a number of subscriber stations that are interconnected with each other and with the BS via the power line transmission medium. An orthogonal frequency division multiplexing based transmission technique is assumed to be used for providing the transmission channels in a frequency spectrum. The channels are subect to failure during service due to noise/disturbance. When a channel is in failure, its associated call may be simply dropped from the system or wait at the channel until the channel is recovered. We analyze both cases and determine the steady-state solution for each of them and derive several performance metrics of interest. Numerical and simulation results are presented for the purpose of performance evaluation and comparison. The proposed modeling method can be used for evaluation and design of future PLC networks. Keywords: Power line communication (PLC), Performance modeling, Queueing theory, Channel failure. 1. Introduction Power line communication (PLC) is a promising technique for information transmission using existing power lines. PLC technologies can be used in an inside-building low voltage environment, a short-distance medium voltage environment, or a long-distance high voltage environment. Mixed highvoltage, medium-voltage, and low-voltage power supply networks could be bridged to form very large networks for communications, as alternative telecommunication networks. In October 24, the U.S. FCC adopted rules to facilitate the deployment of Access BPL (Broadband over Power Line), i.e., use of BPL to deliver broadband service to homes and businesses. Several competing organizations have developed specifications, including the HomePlug Powerline Alliance, Universal Powerline Association and HD-PLC Alliance. In October 29, the ITU-T approved Recommendation G.hn/G.996 as a standard for supporting high-speed home networking over power lines, phone lines and coaxial cables [1]. In January 21, IEEE published its P191 Draft Standard for Broadband over Power Line Networks: Medium Access Control and Physical Layer Specifications [2]. The great advantage of PLC is that the power lines exist in every home and every room. For example, a computer would need only to plug a BPL modem into any outlet in an equipped building to have high-speed Internet access. Therefore, huge cost of running wires such as Ethernet in many buildings can be saved. However, there are still lots of challenges for implementation in reality. Since the power line network has originally been designed for electricity distribution, rather than for data transfer, the power line as communication channel has various noise and disturbance characteristics, resulting in an unreliable channel. Many factors, such as channel attenuation, white noise, RF noise from nearby radio transmitters, impulse noise from electrical machines and relays, may cause the channel unreliability. In practice, the impact of RF noise on a channel can be reduced significantly with orthogonal frequency division multiplexing (OFDM) [3]. Based on the measurements reported in [4], [5], the noise in the power line communication channels is categorized in five types: colored background noise, narrow band noise, periodic impulsive noise - asynchronous to the mains frequency, periodic impulsive noise - synchronous to the mains frequency, and asynchronous impulsive noise, where the last type is the most unfavorable one and makes more difficulties to the power line channels. The asynchronous impulsive noise has durations of some microseconds up to a few milliseconds with random arrival times. The power spectral density of this type of noise can reach values of more than 5dB above the background noise. Much research works about PLC have been developed in the past a few years. Most of them focused on MAC (medium access control) protocols [6], [7], noise and channel modeling [5], [8], modulation and multiple access techniques [9], [1], or modem design [11]. In [6], some reservation MAC protocols were proposed for the PLC network which provides collision free data transmission. A simulation model was developed for the investigation of the PLC MAC layer which includes different disturbance scenarios. In [7], an analytic model was proposed to evaluate MAC throughput and delay of HomePlug 1. both under saturation and under normal traffic conditions. In [5], it was examined that the impulsive noise introduces significant time variance into the powerline channel. Spectral analysis and time-domain analysis of impulsive noise were presented in details. In [8], a mathematically tractable model of narrowband power line noise was introduced based on experimental measurements. With the assumption of Gaussian noise with instantaneous variance of a periodic time function, the cyclostationary features of power line noise can be described in close form. In [9], the performance of the OFDM transmission scheme corrupted by impulsive noise was analyzed. It showed that the conventional Gaussian noise OFDM

2 179 International Journal of Communication Networks and Information Security (IJCNIS) Vol. 3, No. 2, August 211 receiver in an impulsive noise environment results in strong performance degradation, and proposed an iterative algorithm to mitigate the influence of the impulsive noise. In [1], the bit error rate (BER) performance of the OFDM system under impulsive noise and frequency selective fading was analyzed and closed form formulas for this performance was derived. In [11], a PLC modem applicable to central monitoring and control systems was designed using a multicarrier CPFSK modulation scheme with adaptive impedance matching, to make the designed modem robust to frequency-selective and time-varying channel condition. All the above research was done at the link level or component level. Very little research studied the performance at the system level. In [3], a MAC protocol was proposed for a last mile PLC network consisting of one transformer station with branches that can supply about 35 households. A call-level network model was introduced and a numerical example was provided and solved by the MOSEL tool [12], but no analytic solution was developed. In this paper, we study the performance of PLC networks at the system level through detailed analytic modeling. Specifically, we analytically model a PLC network with finite population and evaluate its performance through a queueing theoretic framework. The proposed PLC network model consists of a base station (BS), which is located at a transformer station and connected to the backbone communication networks, and a number of subscriber stations (SSs) that are interconnected with each other and with the BS via the power line transmission medium. An OFDM based transmission technique is assumed to be used for providing the transmission channels in a frequency spectrum, which is divided into a set of narrowband subcarriers (or subchannels). The subchannels are subect to failure during service due to the noise/disturbance on the power lines. When a channel is in failure, its associated call may be subect to two results: The call is simply dropped from the system. The call waits at the channel until the channel is recovered (i.e., the noise/disturbance is gone), then the call continues its service. The failure events in different subchannels are independent due to the flat fading characteristic in each subchannel. The BS knows about the occupancy status of the OFDM subchannels and allocates the available resource to the requested SSs. The remainder of the paper is organized as follows. Section 2 presents the system description. Section 3 develops a two-dimensional Markov model of the system dynamics and solves the global balance equations of the system. Section 4 derives the several performance metrics of interest. Section 5 presents numerical and simulation results in terms of these metrics. Finally, the paper is concluded in Section System Description The proposed PLC access network is discussed in the range of a low-voltage power supply network, as shown in Fig. 1. It consists of a BS, which is located at a transformer station and connected to a backbone telecommunication network, and a number of subscriber stations (SSs), say N, that are interconnected with each other and with the BS via the power lines. The transformer station distributes power to the covered low-voltage power supply network and receives power from a medium-voltage or high-voltage power supply network, depending on the location of the transformer station. When an SS is located near the BS, the communication can be organized directly between the SS and the BS. Otherwise, one or more repeaters (RPs) may be necessary to embed inside the network to compensate for signal attenuation. The signal attenuation at frequencies of interest for communications is usually very large in power lines. The RP is used for increasing signal strength when it falls below some predefined value. Figure 1. A PLC network architecture The BS is an access point for the communication between a subscriber of the PLC network and a user of an external network, as well as the communication between the subscribers inside the PLC network. The signal transmission directions in a PLC network include downlink from the BS to the SSs and uplink from an SS to the BS. In the downlink, the BS sends a transmission signal to all the SSs in the PLC network. In the uplink, a signal sent by an SS can not only be received by the BS, but also be received by all other SSs. Hence, the PLC access network holds a logical bus topology, where a set of SSs are connected via a shared communication media power line, called bus. This type of networks may have problems when two or more SSs want to transmit at the same time on the same bus. Hence, some scheme of collision handling or collision avoidance is required for communications, such as carrier sense multiple access (CSMA) or an access control by the BS. The latter is assumed here. The OFDM is recommended by ITU-T G.hn as the modulation scheme for PLC networks due to the fact that it can cope with frequency selectivity (or time dispersion) the most distinct property of power line channel, without complex equalization filters. Moreover, OFDM can perform better than single carrier modulation in the presence of impulsive noise, because it spreads the effect of impulsive noise over multiple subcarriers. The available spectrum is

3 18 International Journal of Communication Networks and Information Security (IJCNIS) Vol. 3, No. 2, August 211 divided into a group of narrowband subcarriers (or subchannels), say m, which are overlapping in frequency and orthogonal in time. We assume that these m channels are all traffic channels. The signaling control is assumed to be ideal and is not discussed here. As mentioned in [4], [5], the impulsive noise introduces significant time variance into the power line channel, which indicates a high likelihood of bit or even burst errors for digital communications over power lines. The statistics of the measured interarrival times of impulsive noise above 2ms follows an exponential distribution. Probably for this sake, in [6], the channel was modeled by a Markov chain with two states, T on and T off, represented by two exponentially distributed random variables, where T on denotes the absence of impulses and the channel is available for utilization, and T off denotes the duration that the channel is disturbed by an impulse and no information transmission is possible. The BS knows about the occupancy status of the channels, i.e., the OFDM subchannels. The BS allocates the available channels to the requested calls from the SSs. When a requested call arrives, it will enter the system if there is at least one channel available; otherwise, it will be reected. A buffer may be maintained to hold the reected call, which can then get service when an idle channel becomes available. For simplicity, here we do not consider the buffer case. Note that the channels are subect to failure during service due to the noise/disturbance. The failure events in different channels are independent and identicallydistributed (i.i.d.). When a channel happens to be in failure, the associated call is affected in two different ways. Case A: The call is dropped from the system. When the failed channel is recovered, i.e., the noise/disturbance is gone, it can be used for future call request. Case B: The call holds at the channel until the channel is recovered. Once the failed channel is recovered, the call waiting at the channel can immediately continue its service. 3. Performance Analysis For the above PLC network with N SSs and m traffic channels, we assume that the arrival process of an individual idle SS is a Poisson process with rate λ. The channel holding time of a call is exponentially distributed with mean 1/µ. We further assume that each call occupies one channel for simplicity. However, the analysis method can be extended to handle bandwidth requests of variable size (cf. [13]). Due to noise/disturbance, the channel may be subect to failure. We assume that the occurrence of channel failures follows a Poisson process with rate α, i.e., the interarrival time of the failure events follows exponentially distributed with mean 1/α. In each failure event, it is assumed that the remaining duration (i.e., the recovery time) is exponentially distributed with mean 1/β. Let X(t) denote the number of failed channels at time t. Similarly, let Y(t) be the number of calls being served at time t. The process (X(t),Y(t)) is a two-dimensional Markov process with state space S = { ( ) i m, m-i }. Figure 2. The state diagram of the PLC network in Case A We first analyze Case A, i.e., the call subect to channel failure is dropped from the system. The state diagram is determined as Fig. 2. We denote the transition rate from state i', ' ( i, ) to ( i ', ' ) by T and specify the different transition rates as follows., + 1 ( N i ) λ, i m 1, < m T ii, = (1), otherwise., 1 T ii, T i+ 1, 1 T i 1, µ, =, α, =, iβ, =, i m 1,1 m otherwise. i m 1, 1 m otherwise. 1 i m, m otherwise. Let π( ) denote the steady-state probability that the PLC network is at state ( ). The global balance equations of the system are given as follows: π ( )[( N i ) λ + ( µ + α) + iβ ] = π ( 1)( N i + 1) λ + π ( i + 1, )( i + 1) β + π ( + 1)( + 1) µ + π ( i 1, + 1)( + 1) α, i < m, π ( )[ ( µ + α) + iβ ] i m, < m = π ( 1)( N i + 1) λ + π ( i 1, + 1)( + 1) α, = m where π( -1) =, π(-1, ) =, and π( ) = if i + > m. The above equations contain (m + 1)(m + 2) /2 unknowns, i.e., the probabilities π( ) with i m, and m of which, however, there are only m (m + 1) /2 independent equations. Thus, (m + 1) more equations are required to solve the problem. Observing the structure of Fig. 2, it is found that only the first row exists if α = and β =. From [14, Chapter 5], we (2) (3) (4) (5) (6)

4 181 International Journal of Communication Networks and Information Security (IJCNIS) Vol. 3, No. 2, August 211 can determine a set of particular solutions, π(, ), = 1, 2,, m, as follows. N λ π (, ) = π (,), = 1, 2, L, m. (7) µ The final equation is provided by the normalization condition: m m i = π ( ) = 1. (8) Equations (5), (6), (7), and (8) are sufficient to evaluate the state probabilities π( ), i m, m - i. Observing the structure of Fig. 3, it is also found that only the first row exists if α = and β =. From [14, Chapter 5], we can determine a set of particular solutions, ω( ), = 1, 2,, m, as follows. N λ ω (, ) = ω(,), = 1, 2, L, m. (12) µ The final equation is provided by the normalization condition: m m i = ω ( ) = 1. (13) Equations (1), (11), (12), and (13) are sufficient to evaluate the state probabilities ω( ), i m, m - i. After obtaining the steady state probabilities π( ) or ω( ), we can determine various performance metrics of interest. 4. Performance Metrics Figure 3. The state diagram of the PLC network in Case B Next, we analyze Case B, i.e., the call subect to channel failure holds at the channel until the channel is recovered. The state diagram is determined as Fig. 3. The transition rates from state ( ) to ( +1), ( -1), and (i+1, -1) are the same as that in (1), (2), and (3), respectively. The transition rate from state ( ) to (i-1, +1) is determined as T i 1, + 1 iβ, 1 i m, m = (9), otherwise. Let ω( ) denote the steady-state probability that the PLC network is at state ( ). The global balance equations of the system are given as follows: ω( )[( N i ) λ + ( µ + α) + iβ ] = ω( 1)( N i + 1) λ + ω( i + 1, 1)( i + 1) β + ω( + 1)( + 1) µ + ω( i 1, + 1)( + 1) α, i < m, i m, < m ω( )[ ( µ + α) + iβ ] = ω( 1)( N i + 1) λ + ω( i 1, + 1)( + 1) α + ω( i + 1, 1)( i + 1) β, = m (1) (11) where ω( -1) =, ω(-1, ) =, and ω( ) = if i + > m. Similar to Case A, the equations in (1) and (11) contain (m+1)(m+2)/2 unknowns, but of which there are only m(m+1)/2 independent equations. Therefore, (m+1) more equations are required. 4.1 The Probability That All Channels Are Not Available The probability that all channels are not available (either in service or in failure), denoted by P ex, is the sum of the state probabilities with i + = m, i m. This event is seen by an external observer. m P = π ( m i). (14) ex The corresponding P ex in Case B is the same as (14) except substituting π by ω. 4.2 The Probability That an Arriving Call Sees All Channels Not Available The probability that an arriving call sees all channels not available (either in service or in failure), denoted by P in, is the probability that the initiating SS finds all channels not available when placing a call request. This metric is similar to P ex except that the observer is an internal source. Note that the proposed model is a finite source system, the PASTA (Poisson Arrivals See Time Averages) property does not hold. By using the arrival theorem [15, Section 6.2.4], the P in that one of the N SSs finds all channels not available when placing a call request is obtained by replacing N with N -1 in (14). Thus, we have m P = π ( m i), (15) in [ N 1] where π ( ) means the steady state probability at ( ) [ N 1] when the total number of SSs in the network is N-1. Following this notation, the equation (14) can be re-written as m P = π ex [ N ] ( m i). The corresponding P in in Case B is the same as (15) except substituting π by ω. 4.3 The Mean System Throughput The mean system throughput, denoted by T sys, is defined as the mean number of calls being served per unit time. Thus, we have

5 182 International Journal of Communication Networks and Information Security (IJCNIS) Vol. 3, No. 2, August 211 T sys = m 1 m i = 1 µ π ( ). (16) [ N ] The corresponding T sys in Case B is the same as (16) except substituting π by ω. 4.4 The Mean Number of Channels in Failure The mean number of channels in failure, denoted by N cf, is defined as the mean number of failed channels in steady state. Thus, we have m m i N = iπ ( ). (17) cf 1 = [ N ] residual service time. In our configuration, the recovery time is much faster than the residual service time, which leads to the decrease of P ex. Similarly, there is also a tradeoff impact of β in Case A model. On one hand, the decrease of the β delays the channel availability to the initiating call requests. On the other hand, the decrease of the β may cause a state ( ) to have a large possibility to directly change to state ( -1) (rather than through state (i-1, ) to ( -1)), which actually hastens the channel availability to the initiating calls (See Fig. 2). The corresponding N cf in Case B is the same as (17) except substituting π by ω. 4.5 The Mean Number of Calls Being Served The mean number of calls being served, denoted by N bs, is defined as the mean number of calls in service in steady state. Thus, we have m 1 m i N = π ( ). (18) bs = 1 [ N ] The corresponding N bs in Case B is the same as (18) except substituting π by ω. Note that in Case B, the mean number of calls in the system should include the calls waiting at the failed channels, which is calculated as N cf +N bs. 5. Numerical Results In this section, we present the numerical results for the obtained performance metrics under the following configuration: N = 4 or 6, m = 1. The arrival rate of an individual idle SS λ changes from 1 to 8. The other parameters µ, α, and β are set separately with variable values in each figure. Note that all parameters are given in dimensionless units, which can be mapped to specific units of measurement. To validate our analysis, we also developed a discreteevent simulator for the proposed model. The simulation was implemented in MATLAB. For convenient illustration, we only show one group of simulation results as a comparison. In the illustrated figures, e.g., Fig. 4, Fig. 6, and Fig. 7, an excellent match between the analysis and simulation can be observed. Each simulated data point was averaged over 5, trials and the associated 95% confidence intervals were computed. Fig. 4 (a) and (b) show how the probability P ex in Case A and Case B changes with various parameters. We observe that P ex increases with the increase of call arrival rate λ or the service time 1/µ. As λ increases, the system is easier to get full channel occupancy. As the service time increases, the system becomes more difficult to release a channel. In our parameter configuration, we also observe that P ex displays different trends in Fig. 4 (a) and Fig. 4 (b) with respect to α and β. In general, the increase of the channel failure rate or the required recovery time delays the channel availability to the initiating call requests, like what Fig. 4 (b) shows. However, in Case A model, the call in service will be dropped when a channel fails; once the channel is recovered, the channel will become available and benefit the initiating calls. Thus, there is a tradeoff impact of α in Case A model, depending on dominance between the recovery time and the (a) P ex-d in Case A ( d denotes drop) (b) P ex-h in Case B ( h denotes hold) Figure 4. The probability that all channels are not available In Fig. 4, we also observe that P ex increases with the increase of the network population N. When N increases, the total call arrivals to the system per unit time will increase and the system is easier to get full channel occupancy. If we compare Fig. 4 (a) and Fig. 4 (b), it can be found that P ex in Fig. 4 (b) is much higher than that in Fig. 4 (a). The reason can be explained as follows: in Fig. 4 (b), a call in channel failure can hold at the channel and continue its service once the channel is recovered, which reduces the chance of the initiating call requests to enter the system. The performance of P in with respect to the various parameters is similar to that of P ex. Due to space limitation, we omit the figures here.

6 183 International Journal of Communication Networks and Information Security (IJCNIS) Vol. 3, No. 2, August 211 Fig. 5 (a) and (b) show how the mean system throughput T sys in Case A and Case B changes with various parameters. We observe that T sys increases with the increase of λ, the service rate µ, or the network population N. As λ, µ, or N increases, the mean number of calls entering the system or the mean number of calls processed per unit time will be increased. We also observe that T sys decreases with the increase of channel failure rate or the required recovery time. A more frequent channel failure event or a longer required recovery time will negatively affect the performance of the system throughput. consider the failure events for idle channels due to no calls being served (although there is a little impact to an initiating call that happens to access an idle channel being in failure). As µ increases, a call completes its service in shorter duration, reducing the chance for a call to encounter a channel failure event. We also observe that N cf increases with the increase of channel failure rate or the required recovery time. The reason is obvious. By comparing Fig. 6 (a) and Fig. 6 (b), we find that N cf in Fig. 6 (b) is a little larger than that in Fig. 6 (a). (a) T sys-d in Case A ( d denotes drop) (a) N cf-d in Case A ( d denotes drop) (b) T sys-h in Case B ( h denotes hold) Figure 5. The mean system throughput If we compare Fig. 5 (a) and Fig. 5 (b), it can be found that T sys in Fig. 5 (b) is larger than that in Fig. 5 (a). The reason is as follows: in Fig. 5 (b), the recovery of a failed channel can lead to an immediate utilization by the call that holds at the channel, while in Fig. 5 (a), the recovered channel has to wait for the next call request to utilize it. Fig. 6 (a) and (b) show how the mean number of channels in failure, N cf, in Case A and Case B, changes with various parameters. We observe that N cf increases with the increase of λ or the network population N, and decreases with the increase of µ. As λ or N increases, more calls occupy the channels per unit time, leading to more channels subect to failure. Note that in our model, it is assumed that the channels are subect to failure during service. We do not (b) N cf-h in Case B ( h denotes hold) Figure 6. The mean number of channels in failure Fig. 7 (a) and (b) show how the mean number of calls being served, N bs, in Case A and Case B, changes with various parameters. We observe that N bs increases with the increase of λ or the network population N, and decreases with the increase of µ. This agrees with our intuition. As λ or N increases, a snapshot in steady state will capture more calls being served. On the other hand, the larger the µ, the faster the processing time of a call in service, and thus less calls in service can be captured by a snapshot. We also observe that N bs decreases with the increase of channel failure rate α or the required recovery time 1/β. As α is increased or β is decreased, a snapshot in steady state will capture less calls being served. If we compare Fig. 7 (a) and Fig. 7 (b), it can

7 184 International Journal of Communication Networks and Information Security (IJCNIS) Vol. 3, No. 2, August 211 be found that N bs in Fig. 7 (b) is a little larger than that in Fig. 7 (a). The reason is similar to that in Fig. 5. the derived metrics can be used for evaluation and design of future PLC networks. References (a) N bs-d in Case A ( d denotes drop) (b) N bs-h in Case B ( h denotes hold) Figure 7. The mean number of calls being served 6. Conclusions We analytically modeled a PLC network with finite population and evaluate its performance in accordance with two possible cases caused by channel failure through a queueing theoretic framework. The call subect to channel failure in Case A is dropped from the system and in Case B, holds at the channel until the channel is recovered. The proposed PLC network consists of a BS, which is located at a transformer station and connected to the backbone communication networks, and a number of subscriber stations (SSs) that are interconnected with each other and with the BS via the power lines. An OFDM based transmission technique is assumed to be used for providing the transmission channels in a frequency spectrum. The channels are subect to failure during service due to noise/disturbance. We determine the steady-state solution of the proposed model and derive several performance metrics of interest. Numerical and simulation results are presented to show the impact of system parameters on the derived performance metrics. The proposed modeling method and [1] ITU Recommendation G.996, Unified high-speed wireline based home networking transceivers Foundation. Oct. 29. [2] IEEE P191 Draft Standard, Broadband over Power Line Networks: Medium Access Control and Physical Layer Specifications. Jan. 21. [3] M. Stantcheva, K. Begain, H. Hrasnica, and R. Lehnert, Suitable MAC protocols for an OFDM based PLC network, 4th International Symposium on Power-Line Communications and its Applications (ISPLC2), Apr. 2. [4] M. Zimmerman and K. Dostert, The low voltage power distribution network as last mile access network signal propagation and noise scenario in the HF-range, International Journal of Electronics and Communications, vol. 54, no. 1, pp , 2. [5] M. Zimmerman and K. Dostert, Analysis and modeling of impulsive noise in broad-band powerline communications, IEEE Trans. on Electromagnetic Compatibility, vol. 44, pp , Feb. 22. [6] H. Hrasnica and A. Haidine, Modeling MAC layer for powerline communications networks, 4th International Symposium on Power-Line Communications and its Applications (ISPLC2), Apr. 2. [7] M. Chung, M.-H. Jung, T.-J. Lee, and Y. Lee, Performance analysis of HomePlug 1. MAC with CSMA/CA, IEEE J. Select. Areas Comm., vol. 24, pp , Jul. 26. [8] M. Katayama, T. Yamazato, and H. Okada, A Mathematical Model of Noise in Narrowband Power Line Communication Systems, IEEE J. Selected Areas in Comm., vol. 24, pp , Jul. 26. [9] J. Haring and H. Vinck, Ofdm transmission corrupted by impulsive noise, 4th International Symposium on Power-Line Communications and its Applications (ISPLC2), Apr. 2. [1] P. Amirshah S. Navidpour, and M. Kavehrad, Performance analysis of OFDM broadband communications system over low voltage powerline with impulsive noise, in Proc. IEEE ICC 6, pp , Jun. 26. [11] J. Yu, H. Yu, and Y.-H. Lee, Design of a power-line modem for monitoring and control systems, 7th International Symposium on Power-Line Communications and its Applications (ISPLC23), Mar. 23. [12] K. Begain, G. Bolch, and H. Herold, Practical Performance Modeling Application of MOSEL Language. Kluwer Academic Publishers, 2. [13] S. Tang and W. L An adaptive bandwidth allocation scheme with preemptive priority for integrated voice/data mobile networks, IEEE Trans. on Wireless Communications, vol. 5, pp , Oct. 26. [14] P. G. Harrison and N. M. Patel, Performance Modelling of Communication Networks and Computer Architectures. Boston, MA, USA: Addison-Wesley, Jan

8 185 International Journal of Communication Networks and Information Security (IJCNIS) Vol. 3, No. 2, August 211 [15] H. Kobayashi and B. L. Mark, System Modeling and Analysis: Foundations of System Performance Evaluation. Upper Saddle River, NJ: Pearson Education, Inc., 29.