The MAC layer consists of number of 64 kbit/s transmission channels, which ... very important for the quality of the network services and data transmission ...
Suitable MAC Protocols for an OFDM Based PLC Network Mariana Stantcheva, Khalid Begain, Halid Hrasnica, and Ralf Lehnert Chair for Telecommunications Dresden University of Technology 01062 Dresden, Germany Email: {stantchm | begain | hrasnica | lehnert}@ifn.et.tu-dresden.de Phone: +49 351 463-4621 Fax: +49 351 463-7163
Abstract - In this paper we propose a MAC protocol for PLC networks. The model for our PLC network is typical for the “last mile”- network in Germany and consists of one transformer station with branches, where about 35 households are supplied. The physical layer is based on OFDM-technique. We discuss solutions about organization of the MAC layer. The MAC layer consists of number of 64 kbit/s transmission channels, which can be allocated to one particular or more stations. For this proposal we derive an analytical model at the call level to see how many subscriber stations (access units) is reasonable to connect. We investigate the utilization, the blocking probability of voice, and the average rate of the data transmission depending on the load in the system. The analytical results take in consideration the channel outages because of erasures.
1. Introduction After the deregulation of the telecommunications market powerline communications (PLC) gained big importance for the last mile (or access) network providers. The great advantage of PLC is that in every home and in every room there are sockets, which can be used for telecommunications, too. We consider two different services – telephony and internet, which are currently the most usable services in private homes. The big problem, however, is that the powerline network has been designed for electricity distribution and not for data transfer. As a result, the characteristics of the powerline make it an unreliable channel, dominated by distance, time and frequency dependent attenuation and impulse noise. The development of a suitable MAC protocol requires an appropriate channel model (Chapter 2). There are many factors, which affect the channel characteristics like channel attenuation, white noise, radio frequency noise (RF noise) from nearby radio transmitters, impulse noise from electrical machines and relays (man-made interference), etc. The noise spectrum is highly varying with frequency, location and time. We describe them as rare events. In practice the impact of RF noise on a channel can be reduced significantly with Orthogonal Frequency-Division Multiplexing (OFDM). The investigation and implementation of an appropriate Medium Access Control (MAC) protocol is very important for the quality of the network services and data transmission (Chapter 3). In our model we investigate two types of traffic – telephony and data transmission (Internet). For both of them we analyse the performance following features: blocking probability, throughput, and average data rate depending on the load in the system (Chapter 4).
2. Network Description 2.1. System Structure The system model consists of one head (base) station, which is normally situated in the transformer substation, see Figure 2.1. The subscriber stations (access units) are interconnected with each other and with the base station via the powerline transmission medium and every branch can be considered as logical bus structure with M access units (AU) and B bidirectional channels with transmission capacity of 64 kbit/s in each direction. The other side of the base station is connected to the backbone network. Because of the physical topology and the interference-affected transmission conditions, leading to frequent subcarrier erasures (in the context of OFDM [1]) and resulting connection failures we propose that the logical system structure be centrally organized. This means, that the bandwidth management and the access control are done from the base station.The access units are able to use all B transmission channels. They can receive and transmit over all subcarriers in parallel. A number of channels can be allocated to the particular access unit. In this case the AU is able to send or receive (or both) over the allocated channel(s). The other channels (not allocated to this AU) are made available to other access units.
Subscriber station (Access unit)
11 . 00 11 00
. .
00 11 11 00
. 11 00 00 11
. .
11 00 00 11
........
Base Station (Transformer)
11. 00 11 00
. .
00 11 11 00
. 11 00 00 11
. .
Figure 2.1 System Model
11 00 00 11
2.2. The OFDM System An OFDM system is that, it allows high bandwidth efficiency and simple receiver implementation in frequencyselective (or time-dispersive) wired channels. The available spectrum is divided into several subcarriers which are narrowband and experience almost flat fading. To obtain high spectral efficiency the subchannels are overlapping in frequency and orthogonal in time. For our system we make the following assumptions: Subchannel modulation: M-PSK Bandwidth: B = 5 MHz Guard interval (GI) TGuard = 2.8µs The Guard interval is a cyclic prefix which makes the transmitted signal periodic, and avoids intersymbol and subcarrier interference. Its length must be equal to or longer than the maximum channel dispersion + transmission delay difference between two AUs TGuard > τmax Therefore the following parameters may be derived: Length of OFDM symbol () TOFDM = 15.6 µs (TGuard =18 %) TGuard
TOFDM
GI
Data Copy
Figure 2.2 Illustration of an OFDM symbol with guard interval Subcarrier spacing ∆f = 1/(TOFDM - TGuard)= 78.125kHz Total number of subcarriers = B/∆f = 64 Number of used subcarriers = 52 Net data rate of one OFDM subcarrier with ( QPSKmodulation and coding rate 0.5)
rOFDM =
2 × 0. 5 = 64 kBit s TOFDM
2.3. Logical Channel Structure The MAC layer has to enable the transmission of connectionless (packet switching) and connection-oriented (circuit switching) services. For the connection-oriented services, the capacity is reserved for the duration of the connection. In this case a number of channels are allocated for the connection (for telephony there are be two allocated channels, one for uplink and one for downlink transmission direction). The remaining transmission channels are used for the connectionless services in both transmission directions and for the signaling. The data transmission should be collision-free. That means, the transmission capacity for a particular access unit has to be reserved only for its transmission. Unsuccessful data transmission may take place only in the case of channel errors. We assume that one pair of channels (uplink and downlink) is used for signaling. The uplink signaling channel is used for requests to the access unit for data transmission or channel allocation. The downlink signaling channel transmits control information and positive or negative acknowledgements of reception of the AUs’ requests from the base station to the access units. Each unidirectional channel can be used as a signaling (Sig), data (D) or circuit switched (CS) channel. We also provide some channels to be assigned as reserved channels (RES), which are used as substitution for channels in erasure condition. The signaling and circuit switched channels are replaced with a higher priority and it is done immediately. For the case that channel with non real time data is in error the reserve channel go idle and than can be occupied. This can be visualized in following state diagram, see Figure 2.3. In idle state a channel is not used for any transmission. From this state it can be allocated to one of possible transmission states or in reserved
state. The channels can move from each of the transmission states and also from idle and reserved to error state. RES
Sig-DL
Sig-UL
Idle
CS-UL
CS-DL
Data-UL
Data-DL
Error
Figure 2.3: Channel state diagram In this case the channel can not be used for any transmission and if the channel is ready to be used again, it moves to idle state and can be assigned for transmission or go to reserved. The physical layer of the system must be able to measure the quality of the transmission channels in each of its states. The base station knows at every moment about the availability of the OFDM subchannels. It controls the bandwidth among the subscriber stations. We study a simple channel outage model with two states: „channel available“ (state 0) and „channel erroneous“ (state 1) with state probabilities P0 and P1, respectively. In order to determine them statistical data are needed, e.g. how often the channel changes its state and how long it keeps the state (TH0 and TH1, respectively).
3. Proposal for a MAC Protocol In this section we describe a MAC protocol which is based on the following system assumptions: • Only the transmission channels as pairs of an uplink an a downlink unidirectional channel can be allocated as a bi-directional channel with 64 kbit/s capacity per transmission direction. The transmission direction of an unidirectional channel can not be changed, so we have a firm number of uplink and downlink channels. • The access units can transmit only over uplink unidirectional channels and they are not able to listen the uplink channels. Also, they can listen the downlink channels and they are not able to transmit over the downlink channels . On the other hand, the base station receives the information over the uplink channels and transmits over the downlink channels. Organization of the proposed MAC layer is strictly based on this channel structure in the analyzed PLC system. A task of the MAC protocol is to organize the channel allocation between access units and the base station. We assume that the data transmission in downlink transmission direction seems to be not complicated, because there is always a information flow from the base station to an access unit and a collision is not possible. Also the circuit switched channels remains allocated for the whole duration of a connection and should be only reallocated in the case of channel erasures. There are two main tasks of the MAC protocol: • First, it is necessary to organize the data transmission in uplink direction without the collision between data packets of different access units. Therefore, there has to be an arbitration mechanism which can manage the collision free uplink data transmission. For the realization of this mechanism, a kind of signaling protocol has to be realized. The signaling has to include requests for the transmission or channel allocation from the access units and also reservations of data transmission capacities and channel allocations. • Second, the allocation of the transmission channels and also channel reallocation in the case of error have to be organized by the MAC. Accordingly, a management of reserved and idle channels has to be realized by the MAC layer, too.
3.1. Data and Signaling Channels The transmission over data and signaling channels is organized in layer 2 frames, which consist of header and payload fields (Figure 3.1). The payload is used for the transmission of user information in data channels and control messages in signaling channels. The layer 2 frames are transmitted in parallel over both data and signaling channels and they are characterized by their constant duration (T). The frame duration corresponds to the duration of a system time slot. Depending on the time slot duration, there is a number of bytes which can be transmitted in the frame (N) according to the channel transmission capacity (64 kbit/s). A common network capacity depends on number of used channels for the data transmission (Each channel transmits a frame during the time slot).
The frame header contains an information which can be recognized by access unit and assigns a beginning of new frame (new time slot). In downlink direction the header contains also an indication for data or a signaling channel. So, the access unit knows which of the channels are assigned for data transmission and which channel is used for signaling in current time slot. T header Nh
payload Np N = Nh + Np bytes
Figure 3.1 Layer 2 Frame Format
Data Format The user packets (IP packets, ATM cells, ...) are reassembled into PLC segments. The length of a PLC segment is chosen according to the payload length of the layer 2 frame (Np, Figure 3.1). That makes possible the transmission of a PLC segment during the time slot over a transmission channel (K segments over K channels during the time slot). We define four kinds of PLC segments (e.g. like in DQDB network): • BOM (Beginning of Message) – first segment of packet, containing receiver ID • EOM (End of Message) – last segment of packet • COM (Continuing of Message) – a segment between BOM and EOM segments • SSM (Single Segment Message) – single segment, also containing receiver ID Each access unit listens in downlink to all data channels and can recognize if a BOM or SSM segment arrived. According to the receiver ID contained in the segment the access unit decides to receive (or not receive if wrong ID) also the following COM segments until the EOM segment arrived. In the case of SSM segment with corresponding ID, only this segment is received by the access unit. This is one of the variants which can be chosen for the organization of the segment transmission. It could be also done without assigning of segments (BOM, COM, ...). For example, the access units or base station can always know how many segments should be received to have a complete packet (message). In this case the receiver has to know when does the receiving process start and after that the received segments can be counted until last segment is received. In this variant there is less overhead during data transmission but more signaling load. The increase of the signaling load can occur on a need for usage of more than one signaling channel. We assume that there is a limited number of the transmission channels in the PLC system. This limitation can be also raised by the channel disturbance. Because of that we propose the transmission organization with the segment assignment. We assume that data format is same in the uplink transmission direction. In this case the base station is a multiuser signal receiver. The access units use also all available data channels, but the media access has to be organized by an arbitration mechanism which does not allow collisions.
Signaling Channel The uplink part of the signaling channel is used for the transmission requests of access units. First, we discuss some of possible methods which could be implemented in the PLC-Network and afterwards we describe our first proposal. There are several ways for the organization of the uplink signaling channel which could be divided in the following three groups: • Random Access – The uplink part of the signaling channel is organized as a random access channel (as in wireless protocols, e.g. [2] [3]) and the access units make the requests without knowledge about current usage of this channel by other access units (like ALOHA mechanism). Because of that, a collision is possible in the uplink signaling channel and in this case the request will be repeated after a random time. The request message contains a information about the requesting access unit (ID), kind of the requested service etc. Under high traffic load the increasing number of incoming requests can be often blocked in the network using this access method. That causes lower network utilization and lower throughput of user data. • Dedicated Access – There is a predefined time for each access unit, which can be used for the transmission of the request messages over the uplink signaling channel. It could be understood like a token-passing mechanism that does not allow any collision in the uplink signaling channel. This is very good feature if we have mostly active access units in a high loaded network because of good utilization of the network capacity and maximum throughput for all access units. On the other hand, a big number of the simultaneously active access units is not expected in the PLC access network and the active units could have a lower throughput than the current network utilization allows.
•
Polling Access Mechanisms – There is part of the uplink signaling channel reserved for the first access. The access units only inform the base station about their transmission wishes during the first access. After that, the remaining exchange of the request information is controlled by the base station (as in PRMA [2]). The first access can be also organized as a procedure for random access channel or with the dedicated access. In second case, the polling mechanism deals with the problem of the collision in the random access channel, but at the same time the signaling procedure becomes more complex, more capacity is needed for the transmission of the signaling information and a duration of the request procedure takes a longer time, even if the network is not heavy loaded. In the following we discuss the random access procedure in the uplink part of the signaling channel. The random access method seems to be more simple than the other and can also serve to the requirements of the investigated telecommunication services (telephony and internet based data transmission). The requests can be made only in defined time slots (slotted ALOHA) and an access unit can make one request during a system time slot. With the further division of time slot into the request sub-slots we can allow also a multiple access within the time slot. We consider furthermore the possibility of a request per time slot. In the following time slot the confirmation of the request is expected in the downlink part of the signaling channel. If there was collision, the access unit repeats the request after a random time. Otherwise, the access unit start to transmit the segments in a allowed moment. A request can be done only for each transmitting segment or for several segments. In second case an access units can request the transmission of all segments of a transmitting packet (IP-packet, ATM-cell, ...). We propose the requests for multiple segments, because of the decreasing number of the request attempts in the uplink signaling channel and accordingly lower load of the signaling channel in this case.
Access Organization In general we are able to realize a centralized and distributed organization of the medium access. In first case, only the base station cares about the access rights of all units in the network. Accordingly, the base station has to send a message to an access unit each time when it is allowed to send some data. That causes an increase of the traffic load in the downlink part of the signaling channel. To reduce the higher traffic load in the signaling channel we propose a following distributed scheme. The acceptance message for a data request can also contain the number of segments which was requested by the access unit. This information is available for all access units, so they know how many segments are requested to be transmitted by other access units in the network. At the other side, the access units have information how many data channels are available for the data transmission in each time slot and accordingly, how many PLC segments can be transmitted. So, the access units have always a complete information about remaining segments to be transmitted by other access units. If the request of an access unit was accepted (no collision), the access unit will wait for the time needed for the transmission of the remaining segments from other access units. After this time, the access unit can start to transmit its segments. With the distributed scheme of the access organization we reach a lower traffic load of the downlink part of the signaling channel. The remaining transmission capacity of the signaling channel can be used for the signaling in case of the channel disturbance and other kind of usage. At the same time the implementation of the distributed solution in the equipment of the access units seems to be not complicated, according to the functional complexity of the access unit in the analyzed PLC system. However, a centralized variants of the access organization can support a transmission of more complex telecommunications services with much higher requirements regarding the QoS guaranties in the network, and should be further considered [2].
3.2. Circuit Switched Channels The request for the channel allocation (for the telephony) is made in the same way as in case of data transmission request (uplink part of the signaling is same). The request is confirmed in the downlink part of the signaling channel, if there was no collision. The base station allocates a channel for the requested connection and acknowledges it over downlink signaling channel. The information contains channel ID to be allocated for this request. Also in the next time slot the layer 2 frame will be not transmitted over the allocated channel. The end of a connection using the allocated channel has to be recognized by base station. After that, the base station sends a clear over downlink signaling channel. In the next time slot this channel can be again used for the data transmission. That means, the layer 2 frame will be transmitted over this channel in the next time slot. The procedure for an arriving call can be organized as follows: • first a ring signal is transmitted from the base station over downlink signaling channel to inform an access unit that there is a call for it • after the user hooked on the same procedure for the request for the channel allocation will be done, as described above.
The procedure for an arriving call does not allocate a channel before the called user answers. In this way we save a channel if the receiver does not answer. On the other hand, because of the random requesting process, the answering to an arriving call could take longer time.
3.3. Error Handling A very important part of the description of a MAC protocol for the PLC networks is the definition of procedures in the case of disturbance of the transmission media. We propose a simple mechanism for the solution of this problem according to the proposed MAC protocol.
Circuit Switched Channels In the case that the allocated channel is interfered during a connection, the base station has to find other transmission channel and to re-allocate it to the existing connection. A re-allocation message has to be transmitted over downlink signaling channel to inform a particular access unit about new channel to be used. We can reserve some number of channels which are not in error and which can be used for the re-allocation. But in this case we reserve some network capacity which is not used for any transmission and decrease a network throughput. Other possibility is to use all channels which are not allocated for the data transmission. In the case of error in a circuit switched channel (for the telephony), one of the data channels will be allocated to the broken connection in the next time slot. Of course, there is one channel less for the data transmission in the next time slot.
Data and Signaling Channels In the case of error in a channel used for data transmission, the access units are informed about it at the beginning of the next time slot after the interference concerned (no layer 2 frame on the channel). That means, the data transmission from the previous time slot was not complete and the reaction of the access units is to go back in the state at the beginning of the interfered time slot. Following actions have to take place: • If an access unit is not active, it counts a possible number of PLC segments which could be transmitted in a time slot. The number of transmitted segments during the previous interfered time slot is no more valid and the counter has to be set to the old value. • Access unit receiving the segments drops all PLC segments received in the previous time slot. • Access unit transmitting the segments repeats the transmission from the previous time slot according to available capacity for the data transmission in the current time slot. • Base station repeats the transmission of the segments from the previous time slot and drops all received during the interfered time slot. If the signaling channel was in error in the previous time slot, the received control information is not valid. This case can be recognize by the access units after the specific frame header was not received from the channel which used to be the signaling channel before. The access units ignores the signaling information received in the previous time slot and works further according to the control information received before the previous time slot. The requests are considered like after the collision in the uplink signaling channel. In case of the failure of both data and signaling channels, both described repeat procedures have to be done. There are also other mechanisms for the error handling, which could be implemented in the proposed MAC protocol. One of them is a group of the ARQ mechanisms (Automatic Repeat Request), which are considered in the wireless networks.
4. Analytical Call Level Model of PLC Network The previous sections gave a general description of our first proposal for the MAC protocol for the PLC network. The more detailed investigation of the protocol is currently done with a framework of global multi level performance study for the whole PLC network including MAC and call level models by both analysis and simulation. In this section, we present an analytical model for a simple call admission based on the previous system description as part of the mentioned models.
4.1. Assumptions for the Analysis The analyzed system has the following features: • the structure of the system follows the structure described previously and comprises M potential users • the system has B channels in both uplink and downlink directions with one channel reserved for signaling • the system offers two types of services: - voice connections which reserve one channel in each direction during the whole time of the connection - data connections which are served in packet switching mode. In this model, we assume that station using data service will have all IP packets buffered for transmission. So, we shall assume that data call
•
•
will reserve a certain capacity at burst (message) level with bursts having geometrically distributed lengths. - Since the capacity allocation is the responsibility of the BS, it is assumed that all simultaneous data connections will receive the same capacity so that they will transmit always at the same bit rate. - It is assumed that the data connection will utilize the maximum available capacity. Furthermore, we assume that the network provides some QoS guarantee in the form of a minimum bit rate of one data connection. Such an assumption of minimum bit rate is reasonable because of two reasons. First, every TCP connection must have a minimum communication in order to maintain the connection. Secondly, the Internet user community has defined a so-called „Fun factor“ as a measure of user satisfaction which can be expected from the network. From the network point of view, this can also be because of the limited capacity of the signaling channel which can deal only with a limited number of simultaneous connections. the PLC system is subject to disturbances because of different factors as discussed before. It is assumed that the system has in average one channel failure every 1 minute which lasts for 10 seconds. The more detailed characterization of noise and disturbances and their effect on system performance is out of the scope of this paper and will be studied in further works. The system applies a simple call admission policy as follows: New voice or new data call is accepted if after its admission, all data connections will still be able on transmitting at bit rate higher than or equal to the minimum bit rate. In case that no data connections are existing in the system at the instant of call arrival then the call is accepted if there is at least one free channel in the system.
4.2. The model With the above assumptions, we define the state of the system as the vector X=(n, v d) where n denotes the number of available channels, v the number of ongoing voice connections and d the number of Blocking Probability active data connections in state X. 1.0 Regarding the driving processes of the system, 0.1 we assume that the arrival processes are Poisson point processes for both voice and data calls. 0.01 The rates of both processes are state dependent 0.001 because of the limited number of potential users. 1e−4 Therefore, let λv0 and λd0 denote the call Legend Voice generation intensity of one access station for 1e−5 Data voice and data, respectively. Then, the state 1e−6 dependent arrival rates are λv = M-(v+d)* λv0 1e−7 and λd = M-(v+d)* λd0 for voice and data, 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 respectively. Call rate It is also assumed that the call duration for voice connections to be exponentially distributed with Figure 4.1 mean 1/µv. For the data connections, it is assumed that messages have a geometrically distributed lengths. Nevertheless, this can be mapped into exponentially distributed holding times 1/µd which depends on state X. So, with average message size of m, the state dependent rate µd = m/Cdact . The number of available channel is subject to change depending on the intensity and length of disturbances. For this study, we assume that channel failures occur following Poisson process with intensity δ and they remain for an exponentially distributed periods with mean down time = 1/γ . With the above assumptions, we define X(t) as homogeneous, irreducible, time-continuous Markov chain on the state space Ω = {X(n,v,d)}. The infinitesimal rate matrix of the process, Q, can be constructed from the rates of the deriving processes. The process, therefore, has a steady state probability, p, which can be obtained as the solution of the linear equation set given as p Q = 0, with the condition Σpi = 1. Having the steady state probabilities, a number of interesting performance measures can be calculated like blocking probabilities of voice and data connections, average transmission bit rate of a randomly chosen data connection, and the utilization of the network. The derivation of the above measures is not given in this paper due to the space limits.
4.3. Numerical example In this section, we give an example on a realistic medium size PLC network with M=140 access units and 30 channels (29 transmission + 1 signaling). The average holding time of one voice connection is set to 100s, while the average data message length is set to m=1Mbyte. As discussed before, it is assumed that one channel fails
with exponentially distributed intervals with mean of 60s and the down time is also exponentially distributed with mean of 10s. The model has been written and solved using MOSEL system [4] All presented results are drawn versus the offered load expressed in overall call rate in [call/s]. The ratio between voice and data is set to 75% of the calls are voice and 25% are data. Figure 4.1 shows curves for the blocking probabilities of both voice and data. The curves show that the network is capable on providing very low blocking probabilities and the critical load (Blocking probability ~ 1%) is very high (0.3 call/s means that every station by average 5.7 voice calls and 2.1 data calls per hour). Figure 4.2 shows, on the other hand, that the increased load will result on reduced average bit rate of data connections. But with reasonable load rates the network is capable of providing relatively high bit rates (~1Mbps) for data traffic. Finally, Figure 4.3 shows that the network can reach a reasonable utilization even with this low number of potential users. Our investigation (not shown in this paper) showed that the utilization increases dramatically with the increase of data call percentage and/or the length of data messages. Finally, we would like to remind that these are only example results to show the capability of the model which will be further tuned and studied for more detailed investigations.
Average data rate [Kbps]
Utilization
1600
1.0 0.9
1400
0.8 1200
Legend
0.7
Voice Data
1000
0.6
800
0.5 0.4
600
0.3 400
0.2 200
0.1
64 0
0 0
0.05
0.1
0.15
0.2
0.25 0.3 Call rate
Figure 4.2
0.35
0.4
0.45
0.5
0.55
0
0.05
0.1
0.15
0.2
0.25 0.3 Call rate
0.35
0.4
0.45
0.5
0.55
Figure 4.3
5. Conclusions In our paper we discuss a MAC protocol for a PLC network. The OFDM is favored as a suitable transmission technique for such a dispersive (or frequency-selective) channel. The available spectrum is divided into several subchannels which are narrow-band and experience almost flat fading, which makes equalization simple or with differential modulation, even unnecessary. The MAC layer consists of logical channels of 64 kbit/s which can be allocated to the particular access units (connections). There are four possible usage states for the channels: circuit switched, used for connectionoriented services; packet switched for data channels with arbitration mechanism for the access organization; reserved channels as redundant capacity in case of channel erasures, and signaling channels for requests and transport of control information with random access in uplink direction. For transmission over the PLC medium an important feature is the interference situation during the communication phase. Therefore, we made analytical investigations about the traffic behavior depending on the system load under the condition that the channel failures and down times are exponentially distribution.
6. Acknowledgments We would like to thank RegioCom GmbH, Germany for the sponsorship and support of the project.
References [1] Aretz, K., Bolinth, E., Troks, W.: OFDM for Powerline Applications?; 1st Intern. OFDM-Workshop, Hamburg, Sept. ‘99 [2] Akyildiz, I.F., McNair, J.: Media Access Control Protocols for Multimedia Traffic in Wireless Networks; IEEE Network, July/August 1999 [3] Choi, S., Shin, K.G.: Centralized Wireless MAC Protocols using slotted ALOHA and Dynamic TDD transmission; Performance Evaluation 27 & 28, 1996 [4] Begain, K., Bolch, G., Herold, H.: Practical Performance Modeling, Application of MOSEL Language, Kluwer Academic Publishers, 2000.